# Modeling Microwave Emission from Short Vegetation-Covered Surfaces

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

_{1}. The bottom layer 3 is the subsurface with permittivity ε

_{3}. Vegetation belongs to the middle layer 2 with spatially homogeneous scatterers and bulk permittivity ε

_{2}. τ is the optical thickness, μ is the cosine of the incident zenith angle, and R

_{ij}is the reflectivity at the interfaces of different layers. I

_{0}is the downwelling radiance at τ = τ

_{0}from the top layer. I

_{1}is the upwelling radiance at τ = τ

_{1}from the bottom layer. B is the Planck function and T is the thermal temperature.

#### 2.1. Vegetation Volume Scattering

#### 2.1.1. The Geometric Optics Approach for Leaves

_{veg}and thickness d (mm). For a single leaf, the reflectivity, transmissivity, and absorptivity R

_{p}, T

_{p}, and A

_{p}, respectively, where p is v or h and stands for the vertical or horizontal polarization, respectively, are given as follows [1,24]:

- ${k}_{0}=2\pi /\text{\lambda},$
- ${k}_{z0}={k}_{0}\mathrm{cos}\beta ,$
- ${k}_{z1}={k}_{0}{({\epsilon}_{veg}-{\mathrm{sin}}^{2}\beta )}^{1/2},$
- ${r}_{h}=({k}_{z0}-{k}_{z1})/({k}_{z0}+{k}_{z1}),$
- ${r}_{v}=({\epsilon}_{veg}{k}_{z0}-{k}_{z1})/({\epsilon}_{veg}{k}_{z0}+{k}_{z1}).$

^{−1}), λ is the free-space wavelength (mm), β is the incidence angle (°) relative to the leaf normal. Permittivity ε

_{veg}is obtained using the mixing formula, which treats the leaf as a matrix of bound water, saline water, and dry matter [5].

#### 2.1.2. Infinite Cylinder Approximation for Stems

_{r}for the dielectric cylinder, the scattering amplitude tensor ${f}_{pq}(\widehat{s},\widehat{i})$ and absorption cross-section Q

_{ap}in the local frame of the cylinder are written as [27,28]

- $\mu \left(\widehat{s},\widehat{i}\right)=\frac{sin[kh(cos{\theta}_{i}+cos{\theta}_{s})]}{kh(cos{\theta}_{i}+cos{\theta}_{s})}$,
- ${z}_{n}=\frac{{a}^{2}}{{u}^{2}-{{v}_{s}}^{2}}[u{J}_{n}\left({v}_{s}\right){J}_{n+1}\left(u\right)-{v}_{s}{J}_{n}\left(u\right){J}_{n+1}\left({v}_{s}\right)]$,
- $u={\lambda}_{i}a=ka\sqrt{{\epsilon}_{r}-co{s}^{2}{\theta}_{i}}$,
- ${v}_{i}=kasin{\theta}_{i}$,
- ${v}_{s}=kasin{\theta}_{s}$,
- ${e}_{nv}=\frac{jsin{\theta}_{i}}{{R}_{n}{J}_{n}\left(u\right)}\left\{\frac{{{{H}^{\text{'}}}_{n}}^{\left(2\right)}({v}_{i})}{{v}_{i}{{H}_{n}}^{(2)}({v}_{i})}-\frac{{{J}^{\text{'}}}_{n}(u)}{u{J}_{n}\left(u\right)}\right\}$,
- ${e}_{nh}=\frac{-sin{\theta}_{i}}{{R}_{n}{J}_{n}\left(u\right)}\left(\frac{1}{{{v}_{i}}^{2}}-\frac{1}{{u}^{2}}\right)ncos{\theta}_{i}$,
- $\eta {h}_{nv}=\frac{sin{\theta}_{i}}{{R}_{n}{J}_{n}\left(u\right)}\left(\frac{1}{{{v}_{i}}^{2}}-\frac{1}{{u}^{2}}\right)ncos{\theta}_{i}$,
- $\eta {h}_{nh}=\frac{jsin{\theta}_{i}}{{R}_{n}{J}_{n}\left(u\right)}\left\{\frac{{{{H}^{\text{'}}}_{n}}^{\left(2\right)}({v}_{i})}{{v}_{i}{{H}_{n}}^{(2)}({v}_{i})}-\frac{{\epsilon}_{r}{{J}^{\text{'}}}_{n}(u)}{u{J}_{n}\left(u\right)}\right\}$,
- ${R}_{n}=\frac{\pi {{v}_{i}}^{2}{{H}_{n}}^{(2)}({v}_{i})}{2}\left\{\left(\frac{{{{H}^{\text{'}}}_{n}}^{\left(2\right)}({v}_{i})}{{v}_{i}{{H}_{n}}^{(2)}({v}_{i})}-\frac{{{J}^{\text{'}}}_{n}(u)}{u{J}_{n}\left(u\right)}\right)\cdot \left(\frac{{{{H}^{\text{'}}}_{n}}^{\left(2\right)}({v}_{i})}{{v}_{i}{{H}_{n}}^{(2)}({v}_{i})}-\frac{{\epsilon}_{r}{{J}^{\text{'}}}_{n}(u)}{u{J}_{n}\left(u\right)}\right)-{n}^{2}co{s}^{2}{\theta}_{i}{\left(\frac{1}{{u}^{2}}-\frac{1}{{{v}_{i}}^{2}}\right)}^{2}\right\}$,

_{n}is the cylindrical Bessel function and H

_{n}

^{(2)}is the Hankel function. If n = 0, the scale = 1; else n > 0, scale = 2 for Q

_{ap}, and

- ${c}_{np}=\frac{k\left(\eta {h}_{np}-j{e}_{np}cos{\theta}_{i}\right)}{2{\lambda}_{i}},$
- ${d}_{np}=\frac{k\left(\eta {h}_{np}+j{e}_{np}cos{\theta}_{i}\right)}{2{\lambda}_{i}}$,
- ${y}_{n}=\frac{a}{{\omega}^{2}-{\overline{\omega}}^{2}}\left[\omega {J}_{n}\left(\overline{u}\right){J}_{n+1}\left(u\right)-\overline{\omega}{J}_{n+1}\left(\overline{u}\right){J}_{n}\left(u\right)\right]$,
- $\omega =k\sqrt{{\epsilon}_{r}-co{s}^{2}{\theta}_{i}}$,
- $u=a\omega $.

_{pq}in the reference frame is obtained through the Euler angles of rotation

_{vi}and t

_{hi}correspond to the functions of the incident and Euler angles, respectively and t

_{vs}and t

_{hs}correspond to the functions of the scattering and Euler angles, respectively. Finally, the scattering (Q

_{sp}

^{*}) and absorption (Q

_{ap}

^{*}) cross sections for the cylinder in the reference frame are

#### 2.1.3. Vegetation Optic Parameters

_{sp}) and absorption (k

_{ap}) coefficients for the entire vegetation layer are calculated as follows:

^{2}∙m

^{−2}), H is the canopy depth (m) including leaves and stems, ξ is the leaf orientation angle, and N represents the number of cylinders in unit volume. The single-scattering albedo ω

_{p}and the optical thickness τ

_{p}for vegetation are described as

#### 2.2. Rough Surface Reflection

^{s}is the bistatic scattering coefficient, subscript p or q describes the polarization state, $({\theta}_{i},{\varnothing}_{i})$ is the incident direction, and $({\theta}_{s},{\varnothing}_{s})$ is the scattering direction.

## 3. Field Experimental Data

**Figure 2.**A truck-mounted multifrequency microwave radiometer (TMMR) radiometer system (

**left**) and the footprint with −3 dB beamwidth (

**right**).

**Figure 3.**Soybean and cotton fields on different dates used in the TMMR measurements. (

**a**) Soybean on 23 June; (

**b**) soybean on 9 July; (

**c**) cotton on 10 June; and (

**d**) cotton on 23 June.

**Table 1.**Parameters for different vegetation parts and rough soil surface in the experiments (LAI: leaf area index; Mg: gravimetric moisture; SMC: soil moisture content; and RMS: standard deviation of surface height).

Scatterers | Measured Parameters | Soybean | Cotton | ||
---|---|---|---|---|---|

23 June | 9 July | 10 June | 23 June | ||

Vegetation | Depth (m) | 0.11 | 0.33 | 0.19 | 0.37 |

Temperature (°C) | 36.8 | 29.4 | 26.3 | 29.4 | |

Leaves | LAI (m^{2}∙m^{−2}) | 0.58 | 1.35 | 0.71 | 1.57 |

Thickness (mm) | 0.31 | 0.38 | 0.23 | 0.27 | |

Mg (g∙g^{−1}) | 0.85 | 0.75 | 0.82 | 0.80 | |

Stems | Radius (m) | 0.0009 | 0.0013 | 0.0026 | 0.003 |

Length (m) | 0.05 | 0.08 | 0.08 | 0.15 | |

Mg (g∙g^{−1}) | 0.88 | 0.82 | 0.88 | 0.90 | |

Density (m^{−2}) | 277 | 378 | 285 | 327 | |

Angle distribution | oblique | oblique | oblique | oblique | |

Rough soil surface | SMC (cm^{3}∙cm^{−3}) | 0.0138 | 0.162 | 0.30 | 0.05 |

RMS height (m) | 0.03 | 0.03 | 0.02 | 0.03 | |

Correlation length (m) | 0.09 | 0.09 | 0.1 | 0.1 | |

Skin temperature (°C) | 49.5 | 33.2 | 34.5 | 42.1 | |

Soil temperature (°C) | 43.1 | 32.9 | 31.5 | 33.6 |

## 4. Results and Discussion

#### 4.1. Parameters Sensitivity

_{p}and optical depth τ

_{p}for vegetation according to the group of vegetation features in Table 2. Bands C, X, and Ku correspond to frequencies of 6.925 GHz, 10.7 GHz, and 18.7 GHz, respectively, which are also used by the TMMR system. The results presented in Figure 4 suggest that the single-scattering albedo shows distinct polarization characteristics for leaf thickness d between 0.1 mm and 0.4 mm. With increasing leaf thickness, it increases for both V and H polarizations. The single-scattering albedo of H is higher than the corresponding V at ω

_{v}below 0.6 except for d = 0.1 mm, where both are close to the 1:1 line. The difference increases with the leaf thickness and decreases with increasing ω

_{v}. When leaves are thin with thickness 0.1 mm, the single-scattering albedo of H is lower than that of V at ω

_{v}above 0.5. With increasing frequency, ω

_{v}shifts toward low values and ω

_{h}increases slightly. Optical depth τ

_{h}is systematically higher than τ

_{v}. The difference increases with optical depth especially for the X and Ku bands. The range of optical depth decreases for V and H with increasing frequency.

**Table 2.**Parameters of vegetation features used in the polarization analysis (LAI: leaf area index and Mg: gravimetric moisture).

Scatterers | Parameters | Minimum | Maximum | Interval | Number |
---|---|---|---|---|---|

Leaves | LAI (m^{2}∙m^{−2}) | 0.5 | 5.5 | 1.0 | 6 |

Thickness (mm) | 0.1 | 0.4 | 0.1 | 4 | |

Mg (g g^{−1}) | 0.60 | 0.80 | 0.10 | 3 | |

Stems | Radius (m) | 0.002 | 0.022 | 0.004 | 6 |

Height (m) | 0.2 | 1.0 | 0.2 | 5 | |

Mg (g∙g^{−1}) | 0.50 | 0.70 | 0.10 | 3 | |

Density (m^{−2}) | 50 | 200 | 50 | 4 |

**Figure 4.**Polarization characteristics of single-scattering albedo and optical depth for the vegetation in the improved model. (

**a**) Single-scattering albedo and (

**b**) optical depth.

^{3}∙cm

^{−3}), with parameters a = 0.005 m, h = 0.2 m, LAI = 1.56 m

^{2}∙m

^{−2}, d = 0.27 mm, and Mg = 0.80 g∙g

^{−1}. Figure 5 shows that the emissivity slightly increases for V polarization and decreases for H polarization with increasing incidence angle. It becomes also clear that the polarization differences increase with the incidence angles. With increasing frequency, the emissivity for V and H polarizations shows the same trend as the dry soil at high incidence angles. Moreover, for V polarization with high soil moisture, the incidence angle has a stronger effect compared with that for the dry soil scenario. In Figure 6, the emissivity sharply decreases as frequency increases up to 10 GHz and varies slightly above 10 GHz. High soil moisture content causes the emissivity to decrease, especially for a low incidence angle of 20°. This is consistent with the results in Figure 5.

**Figure 5.**Estimated emissivity versus incidence angle for different soil moisture contents (SMC) (

**a**) SMC: 0.05 cm

^{3}∙cm

^{−3}and (

**b**) SMC: 0.30 cm

^{3}∙cm

^{−3}.

**Figure 6.**Estimated emissivity versus frequency for different soil moisture content (SMC) for (

**a**) SMC: 0.05 cm

^{3}∙cm

^{−3}and (

**b**) SMC: 0.30 cm

^{3}∙cm

^{−3}.

#### 4.2. Comparisons with Field Experimental Data

**Figure 7.**Comparisons between the measured brightness temperature and the brightness temperature for the model for soybean at different frequencies and on different dates. (

**a**) Soybean for C band on 23 June 2009; (

**b**) Soybean for X band on 23 June 2009; (

**c**) Soybean for C band on 9 July 2009; and (

**d**) Soybean for X band on 9 July 2009.

**Figure 8.**Comparisons between measured brightness temperature and the brightness temperature for the model for cotton at different frequencies and on different dates. (

**a**) Cotton for C band on 10 June 2009; (

**b**) Cotton for X band on 10 June 2009; (

**c**) Cotton for C band on 23 June 2009; and (

**d**) Cotton for X band on 23 June 2009.

^{2}of the improved_veg model increases for the V polarization but shows little improvement for the H polarization, compared with that of the Weng model. For the improved_soil_veg model, R

^{2}is higher than 0.9 for both V and H polarizations for the C and X bands. For the V polarization, R

^{2}is slightly higher than that for the H polarization. The root-mean-square errors (RMSEs) for the improved_veg and the Weng models are similar at ≥25 K. Moreover, the RMSEs of the improved_soil_veg model also show significant improvement, especially for the V polarization at 5.03 K for the C band and at 5.19 K for the X band, with improvements of 81.1% and 79.8%, respectively. The RMSE values of the H polarization for the improved_soil_veg model decreased to 11.73 K for the C band and 14.92 K for the X band, compared with those of >30 K for the Weng model, with improvements of 64.3% and 53.0%, respectively. The average improvement in accuracy from the improved_soil_veg model is about 80% for the V polarization and 59% for the H polarization.

**Table 3.**Statistics for the brightness temperature (K) with the Weng, improved_veg, and improved_soil_veg models and field experimental data at different frequencies and polarizations.

Models | Weng Model | Improved_veg | Improved_soil_veg | ||||
---|---|---|---|---|---|---|---|

Statistics | C Band | X Band | C Band | X Band | C Band | X Band | |

R^{2} | V | 0.33 | 0.27 | 0.62 | 0.60 | 0.98 | 0.97 |

H | 0.50 | 0.42 | 0.49 | 0.44 | 0.95 | 0.93 | |

RMSE | V | 26.67 | 25.70 | 26.71 | 25.71 | 5.03 | 5.19 |

H | 32.81 | 31.77 | 30.86 | 29.67 | 11.73 | 14.92 |

#### 4.3. Discussion

#### 4.3.1. General Discussion of Results

**Figure 9.**Brightness temperature of model versus measured brightness temperature (Tb) for (

**a**) dry soil: including crop fields for soybean with SMC 0.0138 cm

^{3}cm

^{−3}and cotton with SMC 0.05 cm

^{3}∙cm

^{−3}on 23 June; (

**b**) wet soil: including crop fields soybean with SMC 0.162 cm

^{3}∙cm

^{−3}on 9 July and cotton with SMC 0.3 cm

^{3}∙cm

^{−3}on 10 June.

**Table 4.**Statistics for the Weng, improved_veg, and improved_soil_veg models’ brightness temperature versus measured brightness temperature (K) under dry and wet soil conditions.

Models | Weng Model | Improved_veg | Improved_soil_veg | ||||
---|---|---|---|---|---|---|---|

Statistics | Dry Soil | Wet Soil | Dry Soil | Wet Soil | Dry Soil | Wet Soil | |

R^{2} | V | 0.94 | 0.06 | 0.94 | 0.46 | 0.75 | 0.97 |

H | 0.92 | 0.08 | 0.90 | 0.08 | 0.93 | 0.83 | |

RMSE | V | 16.06 | 33.37 | 3.63 | 36.90 | 5.91 | 4.15 |

H | 12.28 | 43.99 | 9.85 | 41.66 | 12.32 | 14.44 |

#### 4.3.2. Sources of Uncertainty

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Weng, F.Z.; Yan, B.H.; Grody, N.C. A microwave land emissivity model. J. Geophys. Res.
**2001**, 106, 20115–20123. [Google Scholar] [CrossRef] - Paloscia, S. Microwave emission from vegetation. In Passive Microwave Remote Sensing of Land-Atmosphere Interactions; Choudhury, B.J., Kerr, Y.H., Njoku, E.G., Pampaloni, P., Eds.; VSP Press: Utrecht, The Netherlands, 1995; pp. 357–374. [Google Scholar]
- Weng, F.Z.; Grody, N.C. Physical retrieval of land surface temperature using the special sensor microwave imager. J. Geophys. Res.
**1998**, 103, 8839–8848. [Google Scholar] [CrossRef] - Ferrazzoli, P.; Guerriero, L. Modeling microwave emission from vegetation-covered surfaces: A parametric analysis. In Passive Microwave Remote Sensing of Land-Atmosphere Interactions; Choudhury, B.J., Kerr, Y.H., Njoku, E.G., Pampaloni, P., Eds.; VSP Press: Utrecht, The Netherlands, 1995; pp. 389–402. [Google Scholar]
- Ulaby, F.T.; El-Rayes, M.A. Microwave dielectric spectrum of vegetation. Part II: Dual-dispersion model. IEEE Trans. Geos. Remot. Sens.
**1987**, GE-25, 550–556. [Google Scholar] [CrossRef] - Karam, M.A.; Fung, A.K.; Lang, R.H.; Chuahan, N.S. A microwave scattering model for layered vegetation. IEEE Trans. Geosci. Remote Sens.
**1992**, 30, 767–784. [Google Scholar] [CrossRef] - Ulaby, F.T.; Sarabandi; McDonald, K.; Whitt, M.; Dobson, M.C. Michigan canopy scattering model. Int. J. Remote Sens.
**1990**, 11, 1223–1253. [Google Scholar] [CrossRef] - Tsang, L.; Kong, J.A.; Shin, R.T. Radiative transfer theory for active remote sensing ellipsoidal scatters. Radio Sci.
**1984**, 19, 629–642. [Google Scholar] [CrossRef] - Ulaby, F.T.; Moore, R.K.; Fung, A.K. Passive microwave sensing of land. In Microwave Remote Sensing Active and Passive; Artech House Press: Dedham, MA, USA, 1986; Volume III, pp. 1522–1638. [Google Scholar]
- Pampaloni, P.; Paloscia, S. Microwave emission and plant water content: A comparison between field measurements and theory. IEEE Trans. Geosci. Remote Sens.
**1986**, GE-24, 900–905. [Google Scholar] [CrossRef] - Wegmuller, U. Remote Sensing Signature Studies on Agricultural Fields with Ground-based Radiometry and Scatterometry. Ph.D. Thesis, University of Berne, Bern, Switzerland, 1990. [Google Scholar]
- Schwank, M.; Matzler, C.; Guglielmetti, M.; Fluhler, H. L-band radiometer measurements of soil water under growing clover grass. IEEE Trans. Geosci. Remote Sens.
**2005**, 43, 2225–2237. [Google Scholar] [CrossRef] - Vereecken, H.; Weihermüller, L.; Jonard, F.; Montzka, C. Characterization of crop canopies and water stress related phenomena using microwave remote sensing methods: A review. Vadose Zone J.
**2012**, 11. [Google Scholar] [CrossRef] - Choudhury, B.J.; Schmugge, T.J.; Chang, A.; Newton, R.W. Effect of surface roughness on the microwave emission from soils. J. Geophys. Res.
**1979**, 84, 5699–5706. [Google Scholar] [CrossRef] - Au, W.C.; Tsang, L.; Shin, R.T.; Kong, J.A. Collective scattering and absorption in microwave interaction with vegetation canopies. Prog. Electromagn. Res.
**1996**, 14, 181–231. [Google Scholar] - Kurum, M.; Lang, R.H.; O’Neill, P.E.; Joseph, A.T.; Jackson, T. A first-order radiative transfer model for microwave radiometry of forest canopies at L-band. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 3167–3179. [Google Scholar] [CrossRef] - Wigneron, J.P.; Kerr, Y.H.; Waldtufe, P.; Saleh, K.; Richaume, P. L-band microwave emission of the biosphere (L-MEB) model: Results from calibration against experimental data sets over crop fields. Remote Sens. Environ.
**2007**, 107, 639–655. [Google Scholar] [CrossRef] - Mo, T.; Choudhury, B.J.; Schmugge, T.J.; Wang, J.R.; Jackson, T.J. A model for microwave emission from vegetation-covered fields. J. Geophys. Res.
**1982**, 87, 11229–11237. [Google Scholar] [CrossRef] - Fung, A.K.; Eom, H.J. Emission from a rayleigh layer with irregular boundaries. J. Quant. Spectrosc. Radiat. Trans.
**1981**, 26, 397–409. [Google Scholar] [CrossRef] - Ferrazzoli, P.; Solimini, D.; Luzi, G.; Paloscia, S. Model analysis of backscatter and emission from vegetated terrains. JEWA
**1991**, 5, 175–193. [Google Scholar] [CrossRef] - Shi, J.C.; Jiang, L.M.; Zhang, L.X.; Chen, K.S.; Wigneron, J.P.; Chanzy, A. A parameterized multifrequency-polarization surface emission model. IEEE Trans. Geosci. Remote Sens.
**2005**, 43, 2831–2841. [Google Scholar] - Zhao, T.J.; Shi, J.C.; Bindlish, R.; Jackson, T.; Cosh, M.; Jiang, L.M. Parametric Exponentially Correlated Surface Emission Model For L-Band Passive Microwave Soil Moisture Retrieval. Available online: http://dx.doi.org/10.1016/j.pce.2015.04.001 (accessed on 15 May 2015).
- Chen, K.S.; Wu, T.D.; Tsang, L.; Li, Q.; Shi, J.C.; Fung, A.K. The emission of rough surfaces calculated by the integral equation method with a comparison to a three-dimensional moment method simulations. IEEE Trans. Geosci. Remote Sens.
**2003**, 41, 90–101. [Google Scholar] [CrossRef] - Wegmuller, U.; Matzler, C.; Njoku, E. Canopy opacity models. In Passive Microwave Remote Sensing of Land-Atmosphere Interactions; Choudhury, B.J., Kerr, Y.H., Njoku, E.G., Pampaloni, P., Eds.; VSP Press: Utrecht, The Netherlands, 1995; pp. 380–384. [Google Scholar]
- Schiffer, R.; Thielheim, K.O. Light scattering by dielectric needles and disks. J. Appl. Phys.
**1979**, 50, 2476–2483. [Google Scholar] [CrossRef] - Le Vine, D.M.; Meneghini, R.; Lang, R.H.; Seker, S.S. Scattering from arbitrarily oriented dielectric disks in the physical optics regime. J. Opt. Soc. Am.
**1983**, 73, 1255–1262. [Google Scholar] [CrossRef] - Karam, M.A.; Fung, A.K.; Antar, Y.M.M. Electromagnetic wave scattering from some vegetation samples. IEEE Trans. Geosci. Remote Sens.
**1988**, 26, 799–808. [Google Scholar] [CrossRef] - Karam, M.A.; Fung, A.K. Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation. Int. J. Remote Sens.
**1988**, 9, 1109–1134. [Google Scholar] [CrossRef] - Shi, J.C.; Jackson, T.; Tao, J.; Du, J.; Bindlish, R.; Lu, L.; Chen, K.S. Microwave vegetation indices for short vegetation covers from satellite passive microwave sensor AMSR-E. Remote Sens. Environ.
**2008**, 112, 4285–4300. [Google Scholar] [CrossRef] - Zhao, T.J.; Zhang, L.X.; Shi, J.C.; Jiang, L.M. A physically based statistical methodology for surface soil moisture retrieval in the Tibet plateau using microwave vegetation indices. J. Geophys. Res.
**2011**, 116, D08116. [Google Scholar] [CrossRef] - Li, X.; Zhang, L.; Weihermuller, L.; Jiang, L.M.; Vereecken, H. Measurement and simulation of topographic effects on passive microwave remote sensing over mountain areas: A case study from the Tibetan Plateau. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 1489–1501. [Google Scholar] [CrossRef] - Zhao, T.; Zhang, L.; Jiang, L.; Chai, L.; Jin, R. A new soil freeze/thaw discriminant algorithm using AMSR-E passive microwave imagery. Hydrol. Process.
**2011**, 25, 1704–1716. [Google Scholar] [CrossRef] - Chai, L.N. Vegetation Biomass Inversion Algorithm Study Based on Passive Microwave Remote Sensing. Ph.D. Thesis, Beijing Normal University, Beijing, China, 2010. [Google Scholar]
- Fung, A.K. Introduction: brightness temperature. In Microwave Scattering and Emission Models and Their Applications; Artech House: Dedham, MA, USA, 1994; pp. 16–18. [Google Scholar]
- Ulaby, F.T.; Moore, R.K.; Fung, A.K. Microwave Remote Sensing—Active and Passive Volume I: Microwave Remote Sensing Fundamentals and Radiometry; Artech House: Dedham, MA, USA, 1981; p. 57. [Google Scholar]
- Ferrazzoli, P.; Guerriero, L.; Paloscia, S.; Pampaloni, P.; Solimini, D. Modeling polarization properties of emission from soil covered with vegetation. IEEE Trans. Geosci. Remote Sens.
**1992**, 30, 157–165. [Google Scholar] [CrossRef] - Ewe, H.T.; Chuah, H.T. Electromagnetic scattering from an electrically dense vegetation medium. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2093–2105. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xie, Y.; Shi, J.; Lei, Y.; Li, Y.
Modeling Microwave Emission from Short Vegetation-Covered Surfaces. *Remote Sens.* **2015**, *7*, 14099-14118.
https://doi.org/10.3390/rs71014099

**AMA Style**

Xie Y, Shi J, Lei Y, Li Y.
Modeling Microwave Emission from Short Vegetation-Covered Surfaces. *Remote Sensing*. 2015; 7(10):14099-14118.
https://doi.org/10.3390/rs71014099

**Chicago/Turabian Style**

Xie, Yanhui, Jiancheng Shi, Yonghui Lei, and Yunqing Li.
2015. "Modeling Microwave Emission from Short Vegetation-Covered Surfaces" *Remote Sensing* 7, no. 10: 14099-14118.
https://doi.org/10.3390/rs71014099