# L-Band Vegetation Optical Depth Estimation Using Transmitted GNSS Signals: Application to GNSS-Reflectometry and Positioning

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## Abstract

**:**

_{0}) data. These data were compared to different ground-truth datasets (greenness, blueness, and redness indices, sky cover index, rain data, leaf area index or LAI, and normalized difference vegetation index (NDVI)). The highest correlation observed is between C/N

_{0}and NDVI data, obtaining R

^{2}coefficients larger than 0.85 independently from the elevation angle, suggesting that for beech forest, NDVI is a good descriptor of signal attenuation at L-band, which is known to be related to the vegetation optical depth (VOD). Depolarization effects were also studied, and were found to be significant at elevation angles as large as ~50°. Data were also fit to a simple τ-ω model to estimate a single scattering albedo parameter (ω) to try to compensate for vegetation scattering effects in soil moisture retrieval algorithms using GNSS-R. It is found that, even including dependence on the elevation angle (ω(θ

_{e})), at elevation angles smaller than ~67°, the ω(θ

_{e}) model is not related to the NDVI. This limits the range of elevation angles that can be used for soil moisture retrievals using GNSS-R. Finally, errors of the GPS-derived position were computed over time to assess vegetation impact on the accuracy of the positioning.

## 1. Introduction

_{0})can also be used to retrieve vegetation properties that can be related to the vegetation water content. The model widely used in passive microwaves at L-band is the τ-ω model [2,3], where the vegetation opacity (τ) and single scattering albedo (ω) are usually assumed to be constant over all elevation angles. This study uses a dual-input GPS receiver connected to a dual-polarization antenna to extend the work conducted in [4] to characterize both the co-polar (RHCP) and cross-polar (LHCP) received powers as a function of the elevation angle, and the vegetation properties, characterized by the NDVI, the LAI, or the greenness, blueness or redness levels, as derived from zenith-looking images. Section 2 presents the methodology: the instrument developed, the field experiment, and the ground-truth data acquired. Section 3 analyzes and discusses the results obtained. Finally, Section 4 summarizes the main results and presents the conclusions of this study.

## 2. Methodology

#### 2.1. Test Site Description

#### 2.2. The Global Navigation Satellite Systems (GNSS)-Transmissivity Instrument

_{0}values are discretized at 0.1 dB, which prevents the realistic modelling of the observed data. The forest structure leads to different scattering and attenuation processes; while attenuation increases with the leaves’ vegetation water content (VWC), the signal polarization purity degrades with increasing VWC and the presence of branches, etc. Additionally, multiple scattering occurs, which is very difficult to model.

_{0}for different steps of azimuth (Δφ = 10°) and incidence (Δθ = 5°) angles after compensating for the antenna patterns for June 7th. White spots occur because that particular day, the GPS constellation did not pass through that angular extent area. The large white area in the top corresponds to the Northern hemisphere, where there are no GPS satellites.

_{0}values, i.e., it is constant from all directions.

#### 2.3. Ground-truth data

^{2}/m

^{2}. Finally, rain data from a meteorological station located in Olot were used to analyze the effect of rain on the measurements [7].

## 3. Results

_{0}values for the RHCP and LHCP channels, respectively. During the fall seasons, it is clearly seen in the RHCP plot in Figure 6a that the smaller the number of leaves, the smaller the attenuation is. Accordingly, the C/N

_{0}is measured as being higher in December than in October. Leaves also cause depolarization of the waves, but from the two effects (attenuation and scattering), attenuation is dominant since the LHCP received power actually increases after the leaves have fallen, as shown in Figure 7a. Figure 6b and Figure 7b show different examples of the received C/N

_{0}when the leaves are growing in spring. The decrease in the received power shows again that the attenuation effect is dominant for leaves.

_{0}is azimuthally averaged to analyze the evolution with the elevation/incidence angle. Resulting C/N

_{0}curves are analyzed with respect to:

- rain rates, obtained from the regional meteorological station,
- blueness, greenness, redness, and sky cover percentage computed from the RGB and gray scale pictures (Figure 5),
- LAI and NDVI, both computed from MODIS,

#### 3.1. Rain Effects

_{0}curves for different satellite elevation angles as a function of time, together with the rain events during the field campaign. It can be appreciated that rain events induce a fading on the C/N

_{0}plots, especially in the RHCP channel, due to two main factors: (1) the presence of water drops in the atmosphere, and the water that stays on the leaves’ surface, increasing the attenuation induced by the leaves; (2) the fact that after the rain event, trees absorb the water from the soil, increasing the vegetation water content. Note that during the period without leaves (December 2015–April 2016), fading events due to rain are very smaller in depth.

#### 3.2. Dependence on the Greenness/Redness/Blueness

_{G,R,B}is the amount of G,R,B color bits from the pictures taken with the Canon 50-D. Figure 9a shows the evolution of the greenness estimated from the pictures together with the azimuthally averaged RHCP C/N

_{0}curves. It is expected that the larger the greenness parameter, the larger the amount of leaves, and therefore the larger the attenuation. During the defoliation process (October–December 2015), the R

^{2}parameter with a linear fit computed between the greenness and the different C/N

_{0}curves is 0.76–0.87; it does not depend on the incidence angle, and the mean slope of the fit is −31 dB/au (au: arbitrary unit). During the leaf growing period (March–April 2016), the R

^{2}parameter goes down to 0.46–0.66.

_{0}curves together with the redness parameter. The R

^{2}parameter for both the falling and growing season is below 0.05 for any elevation angle, and it does not depend on the season.

_{0}curves together with the blueness parameter. As for the greenness parameter, C/N

_{0}curves and blueness are correlated, but not as correlated as with the greenness. During the defoliation process, R

^{2}is ~0.46–0.58 with a slope of ~14 dB/au, while during the growing process, R

^{2}is ~0.25–0.43, with a slope of 10 dB/au. The correlation between curves appears because the amount of blue is related to the amount of sky observed, and therefore the larger the amount of sky observed, the lower the amount of leaves; however, the amount of blue color seems to be a poor vegetation indicator. Apart from that, on a cloudy day, such as 2015/11/20 or 2016/03/31, the sky is white and not blue (see Figure 4), and therefore the blueness is not such a good indicator.

#### 3.3. Dependence on the Sky Cover

_{0}curves together with the fraction of sky covered computed in two different ways. In Figure 10a, it is computed from the gray-scale image (intensity, 0–255). A value threshold of 155 is selected [8,9] to differentiate between the vegetation (vegetation < 155), and the sky (open sky > 155). In Figure 10b, the blue channel of the RGB image is used for sky classification, and a similar threshold is applied.

^{2}parameter with a linear fit between the different C/N

_{0}curves and the percentage of sky cover is 0.6–0.7 for the falling season, whereas it is between 0.67 and 0.82 for the growing season. However, when using the blue channel to estimate the percentage of sky cover, the R

^{2}parameter is between 0.47 and 0.57 for the fall season, and 0.3 and 0.5 for the spring season. Again, both are independent of the elevation angle.

#### 3.4. Dependence on the LAI

_{0}curves for different elevation angles. The R

^{2}coefficient of the regression lines that relate the RHCP C/N

_{0}to the LAI ranges from 0.50 and 0.62, which is still lower than the greenness parameter. However, a trend can be clearly seen in Figure 11 where the lower the LAI, the larger the C/N

_{0}observed.

#### 3.5. Dependence on NDVI

_{0}curves for different elevation angles. There is a very high correlation between the received signal power or C/N

_{0}and the NDVI.

_{0}value for different satellite elevation angles. For all satellites and elevation angles the R

^{2}parameter is between 0.87 and 0.94, and the slope of the fit from −16.9 dB/au to −22.6 dB/au (au denotes an arbitrary unit of the NDVI from 0 to 1). Table 1 (columns 2 to 5) shows the fitting parameters of the regression of the RHCP C/N

_{0}with respect to NDVI as a function of the elevation angle (Figure 13).

## 4. Discussion

_{0}and the NDVI (Figure 14) is also found to be strongly correlated. Because of the increased attenuation, the larger the NDVI, the lower the received power at LHCP. Table 2 (columns 2 to 5) shows the fitting parameters of the regression of the LHCP C/N

_{0}wrt. NDVI as a function of the elevation angle (Figure 14).

- The correlation drops at high elevation angles (77.5° and 82.5°) because the path through the vegetation layer is shorter, and scattering effects (responsible for signal depolarization) are less important.
- The slope is (in absolute value) smaller for LHCP than for RHCP, suggesting a combined effect of depolarization that transfers power from the RHCP signal to the LHCP.

_{e})) value can be estimated. Figure 15 shows the evolution of the estimated albedo with respect to time for several elevation angles. As it can be appreciated, there is a strong dependence with the elevation angle, and apparently a weak dependence with the NDVI (not shown in this plot, but NDVI varies from 0.6 to 0.9, see Figure 12). Figure 16 shows the regression lines of the albedo with respect to NDVI for different elevation angles, and Table 3 shows the fit parameters of Figure 15. The albedo varies from ~0.1 to 0.2 at the zenith, but up to ~0.35 at 47.5°. Note, however, that only at high elevation angles (θ

_{e}≥ 67.5°) is the single scattering albedo correlated with the NDVI, and at lower elevation angles, the presence of multiple scattering makes the τ-ω model more likely to be invalid.

## 5. Summary and Conclusions

^{2}parameter (>0.85), with sensitivities ranging from −17 dB/au to −23 dB/au. This indicates that at L-band, auxiliary NDVI data can be used as a descriptor for beech forest vegetation attenuation in GNSS-R soil moisture retrievals. Alternatively, L-band multi-angular attenuation measurements can be used to infer the vegetation water content, which is related to the vegetation optical depth (VOD).

_{e}≥ 67.5°), the estimated albedo is significant, and can be related to the NDVI. At lower elevation angles, signal depolarization and multiple scattering effects must be taken into account to properly model vegetation effects in GNSS-Reflectometry, for this type of forest, and probably for other types of dense vegetation as well. This limitation of the model is what nowadays limits the range of elevation angles that can be used for soil moisture retrievals using GNSS-R, as shown in [13].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Antenna pattern measurement test setup in UPC anechoic chamber (https://www.tsc.upc.edu/en/facilities/anechoic-chamber).

**Figure A2.**Antenna pattern measurement errors for two antennas (green and blue plots, left: amplitude, right: phase) associated to: (

**a**) wall reflections; (

**b**) thermal noise; and (

**c**) both wall reflections and thermal noise.

## References

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**Figure 2.**(

**a**) Co-polar (RHCP, blue) and cross-polar (LHCP, red) RHCP antenna pattern; (

**b**) Co-polar (LHCP, blue) and cross-polar (RHCP, red) RHCP antenna pattern. Cuts at φ = 0°, 45°, 90°, and 135°, as indicated.

**Figure 3.**Dual-polarization up-looking antenna and receiver (behind the antenna) installed at La Fageda d’en Jordà (Girona, Spain).

**Figure 4.**(

**a**) RHCP and (

**b**) LHCP average received carrier-to-noise ratio (C/N

_{0}) for 7th June 2015 during the preliminary tests after compensating for the antenna pattern effect. Incidence angle in 5° steps, azimuth angle in 10° steps.

**Figure 5.**Vegetation observed from a camera located at the instrument’s position looking to the zenith during (

**a**) the fall season and (

**b**) during the spring season.

**Figure 6.**RHCP received C/N

_{0}during the (

**a**) fall; and (

**b**) spring season for different dates when vegetation pictures were taken. Incidence angle in 5° steps, azimuth angle in 10° steps.

**Figure 7.**LHCP received C/N

_{0}during (

**a**) the fall and (

**b**) the spring season for different dates when vegetation pictures were taken. Incidence angle in 5° steps, azimuth angle in 10° steps.

**Figure 8.**Effect of rain to the azimuthally averaged C/N

_{0}curves: (

**a**) RHCP; and (

**b**) LHCP. The curves are plotted corresponding to the elevation angles from 47.5° to 82.5° angles in the legend.

**Figure 9.**Evolution of (

**a**) greenness; (

**b**) redness; and (

**c**) blueness, and C/N

_{0}curves as a function of time.

**Figure 10.**(

**a**) Evolution of the percentage of sky covered and C/N

_{0}curves as a function of time: (

**a**) using a gray-scale image; and (

**b**) using the blue channel of the RGB image.

**Figure 13.**Dependence of the RHCP C/N

_{0}and the NDVI for different satellite elevation angles, and linear fits.

**Figure 14.**Dependence of the LHCP C/N

_{0}and the NDVI for different satellite elevation angles, and linear fits.

**Figure 16.**Comparison between the estimated single scattering albedo (ω) and the NDVI for different satellite elevation angles, and linear fits.

**Figure 17.**Evolution of the 6-h position error (stem plot), the weekly root man squared errors (circles), and the median errors (diamonds) in north-south (Y-component, in red) and east-west (X-component, in blue). Six instances with errors larger than 50 m rmse were found.

RHCP | ||||
---|---|---|---|---|

Elevation Angle [deg] | a [dB/au] | b [dB] | RMSE [dB] | R^{2} |

47.5 | −16.90 | 51.57 | 0.55 | 0.89 |

52.5 | −17.52 | 52.38 | 0.49 | 0.92 |

57.5 | −21.13 | 55.93 | 0.61 | 0.91 |

62.5 | −17.89 | 53.36 | 0.65 | 0.86 |

67.5 | −20.65 | 54.93 | 0.48 | 0.94 |

72.5 | −18.79 | 54.06 | 0.62 | 0.89 |

77.5 | −18.78 | 54.59 | 0.66 | 0.88 |

82.5 | −22.61 | 58.40 | 0.71 | 0.90 |

^{2}).

LHCP | RHCP to LHCP Ratio | |||||||
---|---|---|---|---|---|---|---|---|

Elevation Angle [deg] | a [dB/au] | b [dB] | RMSE [dB] | R^{2} | a [dB/au] | b [dB] | RMSE [dB] | R^{2} |

47.5 | −18.55 | 49.59 | 0.80 | 0.82 | 1.65 | 1.98 | 0.97 | 0.86 |

52.5 | −18.34 | 49.39 | 0.62 | 0.88 | 0.82 | 2.99 | 0.79 | 0.73 |

57.5 | −15.67 | 47.62 | 1.09 | 0.65 | −5.46 | 8.31 | 1.25 | 0.59 |

62.5 | −13.42 | 45.70 | 0.96 | 0.63 | −4.47 | 7.66 | 1.16 | 0.54 |

67.5 | −12.31 | 44.28 | 0.98 | 0.59 | −8.34 | 10.65 | 1.09 | 0.55 |

72.5 | −3.51 | 37.86 | 0.79 | 0.76 | −15.28 | 16.20 | 1.00 | 0.68 |

77.5 | −8.84 | 41.48 | 1.31 | 0.31 | −9.94 | 13.11 | 1.47 | 0.27 |

82.5 | −12.77 | 43.81 | 1.31 | 0.43 | −9.90 | 14.59 | 1.49 | 0.39 |

^{2}).

Elevation Angle | a [-] | b [-] | RMSE [-] | R^{2} |
---|---|---|---|---|

47.5 | −0.08 | 0.38 | 0.05 | −0.17 |

52.5 | −0.02 | 0.32 | 0.03 | −0.20 |

57.5 | 0.16 | 0.14 | 0.04 | 0.05 |

62.5 | 0.10 | 0.18 | 0.04 | 0.05 |

67.5 * | 0.26 | 0.06 | 0.04 | 0.52 |

72.5 * | 0.17 | 0.07 | 0.05 | 0.46 |

77.5 | 0.22 | 0.03 | 0.05 | 0.19 |

82.5 * | 0.21 | 0.00 | 0.03 | 0.66 |

^{2}> 0.4).

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## Share and Cite

**MDPI and ACS Style**

Camps, A.; Alonso-Arroyo, A.; Park, H.; Onrubia, R.; Pascual, D.; Querol, J. L-Band Vegetation Optical Depth Estimation Using Transmitted GNSS Signals: Application to GNSS-Reflectometry and Positioning. *Remote Sens.* **2020**, *12*, 2352.
https://doi.org/10.3390/rs12152352

**AMA Style**

Camps A, Alonso-Arroyo A, Park H, Onrubia R, Pascual D, Querol J. L-Band Vegetation Optical Depth Estimation Using Transmitted GNSS Signals: Application to GNSS-Reflectometry and Positioning. *Remote Sensing*. 2020; 12(15):2352.
https://doi.org/10.3390/rs12152352

**Chicago/Turabian Style**

Camps, Adriano, Alberto Alonso-Arroyo, Hyuk Park, Raul Onrubia, Daniel Pascual, and Jorge Querol. 2020. "L-Band Vegetation Optical Depth Estimation Using Transmitted GNSS Signals: Application to GNSS-Reflectometry and Positioning" *Remote Sensing* 12, no. 15: 2352.
https://doi.org/10.3390/rs12152352