# Study of Soil Scattering Coefficients in Combination with Diesel for a Slightly Rough Surface in the Cj Band

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Scattering Coefficient

- Perturbation model
- Physical optics model
- Geometric optics model

Model | Validity condition |
---|---|

Physical optics model (Kirchoffs’ model with scalar approximation) | M < 0.25 Kl > 6 |

Geometric optics model (Kirchoffs’ Model with stationary phase approximation) | (2Kσ cosθ)2 > 10 l 2 = 2.76σλ |

Perturbation model | M < 0.3 Kσ < 0.3 |

#### 2.2. Perturbation Model

^{1/2}/l < 0.3

^{ο}

_{ppn}(θ) = 8k

^{4}σ

^{2}cos

^{4}θ |α

_{pp}θ|

^{2}W (2k sin θ)

_{nn}(θ)|

^{2}= Γ

_{n}(θ) is the Fresnel reflection coefficient. The value for Fresnel reflection coefficient for horizontal polarization is given by:

_{vv}is given by:

_{s}= The dielectric constant of soil and θ is the angle of incident

**ξ**) = expo (−

**ξ**

^{2}/l

^{2}), the normalized roughness is given by [3]:

^{2}expo [−(k l sinθ)

^{2}]

#### 2.3. Computation of Scattering Coefficient

- Either directly, by measuring the scattering coefficient of the material using scatterometers or radars,
- By measurement of dielectric constant and available models.

^{−3}. The density of the soil sample is approximately the same as the density of diesel. The physical and chemical properties of diesel are very important factors for calculating the dielectric constant and estimating the emissivity. The density of diesel is about 780–1,074 kg m

^{−3}at 15 °C.

## 3. Results and Discussions

**Figure 1.**Variation of the scattering coefficient of soil with different weight percentages of diesel (1, 15 and 22) in respect to different look angles.

**Figure 2.**Variation of the scattering coefficient of soil with different weight percentages of diesel (2, 14 and 21) in respect to different look angles.

**Figure 3.**Variation of the scattering coefficient of soil with different weight percentages of diesel (3, 13 and 20) in respect to different look angles.

**Figure 4.**Variation of the scattering coefficient of soil with different weight percentages of diesel (7, 9 and 16) in respect to different look angles.

**Figure 5.**Variation of the scattering coefficient of soil with different weight percentages of diesel (4, 12 and 19) in respect to different look angles.

**Figure 6.**Variation of the scattering coefficient of soil with different weight percentages of diesel (5, 11 and 18) in respect to different look angles.

**Figure 7.**Variation of the scattering coefficient of soil with different weight percentages of diesel (6, 10 and 17) in respect to different look angles.

**Figure 8.**Variation of the scattering coefficient of soil with different weight percentages of diesel in three different angles (45, 50 and 55) degree.

Equation | Correlation Coefficient(R^{2}) | |
---|---|---|

45(HH) | y = −0.1338x − 28.469 | 0.9574 |

45(VV) | y = −0.1864x − 21.321 | 0.9627 |

50(HH) | y = −0.1238x − 32.892 | 0.9569 |

50(VV) | y = −0.1873x − 24.584 | 0.9636 |

55(HH) | y = −0.1124x − 37.485 | 0.9563 |

55(VV) | y = −0.1882x − 27.986 | 0.9646 |

## 4. Summary and Conclusions

- Scattering coefficient decreases with increase in weight percentage of diesel.
- Scattering coefficient decreases with increase in look angle for both horizontal and vertical polarizations but the value of scattering coefficient for horizontal polarization is less than that for vertical polarization.

## References

- Warner, E.D.; Peterson, G.W. Remote sensing of soil moisture: passive and active microwave. In Encylopedia of Soil Science Second Edition; Taylor & Francis: London, UK, 2006; Volume 2. [Google Scholar]
- Fingas, M.F.; Brown, C.E. Review of oil spill remote sensing. In Proceedings of the Fifth International Conference on Remote Sensing for Marine and Coastal Environments 2000, Ann Arbor, MI, USA, 2000; pp. 1211–1218.
- Chaudhari, H.C.; Shinde, V.J. Dielectric study of moisture laden soils at X-band microwave frequency. Int. J. Phys. Sci.
**2008**, 3, 075–078. [Google Scholar] - Song, H.G.; Bartha, R. Effects of jet fuel spills on the microbial community of soil. Appl. Environ. Microb
**1999**, 56, 646–651. [Google Scholar] - Troch, F.R.; Thompson, L.M. Soil and Soil Fertility; Oxford University Press: New York, NY, USA, 1993. [Google Scholar]
- Ulaby, F.T.; Moore, R.K.; Fung, A.K. Microwave Remote Sensing; Addison-Wesley: Reading, MA, USA, 1986. [Google Scholar]
- Ulaby, F.T.; Moore, R.K.; Fung, A.K. Microwave remote sensing Active and Passive. In Microwave Remote Sensing Fundamentals and Radiometry; Addison-Wesley Publishing Company: Reading, MA, USA, 1981; Volume 1, p. 76. [Google Scholar]
- Ajo-Franklin, J.B.; Geller, J.T.; Harris, J.M. The dielectric properties of granular media saturated with DNAPL//water mixtures. Geophys. Res. Lett.
**2004**, 31, 4. [Google Scholar] [CrossRef] - Calla, O.P.N.; Mathur, M.; Upadhayay, M.; Punia, R.; Chaudhary, P. Image generation for microwave remote sensing using java language. In Proceedings of 1st International Conference on Microwave, Antenna, Propagation and Remote Sensing (ICMARS-2003), Jodhpur, India, 2003; pp. 93–98.
- Wyszkowski, M.; Ziółkowska, A. Effect of soil contamination with diesel oilon yellow lupine yield and macroelements content. Plant Soil Environ.
**2004**, 5, 218–226. [Google Scholar] - Schmugge, T.; Gloersen, P.; Wilheit, T.; Geiger, F. Remote sensing of soil moisture with microwave radiometers. J. Geophys. Res.
**1974**, 79, 317–323. [Google Scholar] [CrossRef] - Lu, J.; Lim, H.; Liew, S.; Bao, M.; Kwoh, L. Ocean oil pollution mapping with ERS synthetic aperture radar imagery. In Proceedings of IEEE 1999 International Geoscience and Remote Sensing Symposium, Hamburg, Germany, 1999; pp. 212–214.

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**MDPI and ACS Style**

Najafabadi, A.T.
Study of Soil Scattering Coefficients in Combination with Diesel for a Slightly Rough Surface in the Cj Band. *Remote Sens.* **2010**, *2*, 115-123.
https://doi.org/10.3390/rs2010115

**AMA Style**

Najafabadi AT.
Study of Soil Scattering Coefficients in Combination with Diesel for a Slightly Rough Surface in the Cj Band. *Remote Sensing*. 2010; 2(1):115-123.
https://doi.org/10.3390/rs2010115

**Chicago/Turabian Style**

Najafabadi, Alireza Taravat.
2010. "Study of Soil Scattering Coefficients in Combination with Diesel for a Slightly Rough Surface in the Cj Band" *Remote Sensing* 2, no. 1: 115-123.
https://doi.org/10.3390/rs2010115