Abstract. The Mediterranean region is one of the climate hotspots where the climate change impacts are both pronounced and documented. The HyMeX (Hydrometeorological Mediterranean eXperiment) aims to improve our understanding of the water cycle from the meteorological to climate scales. However, monitoring the water cycle with Earth observations (EO) is still a challenge: EO products are multiple, and their utility is degraded by large uncertainties and incoherences among the products. Over the Mediterranean region, these difficulties are exacerbated by the coastal/mountainous regions and the small size of the hydrological basins. Therefore, merging/integration techniques have been developed to reduce these issues. We introduce here an improved methodology that closes not only the terrestrial but also the atmospheric and ocean budgets. The new scheme allows us to impose a spatial and temporal multi-scale budget closure constraint. A new approach is also proposed to downscale the results from the basin to pixel scales (at the resolution of 0.25∘). The provided Mediterranean WC budget is, for the first time, based mostly on observations such as the GRACE water storage or the netflow at the Gibraltar Strait. The integrated dataset is in better agreement with in situ measurements, and we are now able to estimate the Bosporus Strait annual mean netflow.

As the largest river basin on Earth, the Amazon is of major importance to the world's climate and water resources. Over the past decades, advances in satellite‐based remote sensing (RS) have brought our understanding of its terrestrial water cycle and the associated hydrological processes to a new era. Here, we review major studies and the various techniques using satellite RS in the Amazon. We show how RS played a major role in supporting new research and key findings regarding the Amazon water cycle, and how the region became a laboratory for groundbreaking investigations of new satellite retrievals and analyses. At the basin‐scale, the understanding of several hydrological processes was only possible with the advent of RS observations, such as the characterization of "rainfall hotspots" in the Andes‐Amazon transition, evapotranspiration rates, and variations of surface waters and groundwater storage. These results strongly contribute to the recent advances of hydrological models and to our new understanding of the Amazon water budget and aquatic environments. In the context of upcoming hydrology‐oriented satellite missions, which will offer the opportunity for new synergies and new observations with finer space‐time resolution, this review aims to guide future research agenda toward integrated monitoring and understanding of the Amazon water from space. Integrated multidisciplinary studies, fostered by international collaborations, set up future directions to tackle the great challenges the Amazon is currently facing, from climate change to increased anthropogenic pressure.

Abstract. Integration techniques are used to combine Earth Observation (EO) datasets to study the Water Cycle (WC). By merging several datasets, they reduce uncertainty and introduce coherency among them. Several EO integration methods are presented and compared: The Optimal Selection (OS) simply choses the best individual datasets. Simple Weighting (SW) is a weighted sum of the datasets to reduce uncertainties. Three other techniques introduce a closure-constraint on the WC budget:(1) The SW plus Post-Filtering (PF) is very efficient but it is applied at the basin-scale only, and lacks in spatial information. 5(2) By using a spatial interpolation scheme, the INTegration (INT) solution allows obtaining a pixel-scale database, but only for the common period of the all the water components. (3) A simple CALibration (CAL) of the EO datasets is therefore introduced to reproduce the INT results over the longer temporal extent of the EO datasets, but its closure constraint is relaxed.Results are presented over the Mediterranean region, one of the more complex environnements and a hot-spot for climate change. We extended previous techniques to close simultaneously the terrestrial, oceanic and atmospheric WC budgets. We also 10 introduce temporal and spatial multi-scaling constraints. The evaluation is performed for precipitation and evapotranspiration: in addition to better close the WC budget, the integrated database is also closer to in situ measurements. The resulting integrated database provides new estimates for the WC components: stock and flux annual-means are re-evaluated, and we now estimate the Bosporus net-flow mean value at 129 mm.yr

With the increasing volume of satellite observations, dimension reduction techniques are more and more important for storage or transmission. Furthermore, they are essential for inversion schemes that, in practice, cannot handle the huge amount of information provided by modern instruments for near‐real‐time inversion. In this article, we compare the theoretical advantages and limitations of the two general strategies: compression (i.e. feature extraction) and channel selection (i.e. feature selection). The statistical ‘input variable selection’ framework is adopted to revisit the basis of these remote‐sensing techniques. The flexibility of these methods to specific applications is demonstrated. Special emphasis is put on the optimization of observation dimension reduction for the simultaneous retrieval of several variables (e.g. temperature and humidity). In addition to considering the signal‐to‐noise ratio for the variable to retrieve, we propose to account for contamination by other unknown variables. We also introduce a new approach named ‘bottleneck channels’ (BC), which combines compression and channel selection techniques and can therefore benefit from the advantages of both strategies. Various configurations of the BC approach can be considered: strict, linearly or nonlinearly projected, each with advantages and drawbacks. In the companion article, experiments will be conducted on microwave data to illustrate the practical advantages of each approach. BC are able to compress and suppress noise in a similar way to principal component analysis (PCA) and they can be interpreted as channels, as in channel selection.