# Evaluation of the Land GNSS-Reflected DDM Coherence on Soil Moisture Estimation from CYGNSS Data

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## Abstract

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^{3}.

## 1. Introduction

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^{3}[21,22,23,24,25,26,27,28,29,30].

## 2. Methods and Datasets

#### 2.1. Bistatic Forward Scattering

#### 2.2. Definition of Classification Estimator

- TES: It is the trailing edge slope of the normalized DW and determined using the least-squares fitting within the time-delay window to a linear expression:$${a}_{\mathrm{TES}}^{N}=\frac{n{\displaystyle \sum _{i=1}^{n}{\tau}_{i}{P}_{i}^{N}-}{\displaystyle \sum _{i=1}^{n}{\tau}_{i}{\displaystyle \sum _{i=1}^{n}{P}_{i}^{N}}}}{n{\displaystyle \sum _{i=1}^{n}{\tau}_{i}^{2}-{({\displaystyle \sum _{i=1}^{n}{\tau}_{i}})}^{2}}}$$
- TEV: It is the average volume of the normalized DW trailing edge:$${\overline{P}}_{\mathrm{TEV}}^{N}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{P}_{i}^{N}}$$
- TEV_POW: It is the average absolute scattering power of the DW trailing edge:$${\overline{P}}_{\mathrm{TEV}\_\mathrm{POW}}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{P}_{i}}$$
- DDMA: It is the average of the normalized scattering power DDM near its peak:$${\overline{\sigma}}_{\mathrm{DDMA}}^{N}=\frac{1}{nm}{\displaystyle \sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}{P}_{i,j}^{N}}}$$
- DDMA_POW: It is the average of the absolute scattering power DDM near the peak:$${\overline{\sigma}}_{\mathrm{DDMA}\_\mathrm{POW}}=\frac{1}{mn}{\displaystyle \sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}{P}_{i,j}}}$$
- MF: It is known as the WAF-matched filter (MF) approach, which directly calculates the correlation coefficient of normalized DDM and unitary energy WAF:$${R}_{\mathrm{MF}}=\frac{{\left|\u2329\u2329{\left|P(\widehat{\tau},{\widehat{f}}_{D})\right|}^{2}\u232a,\chi (\widehat{\tau},{\widehat{f}}_{D})\u232a\right|}^{2}}{\u2329\u2329{\left|P(\widehat{\tau},{\widehat{f}}_{D})\right|}^{2}\u232a,\u2329{\left|P(\widehat{\tau},{\widehat{f}}_{D})\right|}^{2}\u232a\u232a\u2329\chi (\widehat{\tau},{\widehat{f}}_{D}),\chi (\widehat{\tau},{\widehat{f}}_{D})\u232a}$$

#### 2.3. Dataset for Soil Moisture Retrieval

#### 2.4. Soil Moisture Retrieval Algorithm

^{3}/cm

^{3}to 0.7 cm

^{3}/cm

^{3}can reach 10 dB. The effect of the incidence angle on the mapping relationship between SM and reflectivity is negligible when the incidence angle is less than 60°. In our CYGNSS SM inversion experiements, the DDM peak value of coherent scattered power is picked in the CYGNSS level-1 data as the left term of Equation (7). Since the small scale roughness and upwelling vegetation cover can attenuate the scattering signal, the roughness and vegetation correction in Equation (7) directly use the roughness coefficient and VOD parameter provided in SMAP product for individual observation. Although the influence of the signal incidence angle is small, the method proposed in [25] is still used in this work. The effect of the incidence angle correction is represented by the dashed lines in Figure 3 as well.

## 3. Results and Analysis

#### 3.1. Performance Evaluation of DDM Observables

#### 3.2. Coherent and Incoherent DDM Observations

#### 3.3. GNSS-R Soil Moisture Retrieval

^{3}/cm

^{3}. To further evaluate the performance of the established SM model over the high-humidity areas, the accuracy of the inversion model is evaluated when the referenced SM value is greater than 0.1 cm

^{3}/cm

^{3}.

^{3}/cm

^{3}, 0.0274 cm

^{3}/cm

^{3}, and 0.0416 cm

^{3}/cm

^{3}, respectively. The inversion results with the distinguished coherent observation training dataset constructed retrieval model show that the bias, MAE, and RMSE are −0.0003 cm

^{3}/cm

^{3}, 0.0269 cm

^{3}/cm

^{3}, and 0.0408 cm

^{3}/cm

^{3}, respectively. The model performance between the two strategies is very close. When the SM reference values are greater than 0.1 cm

^{3}/cm

^{3}, the model accuracy of the two methods is 0.0569 cm

^{3}/cm

^{3}and 0.0564 cm

^{3}/cm

^{3}, respectively, and the inversion results did not show a big difference. Figure 7b shows the density scatterplot between SMAP reference SM and GNSS-R-derived SM generated from a split of k-fold cross-validation with the coherent observation established model. The red line represents the linear fitting line; the predicted SM shows an overall fairly good agreement with the SMAP SM, all CYGNSS land data retrieved SM show an identical situation. Figure 8 presents the coherent inversion accuracy at each grid pixel with k-fold cross-validation. The analysis shows that CYGNSS incoherent observations will not cause any noticeable SM spatial inversion accuracy differences compared to the coherent results, so it is not given here.

## 4. Discussion

^{3}/cm

^{3}, 0.0265 cm

^{3}/cm

^{3}, and 0.0403 cm

^{3}/cm

^{3}, respectively. The RMSE is reduced by 3.1% compared to the constructed model with assuming all coherent land observations. When the reference SM value is greater than 0.1 cm

^{3}/cm

^{3}, the inversion bias is −0.0145 cm

^{3}/cm

^{3}, MAE values is 0.0416 cm

^{3}/cm

^{3}, and RMSE is 0.0558 cm

^{3}/cm

^{3}.

^{3}/cm

^{3}, while most of the previous studies also show the same problem. Since most training samples are concentrated in the lower SM range, the regression model is more affected by this part of the data. Therefore, there should be a better weighting strategy to solve this problem in future work.

## 5. Conclusions

^{3}/cm

^{3}. Incoherent observations have not seriously impaired the accuracy of CYGNSS soil moisture inversion.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical scattering-power delay-Doppler map (DDM) and delay waveforms over the land surface (

**a**,

**c**) and ocean surface (

**b**,

**d**).

**Figure 2.**The delay spreading function (

**a**), Doppler-spreading function (

**b**), and Woodward ambiguity function (

**c**).

**Figure 3.**The relationship between reflectivity and soil moisture under different incidence angles of GPS signal and the performance of incidence angle correction.

**Figure 4.**Statistic performance of trailing edge slope (TES), the average volume of the normalized time-delay waveform (DW) trailing edge (TEV), average absolute scattering power of the DW trailing edge (TEV_POW) derived from central Doppler time-delay waveform (CDW;

**a**–

**c**), integrated time-delay waveform (IDW;

**d**–

**f**), and deviation of time-delay waveform (DDW,

**g**–

**i**) over land and ocean surface, dataset collected from the cyclone global navigation satellite system (CYGNSS) level-1B in January 2018.

**Figure 5.**Average of the normalized scattering power DDM near its peak (DDMA) (

**a**), an average of the absolute scattering power DDM near the peak (DDMA_POW) (

**b**), and WAF-matched filter (MF) (

**c**) statistic performance over land and ocean area, dataset collected from the CYGNSS level-1B in January 2018.

**Figure 6.**The global distribution of monthly average Soil Moisture Active Passive (SAMP) soil moisture (SM) (

**a**), coherent reflectivity (

**b**), and incoherent observations (

**c**) in January 2018.

**Figure 7.**Monthly SMAP soil moisture probability density function (

**a**) and density scatterplot of GNSS-R derived soil moisture and surface SM reference values in a split of k-fold cross-validation (

**b**).

**Figure 9.**The probability density function of coherent and incoherent reflectivity derived from CYGNSS land observations in January 2018.

Observables | ${\mathit{a}}_{\mathrm{TES}}^{\mathit{N},\mathrm{CDW}}$ | ${\overline{\mathit{P}}}_{\mathrm{TEV}}^{\mathit{N},\mathrm{CDW}}$ | ${\mathit{a}}_{\mathrm{TES}}^{\mathit{N},\mathrm{IDW}}$ | ${\overline{\mathit{P}}}_{\mathrm{TEV}}^{\mathit{N},\mathrm{IDW}}$ | ${\mathit{a}}_{\mathrm{TES}}^{\mathit{N},\mathrm{DDW}}$ | ${\overline{\mathit{P}}}_{\mathrm{TEV}}^{\mathit{N},\mathrm{DDW}}$ | ${\overline{\mathit{\sigma}}}_{\mathrm{DDMA}}^{\mathit{N}}$ | ${\mathit{R}}_{\mathrm{MF}}$ |
---|---|---|---|---|---|---|---|---|

Threshold | −0.6191 | 0.6878 | −0.1798 | 0.8726 | −0.0394 | 0.8144 | 0.7053 | 0.6171 |

PD | 0.9146 | 0.8789 | 0.9379 | 0.9132 | 0.9192 | 0.7307 | 0.9368 | 0.9362 |

PFA | 0.0284 | 0.0360 | 0.0289 | 0.0376 | 0.0312 | 0.0808 | 0.0310 | 0.0381 |

PE | 0.0569 | 0.0786 | 0.0455 | 0.0622 | 0.0560 | 0.1751 | 0.0471 | 0.0510 |

**Table 2.**Soil moisture retrieval model evaluating with k-fold cross-validation (unit: cm

^{3}/cm

^{3}).

Dataset | Total Bias | Total MAE | Total RMSE | SM > 0.1, Bias | SM > 0.1, MAE | SM > 0.1, RMSE |
---|---|---|---|---|---|---|

All land observations | −0.0003 | 0.0274 | 0.0416 | −0.0124 | 0.0426 | 0.0569 |

Coherent observations | −0.0003 | 0.0269 | 0.0408 | −0.0123 | 0.0421 | 0.0564 |

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**MDPI and ACS Style**

Dong, Z.; Jin, S.
Evaluation of the Land GNSS-Reflected DDM Coherence on Soil Moisture Estimation from CYGNSS Data. *Remote Sens.* **2021**, *13*, 570.
https://doi.org/10.3390/rs13040570

**AMA Style**

Dong Z, Jin S.
Evaluation of the Land GNSS-Reflected DDM Coherence on Soil Moisture Estimation from CYGNSS Data. *Remote Sensing*. 2021; 13(4):570.
https://doi.org/10.3390/rs13040570

**Chicago/Turabian Style**

Dong, Zhounan, and Shuanggen Jin.
2021. "Evaluation of the Land GNSS-Reflected DDM Coherence on Soil Moisture Estimation from CYGNSS Data" *Remote Sensing* 13, no. 4: 570.
https://doi.org/10.3390/rs13040570