The frequent coverage and the systematic observations of S1 & S2 have opened the door to data-fusion-based RS applications for crop monitoring, land surface change detection and land cover mapping [26; 27]. Several research efforts took advantage of the high radiometric quality of S1 in synergy with the improved optical sensor of S2 [28; 29; 30; 31]. However, processing S2 optical and S1 radar time series has always been tedious, particularly when a substantial number of preprocessing steps must be implemented for the whole dataset. Downloading S1 and S2 images from the Copernicus data hub [32] usually requires a lot of time and storage space. In this regard, seeking to achieve fully automated preprocessing of EO data streams, migration to cloud-computing platforms offers a solution [33]. Recently, the Google Earth Engine (GEE) platform emerged as a promising, free-access, high-performance computing platform that enables cloud-based processing of petabytes of S1 and S2 satellite data, among others [34]. The GEE platform not only provides the powerful computational capability and access to the Copernicus catalog, but also allows for the integration of machine learning (ML) algorithms [33; 35]. Regarding the creation of continuous, cloud-free S1 & S2 time series data streams, ML techniques can be implemented to explicitly learn and exploit the joint relationships of both data streams. Gaussian processes (GP), a nonparametric Bayesian ML regression algorithm, has had a notable impact on the remote sensing community following the pioneering publication by [PERSON] and [PERSON] [36]. GP has been openly and successfully applied for the learning task of analyzing the auto-correlations of single-EO-dataset-channel models [33; 37]. GP regression has advanced considerably in recent years, extending the GP concept to multiple-channel models. For computing non-trivial dependencies between multiple and related model outputs, multi-task Gaussian process prediction [38] widely known as multi-output Gaussian process (MOGP) offers a set of kernel models to learn such correlations [39]. The concept of multi-output learning emerged from the field of geostatistics [40]. The MOGP modeling approach can capture valuable information across correlated outputs to provide more accurate predictions than directly modeling these outputs independently [41]. In the context of EO data streams, developing models that exploit the dependencies between optical and radar sensors results particularly convenient when the optical data are affected by cloudy sky conditions leading to gaps in the data stream. Thus, SAR imagery can be used to complement optical sources [29; 33; 42]. A differentiating attribute of MOGP is the ability of the models to perform multiple channel prediction tasks in the presence of missing input data [43]. This makes MOGP particularly appealing for the fusion of S1 and S2 data streams. To date, the usage of MOGP to fuse S1 and S2 data streams has only been investigated by [PERSON] et al. [29] with the purpose of producing continuous LAI time series. Radar-optical data fusion for crop monitoring purposes is a novel field of research that warrants greater attention. For instance, the synergistic usage of S1 & S2 data streams for crop monitoring in a cloud-computing platform by exploiting the cross-correlations of the MOGP model's output channels have yet to be fully explored. Therefore, this study aims to fulfill the following three main objectives: (1) to train several MOGP models with S1 radar vegetation index (RVI) [44] & S2 GP VWC time series data over two irrigated winter wheat paddocks and select the best model for posterior data fusing; (2) to examine if the best-performing MOGP model effectively retrieves crop traits under simulated cloudy conditions; (3) to map the S1 & S2 MOGP-reconstructed VWC values for the gap-filled intervals at the pixel level and evaluate the MOGP's capacity for reconstructing the complete phenological cycle of winter wheat in the absence of optical data.