# Theoretical Evaluation of Water Cloud Model Vegetation Parameters

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Water Cloud Model

^{−3}). The simplification of the vegetation layer permits the relation of the scattering characteristics to bulk vegetation parameters. In the case of uniformly distributed water particles, the extinction coefficient can be assumed to be proportional to the total water content in the unit volume $W$ (kg/m

^{3}), such as [6]

^{−2}), and the VWC (kg/m

^{2}), as shown in Figure 1 and Figure 2. The areal density and VWC are defined as

^{3}, [20]) and particle volume ${v}_{p}=(4\pi /3){r}^{3}$.

## 3. WCM Parameters for Non-Spherical Particles

#### 3.1. Effect of Particle Shape

#### 3.2. Effect of Particle Orientation

## 4. Discussion

#### 4.1. Effect of Radar Observation Condition

#### 4.2. Comparison with Previous Studies

#### 4.3. Validity of WCM

_{g}= 0.5 gg

^{−1}, N = 3000 m

^{−3}, h = 3 m). In addition, the root-mean-square height, the correlation length, and the volumetric moisture content of the soil surface were 0.5 cm, 5 cm, and 0.3 cm

^{3}cm

^{−3}, respectively. It is seen that the relative contribution of elementary scattering mechanisms to the total observed signal can vary significantly with the radar observation conditions. The ground scattering mechanism is an important contributor at the low incidence angle, whereas the relative contribution of the volume scattering component increases as the incidence angle increases. We noticed that there can be a significant amount of contribution from the scattering interaction between vegetation and the ground, particularly at HH-polarization and high incidence angle regions.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Variations of ${A}_{2}{V}_{1}$ in the case of spherical particles as a function of (

**a**) the particle moisture content (${m}_{g}$ [g/g]), (

**b**) the areal density (${N}_{a}$ [m

^{−2}]), and (

**c**) the vegetation water content (VWC [kg/m

^{2}]). Note that both the vertical and horizontal axes are scaled logarithmically.

**Figure 2.**Variations of ${B}_{2}{V}_{2}$ in the case of spherical particles as a function of (

**a**) the particle moisture content (${m}_{g}$), (

**b**) the areal density (${N}_{a}$), and (

**c**) the vegetation water content (VWC).

**Figure 3.**(

**a**) Local orientation of vegetation particle and schematic representation of (

**b**) needle shaped and (

**c**) disk shaped particles, where $t$ and $l$ denote the thickness and length of the particle.

**Figure 4.**Variations of ${\kappa}_{e,pq}h$ in relation to the vegetation descriptors (left: particle moisture content (g/g); middle: the areal density (m

^{−2}); right: the vegetation water content (kg/m

^{2})) for (

**a**–

**c**) needle shaped and (

**d**–

**f**) disk shaped particles.

**Figure 5.**Variations of ${\sigma}_{v,pq}/2{\kappa}_{e,pq}$ in relation to the vegetation descriptors (left: particle moisture content (g/g); middle: the areal density (m

^{−2}); right: the vegetation water content (kg/m

^{2})) for (

**a**–

**c**) needle shaped and (

**d**–

**f**) disk shaped particles.

**Figure 6.**Effect of particle orientation distribution on the relationship between ${\kappa}_{e,pq}h$ and ${B}_{2,pq}VWC$ (left: ${B}_{2,HH}VWC$ and right: ${B}_{2,VV}VWC$) in the case of (

**a**,

**b**) needle shaped and (

**c**,

**d**) disk shaped particles. Colored dots represent simulation results and solid lines are corresponding line fits to the simulated data.

**Figure 7.**Effect of particle orientation distribution on the relationship between ${\sigma}_{v,pq}/2{\kappa}_{e,pq}$ and ${A}_{2,pq}{m}_{g}$ (left: ${A}_{2,HH}{m}_{g}$ and right: ${A}_{2,pVV}{m}_{g}$) in the case of (

**a**,

**b**) needle shaped and (

**c**,

**d**) disk shaped particles.

**Figure 8.**The estimated WCM parameters ${B}_{2,pq}$ (left), ${A}_{2,pq}$ (middle), and ${E}_{pq}$ (right) plotted as a function of (

**a**–

**c**) the incidence angle and (

**d**–

**f**) the radar frequency.

**Figure 9.**Variations of the ${B}_{2,HH}$ (red circle) and ${B}_{2,VV}$ (blue circle) parameters estimated for different simulation configurations. The blue and red lines represent ${B}_{2,HH}$ and ${B}_{2,HH}$ values, respectively, reported in the literature.

**Figure 10.**Variations of the ${A}_{2,pq}$ and ${E}_{pq}$ parameters estimated for different environmental and observation configurations.

**Figure 11.**An example of the variations of backscattering coefficients for the four different scattering mechanisms at (

**a**) HH- and (

**b**) VV-polarizations as a function of the incidence angle.

**Figure 12.**Variations of the relative contribution of each scattering mechanism at (

**a**–

**c**) HH- and (

**d**–

**f**) VV-polarizations. Figures in the left, center, and right correspond to the results obtained for uniform, medium, and vertical distribution of the particle orientation angle, respectively.

**Figure 13.**Prediction errors of the WCM defined by the difference the total backscattered signal and the WCM estimation at (

**a**) HH- and (

**b**) VV-polarizations, as a function of the incidence angle.

Vegetation Parameter | Minimum | Maximum | Interval | Unit |
---|---|---|---|---|

Particle length ($l$) | 3 | 24 | 3 | cm |

Number density ($N$) | 200 | 4200 | 400 | m^{−3} |

Height ($h$) | 1 | 5 | 1 | m |

Particle moisture content (${m}_{g}$) | 0.1 | 0.9 | 0.1 | g/g |

**Table 2.**Different simulation configurations for the GRG-based physical model simulations and results of the WCM parameter estimations.

Configuration | Frequency | Orientation | Thickness | ${\mathit{B}}_{2,\mathit{H}\mathit{H}}$ | ${\mathit{B}}_{2,\mathit{V}\mathit{V}}$ | ${\mathit{A}}_{2,\mathit{H}\mathit{H}}$ | ${\mathit{E}}_{\mathit{H}\mathit{H}}$ | ${\mathit{A}}_{2,\mathit{V}\mathit{V}}$ | ${\mathit{E}}_{\mathit{V}\mathit{V}}$ |
---|---|---|---|---|---|---|---|---|---|

1 | 1.5 GHz | Uniform ($0{}^{\xb0}\le \beta \le 90{}^{\xb0}$) | 0.1 cm | 0.111 | 0.137 | 0.004 | 1.8 | 0.004 | 1.8 |

2 | 0.2 cm | 0.096 | 0.119 | 0.018 | 1.8 | 0.017 | 1.8 | ||

3 | 0.3 cm | 0.085 | 0.105 | 0.041 | 1.8 | 0.038 | 1.8 | ||

4 | Medium ($0{}^{\xb0}\le \beta \le 60{}^{\xb0}$) | 0.1 cm | 0.066 | 0.126 | 0.001 | 1.5 | 0.003 | 1.8 | |

5 | 0.2 cm | 0.058 | 0.109 | 0.005 | 1.5 | 0.013 | 1.8 | ||

6 | 0.3 cm | 0.051 | 0.096 | 0.012 | 1.6 | 0.029 | 1.8 | ||

7 | Vertical ($0{}^{\xb0}\le \beta \le 30{}^{\xb0}$) | 0.1 cm | 0.022 | 0.115 | 0.000 | 1.1 | 0.001 | 1.6 | |

8 | 0.2 cm | 0.020 | 0.100 | 0.002 | 1.1 | 0.003 | 1.6 | ||

9 | 0.3 cm | 0.018 | 0.088 | 0.005 | 1.2 | 0.007 | 1.6 | ||

10 | 5 GHz | Uniform ($0{}^{\xb0}\le \beta \le 90{}^{\xb0}$) | 0.1 cm | 0.339 | 0.420 | 0.052 | 1.9 | 0.049 | 1.9 |

11 | 0.2 cm | 0.299 | 0.369 | 0.211 | 1.9 | 0.197 | 1.9 | ||

12 | 0.3 cm | 0.266 | 0.329 | 0.479 | 1.9 | 0.445 | 1.9 | ||

13 | Medium ($0{}^{\xb0}\le \beta \le 60{}^{\xb0}$) | 0.1 cm | 0.204 | 0.386 | 0.005 | 1.4 | 0.025 | 1.9 | |

14 | 0.2 cm | 0.180 | 0.340 | 0.022 | 1.5 | 0.100 | 1.9 | ||

15 | 0.3 cm | 0.161 | 0.303 | 0.053 | 1.5 | 0.226 | 2.0 | ||

16 | Vertical ($0{}^{\xb0}\le \beta \le 30{}^{\xb0}$) | 0.1 cm | 0.070 | 0.353 | 0.001 | 1.1 | 0.002 | 1.6 | |

17 | 0.2 cm | 0.063 | 0.310 | 0.005 | 1.1 | 0.009 | 1.7 | ||

18 | 0.3 cm | 0.058 | 0.277 | 0.012 | 1.2 | 0.021 | 1.7 | ||

19 | 10 GHz | Uniform ($0{}^{\xb0}\le \beta \le 90{}^{\xb0}$) | 0.1 cm | 0.818 | 1.012 | 0.131 | 1.7 | 0.125 | 1.7 |

20 | 0.2 cm | 0.730 | 0.902 | 0.529 | 1.7 | 0.505 | 1.7 | ||

21 | 0.3 cm | 0.658 | 0.812 | 1.198 | 1.7 | 1.142 | 1.7 | ||

22 | Medium ($0{}^{\xb0}\le \beta \le 60{}^{\xb0}$) | 0.1 cm | 0.493 | 0.930 | 0.006 | 1.1 | 0.045 | 1.8 | |

23 | 0.2 cm | 0.442 | 0.830 | 0.027 | 1.1 | 0.179 | 1.8 | ||

24 | 0.3 cm | 0.400 | 0.748 | 0.065 | 1.2 | 0.402 | 1.8 | ||

25 | Vertical ($0{}^{\xb0}\le \beta \le 30{}^{\xb0}$) | 0.1 cm | 0.172 | 0.850 | 0.002 | 1.0 | 0.003 | 1.4 | |

26 | 0.2 cm | 0.158 | 0.759 | 0.007 | 1.0 | 0.011 | 1.4 | ||

27 | 0.3 cm | 0.146 | 0.684 | 0.018 | 1.1 | 0.026 | 1.4 |

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**MDPI and ACS Style**

Park, S.-E.; Jung, Y.T.; Cho, J.-H.; Moon, H.; Han, S.-h.
Theoretical Evaluation of Water Cloud Model Vegetation Parameters. *Remote Sens.* **2019**, *11*, 894.
https://doi.org/10.3390/rs11080894

**AMA Style**

Park S-E, Jung YT, Cho J-H, Moon H, Han S-h.
Theoretical Evaluation of Water Cloud Model Vegetation Parameters. *Remote Sensing*. 2019; 11(8):894.
https://doi.org/10.3390/rs11080894

**Chicago/Turabian Style**

Park, Sang-Eun, Yoon Taek Jung, Jae-Hyoung Cho, Hyoi Moon, and Seung-hoon Han.
2019. "Theoretical Evaluation of Water Cloud Model Vegetation Parameters" *Remote Sensing* 11, no. 8: 894.
https://doi.org/10.3390/rs11080894