# Synergy of Sentinel-1 and Sentinel-2 Time Series for Cloud-Free Vegetation Water Content Mapping with Multi-Output Gaussian Processes

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Theoretical Background

#### 2.1.1. Single-Output Gaussian Processes Modeling

#### 2.1.2. Multi-Output Gaussian Processes Modeling

#### 2.2. Study Area

#### 2.3. Sentinel-2 Time Series Preprocessing

#### 2.4. Sentinel-1 Time Series Preprocessing

#### 2.5. MOGP Models Parametrization

#### 2.6. Experimental Setup

#### 2.7. Delineation of Retrieval Workflow

- Building of VWC time series applying a GP model trained with in situ data of the BVCR 2020 crop campaign to S2 imagery, and pre-processing of RVI time series for S1 orbit 68 and orbit 141 imagery, respectively;
- Assembling the S1 & S2 dataset containing multitemporal VWC retrieved values and S1 post-processed RVI data for a specific ROI of the BVCR study site;
- Setting up the MOGP kernels with Q = 4 and initializing the parameters using SM;
- Training the MOGP models with the S1 & S2 dataset using the Adam optimizer and assessing the regression statistics error metrics (MAE, MAPE, RMSE, and NRMSE) for best model selection;
- Multi-seasonal mapping of VWC retrieved given the best evaluated MOGP model and S1 & S2 stacked datasets at pixel level over two distinct bounded fields and corresponding process performance;
- Reconstructing of artificially removed S2 GP VWC data gaps over winter wheat cropland considering the BVCR 2020 and 2021 crop campaigns.

## 3. Results

#### 3.1. S1 SAR RVI & S2 GP VWC Temporal Profiles

#### 3.2. Training MOGP Kernels for VWC Time Series Modelling

#### 3.2.1. Cross-Correlation Matrixes for the MOGP Trained Kernels

#### 3.2.2. Optimized MOGP Kernel for Mapping the VWC of the Winter Wheat 2020 and 2021

#### 3.3. Spatiotemporal Mapping of Reconstructed VWC Based on S1 & S2 Synergy

## 4. Discussion

#### 4.1. Time and Frequency Domain Similarities in the S1 & S2 Dataset

#### 4.2. MOGP Modelling and Assessment

#### 4.3. S1 & S2-Based Spatiotemporal Mapping of Vegetation Water Content

#### 4.4. Advantages and Opportunities for Improvement of the Fusing Approach

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Sentinel–1 & Sentinel–2 Acquisition Dates

**Table A1.**Sentinel–2 and Sentinel–1 acquisition dates corresponding to the winter wheat 2020 crop campaign at the BVCR. The (–) symbol means no acquisition. The (

*****) indicates the S2 removed images from the S1 & S2 dataset for model validation.

Winter Wheat 2020 Crop Campaign | ||
---|---|---|

S2 Acquisition Date | S1_{(Orbit 68)} Acquisition Date | S1_{(Orbit 141)} Acquisition Date |

- | 2020-08-27 | - |

2020-08-29 | - | - |

- | - | 2020-09-01 |

- | 2020-09-02 | - |

2020-09-13 * | - | 2020-09-13 |

2020-09-18 * | - | - |

- | 2020-09-20 | - |

2020-09-23 * | - | - |

- | - | 2020-09-25 |

- | 2020-09-26 | - |

2020-09-28 * | - | - |

- | 2020-10-02 | - |

- | - | 2020-10-07 |

- | 2020-10-08 | - |

2020-10-13 * | - | - |

- | 2020-10-14 | - |

- | - | 2020-10-19 |

- | 2020-10-20 | - |

- | 2020-10-26 | - |

- | - | 2020-10-31 |

- | 2020-11-01 | - |

2020-11-02 * | - | - |

- | 2020-11-07 | - |

- | - | 2020-11-12 |

- | 2020-11-13 | - |

2020-11-17 * | - | - |

- | 2020-11-19 | - |

- | - | 2020-11-24 |

- | 2020-11-25 | - |

2020-11-27 * | - | - |

- | 2020-12-01 | - |

- | - | 2020-12-06 |

2020-12-07 * | 2020-12-07 | - |

- | 2020-12-13 | - |

- | - | 2020-12-18 |

- | 2020-12-19 | - |

2020-12-22 | - | - |

- | 2020-12-25 | - |

- | - | 2020-12-30 |

- | 2020-12-31 | - |

- | 2021-01-06 | - |

**Table A2.**Sentinel–2 and Sentinel–1 acquisition dates corresponding to the winter wheat 2021 crop campaign at the BVCR. The (–) symbol means no acquisition. The (

*****) indicates the S2 removed images from the S1 & S2 dataset for model validation.

Winter Wheat 2021 Crop Campaign | ||
---|---|---|

S2 Acquisition Date | S1_{(Orbit 68)} Acquisition Date | S1_{(Orbit 141)} Acquisition Date |

- | 2021-08-16 | - |

- | 2021-08-22 | - |

2021-08-24 * | - | - |

- | - | 2021-08-27 |

- | 2021-08-28 | - |

- | 2021-09-03 | - |

- | - | 2021-09-08 |

- | 2021-09-09 | - |

- | - | 2021-09-20 |

- | 2021-09-21 | - |

- | 2021-09-27 | - |

- | - | 2021-10-02 |

2021-10-03 * | 2021-10-03 | - |

2021-10-08 * | - | - |

- | 2021-10-09 | - |

- | - | 2021-10-14 |

- | 2021-10-15 | - |

2021-10-18 * | - | - |

- | 2021-10-21 | - |

- | - | 2021-10-26 |

- | - | 2021-10-27 |

2021-11-02 * | 2021-11-02 | - |

- | 2021-11-08 | - |

- | 2021-11-14 | - |

2021-11-17 * | - | - |

- | - | 2021-11-19 |

- | 2021-11-20 | - |

- | 2021-11-26 | - |

- | - | 2021-12-01 |

- | 2021-12-02 | - |

2021-12-07 | - | - |

- | 2021-12-08 | - |

- | - | 2021-12-13 |

- | 2021-12-14 | - |

- | 2021-12-20 | - |

2021-12-22 | - | - |

2022-01-01 | 2022-01-01 | - |

## Appendix B. Hyperparameters of the CONV Models Trained over the Winter Wheat Test Sites

**Table A3.**Hyperparameters of the MOGP CONV model trained with the S2 GP VWC and S1 RVI orbits 68 and 141 time series over the winter wheat 2020 ROI-1.

Name | Range | Value |
---|---|---|

M[0].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.16140878 0.12014237 0.25099972] |

M[0].CONV.variance | (0.0, ∞) | [[$4.57955225\times {10}^{-6}$] [$1.48168009\times {10}^{-5}$] [$4.89282973\times {10}^{-5}$]] |

M[0].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [29.65490441] |

M[1].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.18422568 0.12714211 0.09511325] |

M[1].CONV.variance | (0.0, ∞) | [[0.00208712] [0.00021101] [0.00029573]] |

M[1].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [$3.84536139\times {10}^{-6}$] |

M[2].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.161608 0.36756376 0.38364755] |

M[2].CONV.variance | (0.0, ∞) | [[$5.97699880\times {10}^{-6}$] [$8.28188220\times {10}^{-4}$] [$2.73658687\times {10}^{-3}$]] |

M[2].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [55.15439607] |

M[3].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.45055456 0.09223841 0.01531059] |

M[3].CONV.variance | (0.0, ∞) | [[$3.78006500\times {10}^{-6}$] [$2.45277978\times {10}^{-7}$] [$3.81411018\times {10}^{-7}$]] |

M[3].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [54.76679359] |

Gaussian.scale | ($1\times {10}^{-8}$, ∞) | [0.07039943 0.05906305 0.03154559] |

**Table A4.**Hyperparameters of the MOGP model trained with the S2 GP VWC and S1 RVI orbits 68 and 141 time series over the winter wheat 2021 ROI-2.

Name | Range | Value |
---|---|---|

M[0].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.05051712 0.27439207 0.38695247] |

M[0].CONV.variance | (0.0, ∞) | [[$4.86858144\times {10}^{-6}$] [$7.13908231\times {10}^{-6}$] [$1.31486331\times {10}^{-3}$]] |

M[0].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [34.01715996] |

M[1].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.07826687 0.21647057 0.08729357] |

M[1].CONV.variance | (0.0, ∞) | [[$2.67026775\times {10}^{-5}$] [$2.09623224\times {10}^{-6}$] [$3.66018092\times {10}^{-5}$]] |

M[1].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [19.31982864] |

M[2].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.5937755 0.30263363 0.22857684] |

M[2].CONV.variance | (0.0, ∞) | [[$1.10220013\times {10}^{-4}$] [$1.21975560\times {10}^{-2}$] [$6.16156520\times {10}^{-6}$]] |

M[2].CONV.base_variance | ($1\times {10}^{-8}$, ∞) | [49.46172915] |

M[3].CONV.weight | ($1\times {10}^{-8}$, ∞) | [0.0563912 0.01698611 0.03144775] |

M[3].CONV.variance | (0.0, ∞) | [[$2.51113006\times {10}^{-5}$] [$1.23150713\times {10}^{-5}$] [$1.27814011\times {10}^{-2}$]] |

M[3].CONV.base_variance | ($1\times {10}^{-8}$, $\infty )$ | [0.08717407] |

Gaussian.scale | ($1\times {10}^{-8}$, ∞) | [0.04004209 0.06703326 0.0397214 ] |

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**Figure 1.**Overview of BVCR test sites (ROI) for the winter wheat campaigns of the years 2020 and 2021. The red and orange dotted rectangles delimit the MOGP subsets analyzed in Section 3.3. Reference system: WGS84 (EPSG 4326). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article).

**Figure 2.**Illustration of the processing workflow to obtain maps of vegetation water content over irrigated winter wheat, as described in Section 2.7. The ordinal numbers in the graph refer to the workflow processing steps. The maps show the output obtained by our MOGP VWC models over the BVCR study site in Argentina.

**Figure 3.**Temporal profiles (mean value and standard deviation) of averaged selected ROI-1 over a winter wheat parcel belonging to the BVCR 2020 crop campaign. S2 GP VWC time series from December 2018 to the end of January 2021 (

**a**). S1 RVI orbit 141 smoothed (dashed blue line) and original (dashed black line) time series (

**b**). S1 RVI orbit 68 smoothed (dashed red line) and original (dashed black line) time series (

**c**). S1 RVI Orbit 68 (red line) and S1 orbit 141 (blue line) RVI time series (

**d**).

**Figure 4.**Temporal profiles (mean value and standard deviation) of averaged selected ROI-2 over a winter wheat parcel belonging to the BVCR 2021 crop campaign. S2 GP VWC time series from October 2019 to the end of January 2022 (

**a**). S1 RVI orbit 141 smoothed (dashed blue line) and original (dashed black line) time series (

**b**). S1 RVI orbit 68 smoothed (dashed red line) and original (dashed black line) time series (

**c**). S1 RVI Orbit 68 (red line) and S1 orbit 141 (blue line) RVI time series (

**d**).

**Figure 5.**Performance of the SOGP and MOGP models predictions for VWC data reconstruction based on the S1 & S2 synergy. The green dots represent the latent S2 GP VWC data used to compute the error metrics whereas the red dots correspond to the S2 GP VWC cloud-free observations utilized to train the regression models. The red-shaded area represents the artificially created S2 data gap. SOGP and MOGP predictions performance for the selected winter wheat ROI-1 of the year 2020 (

**a**) and 2021 (

**b**).

**Figure 6.**Cross-correlation matrix of the S1 & dataset among the channels of the trained MOGP models. The elements of the matrix’s diagonal show the auto-correlations of each channel in the dataset. MOSM model for wheat 2020 (

**a**). CSM model for wheat 2020 (

**b**). SM-LMC model for wheat 2020 (

**c**). CONV model for wheat 2020 (

**d**). MOSM model for wheat 2021 (

**e**). CSM model for wheat 2021 (

**f**). SM-LMC model for wheat 2021 (

**g**). CONV model for wheat 2021 (

**h**).

**Figure 7.**CONV posterior predicted mean for a three-channel model. Red dots indicate the original observations for S2 GP VWC (CH-1), S1 RVI orbit 68 (CH-2), and S1 RVI orbit 141 (CH-3) while the green ones are the latent samples. Winter wheat 2020 ROI-1 (

**a**). Winter wheat 2020 ROI-2 (

**b**).

**Figure 8.**Comparison of S2 GP VWC (original) and S1 & S2 MOGP VWC (reconstructed) maps over a selected subset of the study site (red-dashed rectangle in Figure 1) corresponding to the artificially removed dates: 2020/9/23, 2020/10/13, 2020/11/2, 2020/11/17, and 2020/11/27 of the winter wheat 2020 phenological cycle. For each assessment date, the position of the extracted samples on the phenological curve (yellow dot), the S2 GP VWC map, the reconstructed S1 & S2 MOGP VWC map and the scatterplot between the original and reconstructed VWC maps are shown.

**Figure 9.**Comparison of S2 GP VWC (original) and S1 & S2 MOGP VWC (reconstructed) maps over a selected subset of the study site (orange-dashed rectangle in Figure 1) corresponding to the artificially removed dates: 2021/10/3, 2021/10/8, 2021/10/18, 2021/11/2, and 2021/11/17 of the winter wheat 2021 phenological cycle. For each assessment date, the position of the extracted samples on the phenological curve (yellow dot), the S2 GP VWC map, the reconstructed S1 & S2 MOGP VWC map and the scatterplot between the original and reconstructed VWC maps are shown.

**Table 1.**ROI boundaries in geographic coordinates (WGS84), x-pixels quantity (Qty-x), y-pixels quantity (Qty-y), and ROI area selected for training the MOGP models with the S1 & S2 dataset. ROI-1 belongs to the winter wheat 2020 site whereas the ROI-2 to 2021 site.

North | West | South | East | Qty-x | Qty-y | Area [ha] | |
---|---|---|---|---|---|---|---|

ROI-1 | −39.398 | −62.645 | −39.404 | −62.636 | 10 | 12 | 1.2 |

ROI-2 | −39.391 | −62.618 | −39.392 | −62.616 | 12 | 13 | 1.56 |

**Table 2.**Error metrics and training time of the MOGP and SOGP evaluated kernels for the 2020 winter wheat averaged ROI-1.

S2 GP VWC and S1 RVI Orbit 68 | |||||
---|---|---|---|---|---|

MOGP Kernel | MAE [g m${}^{-2}$] | MAPE [%] | RMSE [g m${}^{-2}$] | NRMSE [%] | Time [s] |

MOSM | 828.85 | 56.42 | 927.56 | 44.34 | 10.58 |

CSM | 242.7 | 15.43 | 360.55 | 17.24 | 17.85 |

SM-LMC | 346.16 | 22.56 | 495.49 | 23.69 | 12.68 |

CONV | 250.17 | 19.48 | 313.11 | 14.97 | 21.42 |

SM | 881.4 | 58.91 | 1005.71 | 48.07 | 6.03 |

S2 GP VWC and S1 RVI orbit 141 | |||||

MOSM | 1025.79 | 69.92 | 1116.62 | 53.38 | 9.37 |

CSM | 283.95 | 19.76 | 378.01 | 18.07 | 16.06 |

SM-LMC | 482.25 | 31.99 | 580.76 | 27.76 | 11.49 |

CONV | 255.42 | 25.25 | 419.36 | 20.05 | 19.25 |

SM | 883.69 | 59.05 | 1009.05 | 48.23 | 4.98 |

S2 GP VWC, S1 RVI orbit 68 and S1 RVI orbit 141 | |||||

MOSM | 907.21 | 62.61 | 992.18 | 47.43 | 18.56 |

CSM | 472.31 | 32.75 | 512.23 | 24.49 | 35.18 |

SM-LMC | 463.04 | 30.75 | 546.85 | 26.14 | 22.67 |

CONV | 249.3 | 21.83 | 336.74 | 16.1 | 40.27 |

SM | 881.77 | 58.93 | 1006.25 | 48.1 | 10.29 |

**Table 3.**Error metrics and training time of the MOGP and SOGP evaluated kernels for the 2021 winter wheat averaged ROI-2.

S2 GP VWC and S1 RVI Orbit 68 | |||||
---|---|---|---|---|---|

MOGP Kernel | MAE [g m${}^{-2}$] | MAPE [%] | RMSE [g m${}^{-2}$] | NRMSE [%] | Time [s] |

MOSM | 1606.97 | 91.26 | 1746.35 | 77.76 | 11.59 |

CSM | 1420.06 | 79.84 | 1549.94 | 69.02 | 19.85 |

SM-LMC | 1229.57 | 64.98 | 1362.06 | 60.65 | 13.9 |

CONV | 238.07 | 41 | 328.01 | 14.61 | 22.31 |

SM | 1408.52 | 75.06 | 1550.67 | 69.05 | 7.23 |

S2 GP VWC and S1 RVI orbit 141 | |||||

MOSM | 1606.95 | 91.26 | 1746.33 | 77.76 | 9.96 |

CSM | 864.12 | 54.02 | 928.28 | 41.33 | 18.25 |

SM-LMC | 1262.46 | 69.72 | 1378.87 | 61.4 | 12.24 |

CONV | 274.33 | 43.77 | 352.11 | 15.68 | 21.78 |

SM | 1408.52 | 75.06 | 1550.67 | 69.05 | 6.98 |

S2 GP VWC, S1 RVI orbit 68 and S1 RVI orbit 141 | |||||

MOSM | 1640.51 | 94.6 | 1778.6 | 79.2 | 21 |

CSM | 1446.8 | 82.65 | 1576.08 | 70.18 | 36.08 |

SM-LMC | 1395.58 | 74.98 | 1535.22 | 68.36 | 24.21 |

CONV | 190.44 | 25.69 | 227.12 | 10.11 | 45.02 |

SM | 1408.52 | 75.06 | 1550.67 | 69.05 | 10.2 |

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## Share and Cite

**MDPI and ACS Style**

Caballero, G.; Pezzola, A.; Winschel, C.; Sanchez Angonova, P.; Casella, A.; Orden, L.; Salinero-Delgado, M.; Reyes-Muñoz, P.; Berger, K.; Delegido, J.;
et al. Synergy of Sentinel-1 and Sentinel-2 Time Series for Cloud-Free Vegetation Water Content Mapping with Multi-Output Gaussian Processes. *Remote Sens.* **2023**, *15*, 1822.
https://doi.org/10.3390/rs15071822

**AMA Style**

Caballero G, Pezzola A, Winschel C, Sanchez Angonova P, Casella A, Orden L, Salinero-Delgado M, Reyes-Muñoz P, Berger K, Delegido J,
et al. Synergy of Sentinel-1 and Sentinel-2 Time Series for Cloud-Free Vegetation Water Content Mapping with Multi-Output Gaussian Processes. *Remote Sensing*. 2023; 15(7):1822.
https://doi.org/10.3390/rs15071822

**Chicago/Turabian Style**

Caballero, Gabriel, Alejandro Pezzola, Cristina Winschel, Paolo Sanchez Angonova, Alejandra Casella, Luciano Orden, Matías Salinero-Delgado, Pablo Reyes-Muñoz, Katja Berger, Jesús Delegido,
and et al. 2023. "Synergy of Sentinel-1 and Sentinel-2 Time Series for Cloud-Free Vegetation Water Content Mapping with Multi-Output Gaussian Processes" *Remote Sensing* 15, no. 7: 1822.
https://doi.org/10.3390/rs15071822