Synergy of Sentinel-1 and Sentinel-2 Time Series for Cloud-Free Vegetation Water Content Map** with Multi-Output Gaussian Processes
Abstract
: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 map** 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 Map** the VWC of the Winter Wheat 2020 and 2021
3.3. Spatiotemporal Map** 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 Map** 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
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 | - |
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
Name | Range | Value |
---|---|---|
M[0].CONV.weight | (, ∞) | [0.16140878 0.12014237 0.25099972] |
M[0].CONV.variance | (0.0, ∞) | [[] [] []] |
M[0].CONV.base_variance | (, ∞) | [29.65490441] |
M[1].CONV.weight | (, ∞) | [0.18422568 0.12714211 0.09511325] |
M[1].CONV.variance | (0.0, ∞) | [[0.00208712] [0.00021101] [0.00029573]] |
M[1].CONV.base_variance | (, ∞) | [] |
M[2].CONV.weight | (, ∞) | [0.161608 0.36756376 0.38364755] |
M[2].CONV.variance | (0.0, ∞) | [[] [] []] |
M[2].CONV.base_variance | (, ∞) | [55.15439607] |
M[3].CONV.weight | (, ∞) | [0.45055456 0.09223841 0.01531059] |
M[3].CONV.variance | (0.0, ∞) | [[] [] []] |
M[3].CONV.base_variance | (, ∞) | [54.76679359] |
Gaussian.scale | (, ∞) | [0.07039943 0.05906305 0.03154559] |
Name | Range | Value |
---|---|---|
M[0].CONV.weight | (, ∞) | [0.05051712 0.27439207 0.38695247] |
M[0].CONV.variance | (0.0, ∞) | [[] [] []] |
M[0].CONV.base_variance | (, ∞) | [34.01715996] |
M[1].CONV.weight | (, ∞) | [0.07826687 0.21647057 0.08729357] |
M[1].CONV.variance | (0.0, ∞) | [[] [] []] |
M[1].CONV.base_variance | (, ∞) | [19.31982864] |
M[2].CONV.weight | (, ∞) | [0.5937755 0.30263363 0.22857684] |
M[2].CONV.variance | (0.0, ∞) | [[] [] []] |
M[2].CONV.base_variance | (, ∞) | [49.46172915] |
M[3].CONV.weight | (, ∞) | [0.0563912 0.01698611 0.03144775] |
M[3].CONV.variance | (0.0, ∞) | [[] [] []] |
M[3].CONV.base_variance | (, | [0.08717407] |
Gaussian.scale | (, ∞) | [0.04004209 0.06703326 0.0397214 ] |
References
- Verrelst, J.; Camps-Valls, G.; Muñoz-Marí, J.; Rivera, J.P.; Veroustraete, F.; Clevers, J.G.P.W.; Moreno, J. Optical remote sensing and the retrieval of terrestrial vegetation bio-geophysical properties—A review. ISPRS J. Photogramm. Remote Sens. 2015, 108, 273–290. [Google Scholar] [CrossRef]
- Verrelst, J.; Malenovský, Z.; Van der Tol, C.; Camps-Valls, G.; Gastellu-Etchegorry, J.P.; Lewis, P.; North, P.; Moreno, J. Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy Data: A Review on Retrieval Methods. Surv. Geophys. 2019, 40, 589–629. [Google Scholar] [CrossRef] [Green Version]
- Quemada, C.; Pérez-Escudero, J.M.; Gonzalo, R.; Ederra, I.; Santesteban, L.G.; Torres, N.; Iriarte, J.C. Remote Sensing for Plant Water Content Monitoring: A Review. Remote Sens. 2021, 13, 2088. [Google Scholar] [CrossRef]
- D’Urso, G.; Richter, K.; Calera, A.; Osann, M.A.; Escadafal, R.; Garatuza-Pajan, J.; Hanich, L.; Perdigão, A.; Tapia, J.B.; Vuolo, F. Earth Observation products for operational irrigation management in the context of the PLEIADeS project. Agric. Water Manag. 2010, 98, 271–282. [Google Scholar] [CrossRef]
- Clevers, J.G.P.W.; Kooistra, L.; Schaepman, M.E. Estimating canopy water content using hyperspectral remote sensing data. Int. J. Appl. Earth Obs. Geoinf. 2010, 12, 119–125. [Google Scholar] [CrossRef]
- Wocher, M.; Berger, K.; Danner, M.; Mauser, W.; Hank, T. Physically-based retrieval of canopy equivalent water thickness using hyperspectral data. Remote Sens. 2018, 10, 1924. [Google Scholar] [CrossRef] [Green Version]
- Gerhards, M.; Schlerf, M.; Mallick, K.; Udelhoven, T. Challenges and Future Perspectives of Multi-/Hyperspectral Thermal Infrared Remote Sensing for Crop Water-Stress Detection: A Review. Remote Sens. 2019, 11, 1240. [Google Scholar] [CrossRef] [Green Version]
- Bowman, W.D. The relationship between leaf water status, gas exchange, and spectral reflectance in cotton leaves. Remote Sens. Environ. 1989, 30, 249–255. [Google Scholar] [CrossRef]
- Ustin, S.L.; Riaño, D.; Hunt, E.R. Estimating canopy water content from spectroscopy. Israel J. Plant Sci. 2012, 60, 9–23. [Google Scholar] [CrossRef] [Green Version]
- Berger, M.; Moreno, J.; Johannessen, J.A.; Levelt, P.F.; Hanssen, R.F. ESA’s sentinel missions in support of Earth system science. Remote Sens. Environ. 2012, 120, 84–90. [Google Scholar] [CrossRef]
- Drusch, M.; Del Bello, U.; Carlier, S.; Colin, O.; Fernandez, V.; Gascon, F.; Hoersch, B.; Isola, C.; Laberinti, P.; Martimort, P.; et al. Sentinel-2: ESA’s Optical High-Resolution Mission for GMES Operational Services. Remote. Sens. Environ. 2012, 120, 25–36. [Google Scholar] [CrossRef]
- Amin, E.; Verrelst, J.; Rivera-Caicedo, J.P.; Pipia, L.; Ruiz-Verdú, A.; Moreno, J. Prototy** Sentinel-2 green LAI and brown LAI products for cropland monitoring. Remote Sens. Environ. 2021, 255, 112168. [Google Scholar] [CrossRef]
- Delloye, C.; Weiss, M.; Defourny, P. Retrieval of the canopy chlorophyll content from Sentinel-2 spectral bands to estimate nitrogen uptake in intensive winter wheat crop** systems. Remote Sens. Environ. 2018, 216, 245–261. [Google Scholar] [CrossRef]
- Brede, B.; Verrelst, J.; Gastellu-Etchegorry, J.P.; Clevers, J.G.; Goudzwaard, L.; den Ouden, J.; Verbesselt, J.; Herold, M. Assessment of workflow feature selection on forest LAI prediction with sentinel-2A MSI, landsat 7 ETM+ and Landsat 8 OLI. Remote. Sens. 2020, 12, 915. [Google Scholar] [CrossRef] [Green Version]
- Verrelst, J.; Rivera, J.; Veroustraete, F.; Muñoz Marí, J.; Clevers, J.; Camps-Valls, G.; Moreno, J. Experimental Sentinel-2 LAI estimation using parametric, non-parametric and physical retrieval methods—A comparison. ISPRS J. Photogramm. Remote Sens. 2015, 108, 260–272. [Google Scholar] [CrossRef]
- Estévez, J.; Salinero-Delgado, M.; Berger, K.; Pipia, L.; Rivera-Caicedo, J.P.; Wocher, M.; Reyes-Muñoz, P.; Tagliabue, G.; Boschetti, M.; Verrelst, J. Gaussian processes retrieval of crop traits in Google Earth Engine based on Sentinel-2 top-of-atmosphere data. Remote. Sens. Environ. 2022, 273, 112958. [Google Scholar] [CrossRef]
- Torres, R.; Snoeij, P.; Geudtner, D.; Bibby, D.; Davidson, M.; Attema, E.; Potin, P.; Rommen, B.; Floury, N.; Brown, M.; et al. GMES Sentinel-1 mission. Remote Sens. Environ. 2012, 120, 9–24. [Google Scholar] [CrossRef]
- Ulaby, F.T.; Aslam, A.; Dobson, M.C. Effects of Vegetation Cover on the Radar Sensitivity to Soil Moisture. IEEE Trans. Geosci. Remote Sens. 1982, GE-20, 476–481. [Google Scholar] [CrossRef]
- Karam, M.A.; Fung, A.K.; Lang, R.H.; Chauhan, N.S. A microwave scattering model for layered vegetation. IEEE Trans. Geosci. Remote Sens. 1992, 30, 767–784. [Google Scholar] [CrossRef] [Green Version]
- Bousbih, S.; Zribi, M.; Lili-Chabaane, Z.; Baghdadi, N.; El Hajj, M.; Gao, Q.; Mougenot, B. Potential of Sentinel-1 Radar Data for the Assessment of Soil and Cereal Cover Parameters. Sensors 2017, 17, 2617. [Google Scholar] [CrossRef] [Green Version]
- Rozenstein, O.; Siegal, Z.; Blumberg, D.G.; Adamowski, J. Investigating the backscatter contrast anomaly in synthetic aperture radar (SAR) imagery of the dunes along the Israel–Egypt border. Int. J. Appl. Earth Obs. Geoinf. 2016, 46, 13–21. [Google Scholar] [CrossRef]
- Gao, S.; Niu, Z.; Huang, N.; Hou, X. Estimating the Leaf Area Index, height and biomass of maize using HJ-1 and RADARSAT-2. Int. J. Appl. Earth Obs. Geoinf. 2013, 24, 1–8. [Google Scholar] [CrossRef]
- McNairn, H.; Kross, A.; Lapen, D.; Caves, R.; Shang, J. Early season monitoring of corn and soybeans with TerraSAR-X and RADARSAT-2. Int. J. Appl. Earth Obs. Geoinf. 2014, 28, 252–259. [Google Scholar] [CrossRef]
- Zhang, Y.; Venkatachalam, A.S.; Huston, D.; ** Surface Water Dynamics over Mainland China. Remote Sens. 2021, 13, 1663. [Google Scholar] [CrossRef]
- Caballero, G.; Delegido, J.; Verrelst, J. Estimación del LAI de la vegetación a partir de la sinergia Sentinel 1 -Sentinel 2. ResearchGate 2018. [Google Scholar] [CrossRef]
- Tona, C.; Bua, R. Open Source Data Hub System: Free and open framework to enable cooperation to disseminate Earth Observation data and geo-spatial information. EGU Gen. Assem. Conf. Abstr. 2018, 20, 13038. [Google Scholar]
- Pipia, L.; Amin, E.; Belda, S.; Salinero-Delgado, M.; Verrelst, J. Green LAI Map** and Cloud Gap-Filling Using Gaussian Process Regression in Google Earth Engine. Remote. Sens. 2021, 13, 403. [Google Scholar] [CrossRef]
- Gorelick, N.; Hancher, M.; Dixon, M.; Ilyushchenko, S.; Thau, D.; Moore, R. Google Earth Engine: Planetary-scale geospatial analysis for everyone. Remote Sens. Environ. 2017, 202, 18–27. [Google Scholar] [CrossRef]
- Kumar, L.; Mutanga, O. Google Earth Engine Applications Since Inception: Usage, Trends, and Potential. Remote Sens. 2018, 10, 1509. [Google Scholar] [CrossRef] [Green Version]
- Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; The MIT Press: New York, NY, USA, 2006. [Google Scholar]
- Belda, S.; Pipia, L.; Morcillo-Pallarés, P.; Verrelst, J. Optimizing Gaussian Process Regression for Image Time Series Gap-Filling and Crop Monitoring. Agronomy 2020, 10, 618. [Google Scholar] [CrossRef]
- Bonilla, E.V.; Chai, K.; Williams, C. Multi-task Gaussian Process Prediction. Adv. Neural Inf. Process. Syst. 2007, 20. Available online: https://proceedings.neurips.cc/paper/2007/hash/66368270ffd51418ec58bd793f2d9b1b-Abstract.html (accessed on 21 February 2023).
- Álvarez, M.A.; Rosasco, L.; Lawrence, N.D. Kernels for Vector-Valued Functions: A Review. MAL 2012, 4, 195–266. [Google Scholar] [CrossRef] [Green Version]
- Goovaerts, P. Geostatistics for Natural Resources Evaluation; Oxford University Press: Oxford, UK, 1997. [Google Scholar]
- Lin, Q.; Hu, J.; Zhou, Q.; Cheng, Y.; Hu, Z.; Couckuyt, I.; Dhaene, T. Multi-output Gaussian process prediction for computationally expensive problems with multiple levels of fidelity. Knowl.-Based Syst. 2021, 227, 107151. [Google Scholar] [CrossRef]
- Alvarez, M.A.; Ward, W.; Guarnizo, C. Non-linear process convolutions for multi-output Gaussian processes. In Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, Naha, Okinawa, Japan, 16–18 April 2019; pp. 1969–1977. Available online: https://proceedings.mlr.press/v89/alvarez19a.html (accessed on 21 February 2023).
- de Wolff, T.; Cuevas, A.; Tobar, F. MOGPTK: The Multi-Output Gaussian Process Toolkit. Neurocomputing 2020, 424, 49–53. [Google Scholar] [CrossRef]
- Kim, Y.; Jackson, T.; Bindlish, R.; Lee, H.; Hong, S. Radar Vegetation Index for Estimating the Vegetation Water Content of Rice and Soybean. IEEE Geosci. Remote Sens. Lett. 2012, 9, 564–568. [Google Scholar]
- Rasmussen, C.E. Gaussian Processes in Machine Learning. In Advanced Lectures on Machine Learning; Springer: Berlin, Germany, 2004; pp. 63–71. [Google Scholar] [CrossRef] [Green Version]
- Snee, R.D. Validation of Regression Models: Methods and Examples. Technometrics 1977, 19, 415–428. [Google Scholar] [CrossRef]
- Love, B.C.; Jones, M. Bayesian Learning. In Encyclopedia of the Sciences of Learning; Springer: Boston, MA, USA, 2012; pp. 415–417. [Google Scholar] [CrossRef]
- Wackernagel, H. Multivariate Geostatistics: An Introduction with Applications; Springer: Berlin, Germany, 2013. [Google Scholar]
- Barry, R.P.; Hoef, J.M.V. Blackbox Kriging: Spatial Prediction without Specifying Variogram Models on JSTOR. J. Agric. Biol. Environ. Stat. 1996, 1, 297–322. [Google Scholar] [CrossRef]
- Ver Hoef, J.M.; Barry, R.P. Constructing and fitting models for cokriging and multivariable spatial prediction. J. Stat. Plan. Inference 1998, 69, 275–294. [Google Scholar] [CrossRef]
- Higdon, D. Space and Space-Time Modeling using Process Convolutions. In Quantitative Methods for Current Environmental Issues; Springer: London, UK, 2002; pp. 37–56. [Google Scholar] [CrossRef]
- Casella, A.; Orden, L.; Pezzola, N.A.; Bellaccomo, C.; Winschel, C.I.; Caballero, G.R.; Delegido, J.; Gracia, L.M.N.; Verrelst, J. Analysis of Biophysical Variables in an Onion Crop (Allium cepa L.) with Nitrogen Fertilization by Sentinel-2 Observations. Agronomy 2022, 12, 1884. [Google Scholar] [CrossRef]
- Caballero, G.R.; Platzeck, G.; Pezzola, A.; Casella, A.; Winschel, C.; Silva, S.S.; Ludueña, E.; Pasqualotto, N.; Delegido, J. Assessment of Multi-Date Sentinel-1 Polarizations and GLCM Texture Features Capacity for Onion and Sunflower Classification in an Irrigated Valley: An Object Level Approach. Agronomy 2020, 10, 845. [Google Scholar] [CrossRef]
- Caballero, G.; Pezzola, A.; Winschel, C.; Casella, A.; Sanchez Angonova, P.; Rivera-Caicedo, J.P.; Berger, K.; Verrelst, J.; Delegido, J. Seasonal Map** of Irrigated Winter Wheat Traits in Argentina with a Hybrid Retrieval Workflow Using Sentinel-2 Imagery. Remote Sens. 2022, 14, 4531. [Google Scholar] [CrossRef]
- Berger, K.; Rivera Caicedo, J.P.; Martino, L.; Wocher, M.; Hank, T.; Verrelst, J. A Survey of Active Learning for Quantifying Vegetation Traits from Terrestrial Earth Observation Data. Remote. Sens. 2021, 13, 287. [Google Scholar] [CrossRef]
- Settles, B. Active Learning Literature Survey. University of Wisconsin–Madison, Department of Computer Sciences. 2009. Available online: https://minds.wisconsin.edu/handle/1793/60660 (accessed on 21 February 2023).
- Salinero-Delgado, M.; Estévez, J.; Pipia, L.; Belda, S.; Berger, K.; Paredes Gómez, V.; Verrelst, J. Monitoring Cropland Phenology on Google Earth Engine Using Gaussian Process Regression. Remote Sens. 2021, 14, 146. [Google Scholar] [CrossRef]
- Reyes-Muñoz, P.; Pipia, L.; Salinero-Delgado, M.; Belda, S.; Berger, K.; Estévez, J.; Morata, M.; Rivera-Caicedo, J.P.; Verrelst, J. Quantifying Fundamental Vegetation Traits over Europe Using the Sentinel-3 OLCI Catalogue in Google Earth Engine. Remote Sens. 2022, 14, 1347. [Google Scholar] [CrossRef] [PubMed]
- Verrelst, J.; Rivera-Caicedo, J.P.; Reyes-Muñoz, P.; Morata, M.; Amin, E.; Tagliabue, G.; Panigada, C.; Hank, T.; Berger, K. Map** landscape canopy nitrogen content from space using PRISMA data. ISPRS J. Photogramm. Remote. Sens. 2021, 178, 382–395. [Google Scholar] [CrossRef]
- Gutman, G.; Ignatov, A. The derivation of the green vegetation fraction from NOAA/AVHRR data for use in numerical weather prediction models. Int. J. Remote Sens. 1998, 19, 1533–1543. [Google Scholar] [CrossRef]
- Gitelson, A.; Zur, Y.; Chivkunova, O.; Merzlyak, M. Assessing carotenoid content in plant leaves with reflectance spectroscopy. Photochem. Photobiol. 2002, 75, 272–281. [Google Scholar] [CrossRef]
- Jia, K.; Liang, S.; Gu, X.; Baret, F.; Wei, X.; Wang, X.; Yao, Y.; Yang, L.; Li, Y. Fractional vegetation cover estimation algorithm for Chinese GF-1 wide field view data. Remote Sens. Environ. 2016, 177, 184–191. [Google Scholar] [CrossRef]
- Song, W.; Mu, X.; Ruan, G.; Gao, Z.; Li, L.; Yan, G. Estimating fractional vegetation cover and the vegetation index of bare soil and highly dense vegetation with a physically based method. Int. J. Appl. Earth Obs. Geoinf. 2017, 58, 168–176. [Google Scholar] [CrossRef]
- García-Haro, F.J.; Campos-Taberner, M.; Munoz-Mari, J.; Laparra, V.; Camacho, F.; Sanchez-Zapero, J.; Camps-Valls, G. Derivation of global vegetation biophysical parameters from EUMETSAT Polar System. ISPRS J. Photogramm. Remote. Sens. 2018, 139, 57–74. [Google Scholar] [CrossRef]
- Lee, J.S.; Jurkevich, L.; Dewaele, P.; Wambacq, P.; Oosterlinck, A. Speckle filtering of synthetic aperture radar images: A review. Remote. Sens. Rev. 1994, 8, 313–340. [Google Scholar] [CrossRef]
- Lee, J.S. Refined filtering of image noise using local statistics. Comput. Graph. Image Process. 1981, 15, 380–389. [Google Scholar] [CrossRef]
- Pan, Z.; Hu, Y.; Cao, B. Construction of smooth daily remote sensing time series data: A higher spatiotemporal resolution perspective. Open Geospat. Data Softw. Stand. 2017, 2, 1–11. [Google Scholar] [CrossRef] [Green Version]
- Savitzky, A.; Golay, M.J.E. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal. Chem. 1964, 36, 1627–1639. [Google Scholar] [CrossRef]
- Neeff, T.; Dutra, L.V.; Dos Santos, J.R.; Freitas, C.C.; Araujo, L.S. Power spectrum analysis of SAR data for spatial forest characterization in Amazonia. Int. J. Remote Sens. 2005, 26, 2851–2864. [Google Scholar] [CrossRef]
- Parra, G.; Tobar, F. Spectral Mixture Kernels for Multi-Output Gaussian Processes. Adv. Neural Inf. Process. Syst. 2017, 30. [Google Scholar] [CrossRef]
- Ulrich, K.R.; Carlson, D.E.; Dzirasa, K.; Carin, L. GP Kernels for Cross-Spectrum Analysis. Adv. Neural Inf. Process. Syst. 2015, 28. Available online: https://proceedings.neurips.cc/paper/2015/hash/285ab9448d2751ee57ece7f762c39095-Abstract.html (accessed on 21 February 2023).
- Alvarez, M.; Lawrence, N. Sparse Convolved Gaussian Processes for Multi-output Regression. Adv. Neural Inf. Process. Syst. 2008, 21. Available online: https://proceedings.neurips.cc/paper/2008/hash/149e9677a5989fd342ae44213df68868-Abstract.html (accessed on 21 February 2023).
- van der Wilk, M.; Rasmussen, C.E.; Hensman, J. Convolutional Gaussian Processes. 2017. Available online: https://doi.org/10.48550/ARXIV.1709.01894 (accessed on 21 February 2023).
- Kingma, D.P.; Ba, J. Adam: A Method for Stochastic Optimization. ar**v 2014. [Google Scholar] [CrossRef]
- Tobar, F. Bayesian Nonparametric Spectral Estimation. Adv. Neural Inf. Process. Syst. 2018, 31. Available online: https://proceedings.neurips.cc/paper/2018/hash/abd1c782880cc59759f4112fda0b8f98-Abstract.html (accessed on 21 February 2023).
- Verrelst, J.; Rivera, J.; Moreno, J.; Camps-Valls, G. Gaussian processes uncertainty estimates in experimental Sentinel-2 LAI and leaf chlorophyll content retrieval. ISPRS J. Photogramm. Remote Sens. 2013, 86, 157–167. [Google Scholar] [CrossRef]
- Paek, S.W.; Balasubramanian, S.; Kim, S.; de Weck, O. Small-Satellite Synthetic Aperture Radar for Continuous Global Biospheric Monitoring: A Review. Remote Sens. 2020, 12, 2546. [Google Scholar] [CrossRef]
- Titsias, M.K. Variational Model Selection for Sparse Gaussian Process Regression; University of Manchester: Manchester, UK, 2008. [Google Scholar]
- Kiefer, J.; Wolfowitz, J. Stochastic Estimation of the Maximum of a Regression Function. Ann. Math. Stat. 1952, 23, 462–466. [Google Scholar] [CrossRef]
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 |
S2 GP VWC and S1 RVI Orbit 68 | |||||
---|---|---|---|---|---|
MOGP Kernel | MAE [g m] | MAPE [%] | RMSE [g m] | 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 |
S2 GP VWC and S1 RVI Orbit 68 | |||||
---|---|---|---|---|---|
MOGP Kernel | MAE [g m] | MAPE [%] | RMSE [g m] | 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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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 Map** with Multi-Output Gaussian Processes. Remote Sens. 2023, 15, 1822. https://doi.org/10.3390/rs15071822
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 Map** with Multi-Output Gaussian Processes. Remote Sensing. 2023; 15(7):1822. https://doi.org/10.3390/rs15071822
Chicago/Turabian StyleCaballero, 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 Map** with Multi-Output Gaussian Processes" Remote Sensing 15, no. 7: 1822. https://doi.org/10.3390/rs15071822