## 5 Conclusions  
In this paper, we investigated the hydrological conditions over global arid and semi-arid regions, including areas of BSh (Hot semi-arid climate), BSk (Cold semi-arid climate), BWh (Hot desert climate) and BWk (Cold desert climate), through synergistic approaches of remote sensing and modelling. The time series analysis during the last decade (2010-2019) of multiple hydrological variables (ET, SSM and precipitation) and vegetation indices (FPAR, LAI and NDVI) highlighted precipitation pulses that showed less impact on the vegetation indices compared to ET and SSM in some arid regions. Moreover, the trends of ET, SSM and precipitation, as well as land cover changes, that were demonstrated over the same period, emphasized drier trends in the south of Africa and the east of Australia and wetter trends in Mesopotamia and North America. Finally, the comparison of widely-used FLDAS and GLDAS models showed a general consistency, while a strong discrepancy was observed in the downstream Nile Basin, also demonstrating the fact that both LDAS models overestimate SSM and underestimate ET while model outputs of hot areas have better consistency with satellite products than cold areas.  
This work further confirmed the scientific fact of decoupling between ecosystem function and observed optical characteristics (e.g., greenness indicated by vegetation indices), which calls for novel techniques and applications of remote sensing in the arid and semi-arid regions. Some areas (e.g., Mesopotamia, Eastern Africa, Australia and Argentina) experienced intense land cover changes along with noted water storage variations, indicating complex hydrological processes which need further investigations. Our data-driven modelling as a post-processing approach effectively improved the process-based models' performance and recommended that both process-based and satellite-based hydrological products have a higher potential to be improved for the arid and semi-arid regions. However, considering complex hydrological processes and predictions uncertainties, new practices of delivering data-driven probabilistic modelling are suggested for future studies. In addition, the study was fully deployed on the open-source cloud computing and analytical platforms (Google Earth Engine and BigML), which posed their great potential in other global-scale environmental studies.  
The following are available online at [[http://www.mdpi.com/2072-4292/12/23/3973/s1](http://www.mdpi.com/2072-4292/12/23/3973/s1)]([http://www.mdpi.com/2072-4292/12/23/3973/s1](http://www.mdpi.com/2072-4292/12/23/3973/s1)), Table S1: Selected Variables for the Data-driven Machine Learning Modelling, Table S2: The metrics of selected models for SSM and ET.  
Conceptualization, H.E.-A. and W.L.; data analysis, W.L. and R.T.; funding acquisition, H.E.-A.; methodology, H.E.-A., W.L. and R.T.; validation, W.L. and R.T.; writing--original draft, H.E.-A., W.L.; writing--review and editing, H.E.-A., W.L., R.T., T.P., S.P.T., K.P.M. and D.S. All authors have read and agreed to the published version of the manuscript.  
[PERSON] would like to acknowledge the support from the Earth Systems Science and Data Solutions (EssDs) Lab and the Computational and Data Sciences Graduate Program, Schmid College of Science and Technology, Chapman University.  
The first author acknowledge the support from the Earth Systems Science and Data Solutions (EssDs) Lab and Schmid College of Science and Technology, Chapman University.  
The authors declare no conflict of interest.