dataesr/scientific-paragraphs-categorization huggingface dataset:
A full frame acquisition is considered (320 × 256 pixels) with a frame rate of 60 fps (frame per second). X-ray micro-tomography imaging is performed on the dog-bone specimens using UltraTom Xray micro-CT from Rx-Solutions (Chavanod, France) under a fixed voxel size of 14. 31 µm and a detector resolution of 1920 × 1536 pixels. Up to 1440 radiographic images are needed to build the tomogram of the printed PETG using X-Act software from Rx-Solutions. The processed images represent a volume of 17. 5 × 11. 5 × 5. 1 mm 3 , which is based on a resolution of 1224 × 804 × 354 voxels. The raw images are processed using ImageJ software from NIH to isolate the features of interest and measure the amount and distribution of the defects within the printed PETG. X-ray micro-tomography imaging is performed on the dog-bone specimens using UltraTom X-ray micro-CT from Rx-Solutions (Chavanod, France) under a fixed voxel size of 14.
31 µm and a detector resolution of 1920 × 1536 pixels. Up to 1440 radiographic images are needed to build the tomogram of the printed PETG using X-Act software from Rx-Solutions. The processed images represent a volume of 17. 5 × 11. 5 × 5. 1 mm 3 , which is based on a resolution of 1224 × 804 × 354 voxels. The raw images are processed using ImageJ software from NIH to isolate the features of interest and measure the amount and distribution of the defects within the printed PETG. In order to measure the possible loss in mechanical performance, tensile tensing is performed on dog-bone specimens using the same testing equipment and the same testing conditions introduced earlier. Notched specimens are also considered to measure the fracture toughness of PETG prints. The notch lengths represent from 8% to 12% of the sample width.
The new scheme allows us to impose a spatial and temporal multiscale 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.
The WC components are estimated, but their un-Published by Copernicus Publications on behalf of the European Geosciences Union. certainties remain high. Recommendations are made to increase our use of Earth observations (EO) data, in a coordinated way. EO allow for the monitoring of the WC over long time records, in particular in regions with a low number of in situ stations. But the use of EO data for WC monitoring remains a challenge due to (1) the multiplicity of datasets for the same geophysical parameter, (2) the EO uncertainties (systematic and random errors), and (3) the inconsistency between datasets (for the same component or among the components of the WC). In  Pellet et al. (2017) , EO are used to monitor the WC over the Mediterranean region: it is shown that the WC budget is not closed and that some integration technique should be used to optimize them.
Several approaches have been considered in order to optimize EO datasets at the global scale, for the WC analysis. The features of some "integration" methods presented in the following are synthesized in Table  1. The "Princeton" approach -  Pan and Wood (2006)  presented first a work in which they aimed to close the water balance using EO products. In this work, EO datasets such as precipitation were assimilated into a land surface model (the Variable Infiltration Capacity, VIC) using the combination of a Kalman filter and a closure constraint (see Table  1 ). The resulting "analysis" dataset is not a pure EO product since the VIC model is largely used. In fact, the authors show that the Kalman filtering plus the closure constraint is equivalent to a traditional Kalman filtering, and then to the application of an independent post-filtering that constrains the closure  (De Geeter et al.
, 1997; Simon and Chia, 2002; Aires, 2014). This post-filtering acts by redistributing the budget residuals within each water component based on the uncertainties of each EO source. Several papers have been published based on this approach  (Troy and Wood, 2009; McCabe et al. , 2008; Sahoo et al. , 2011; Troy et al. , 2011; Pan et al. , 2012). For instance, in  Sheffield et al. (2009) , two different precipitation datasets were used over the Mississippi basin. Evapotranspiration was calculated using a revised Penman-Monteith formulation and changes in water storage were estimated from GRACE. For comparison, land surface model outputs, reanalyses data and in situ discharge measurements were used too. The authors concluded that a positive bias of the precipitation datasets leads to an overestimation of the discharge component when the estimation relies on EO data.
Meanwhile, the land surface model shows a high degree of agreement with in situ data. The analysis also highlights the importance of error characterization in the individual WC components. Yilmaz et al. (2011)  relaxed the closure constraint during the assimilation. This is an important feature because tight closure constraint can result in high-frequency oscillations in the resulting combined dataset. A large constraint is used in our approach (see Table  1 ). The NASA-NEWS project -the project aims at a better characterization of the WC using EO data. The first step was to improve the coherency of the satellite retrievals, and then to gather the EO dataset and calibrate them. Some information about the uncertainties of the EO datasets was gathered from the data producers, but this information cannot be straightforwardly used further in the integration process since its evaluation is not homogeneous but productdependent.
The WC budget can be closed using the satellite datasets  (Rodell et al. , 2015). However, this closure is obtained at the global and annual scales only, and residuals are still significant at regional and monthly scales. Rodell et al. (2015)  then use interpolation for a monthly closure. Closing the budget at the global scale was a first step, and closure must now be obtained at finer spatial and temporal scales to monitor more precisely the distribution of the water components as the EO data are designed to do. In  Rodell et al. (2015) , the storage terms (e. g. , groundwater storage) had no significant change when considering annual and global means. This hypothesis was then used at the monthly scale with an optimized interpolation scheme to relax the storage change at the monthly scale.
This approach translates into a quadratic quality criterion where storage and fluxes terms are minimized for annual means, at the global scale (see Table  1 ). One interesting feature in this approach is that both the water  (Rodell et al. , 2015)  and energy  (L'Ecuyer et al. , 2015)  cycles were considered simultaneously in the assimilation, taking into account the physical link between the two cycles through the latent heat flux. The ESA water cycle initiative -in the context of the ESA WATCHFUL project on water budget closure,  Aires (2014)  described several methodologies (Table  1 ) to integrate different hydrological datasets with a budget closure constraint. No surface or atmospheric models were used in these integration methods, making the obtained product interesting for model calibration and validation.
One of the proposed methods, the so-called simple weighting + postfiltering (SW + PF), was applied by  Munier et al. (2014)  over the Mississippi basin, using satellite datasets for precipitation, evapotranspiration and water storage, and gauge observations for river discharge. After applying a budget closure constraint at the basin scale, the integrated components were compared to various in situ observations, showing good performances of the method. One of the main limitations is the dataset availability of the in situ river discharges. Another concern was the downscaling of the basin closure constraint to the pixel scale. A closure correction model (CCM) is a calibration of the EO that was developed based on the integrated product as the reference  (Munier et al. , 2014). It allows correction of each dataset independently to greatly reduce the budget residuals.
In particular, we propose to close the WC budget not only over land, but also over ocean and in the atmosphere. Furthermore, the budget closure constraint is used simultaneously at different spatial (basin and sub-basin) and temporal (monthly and annual) scales. A new spatial interpolation scheme is proposed to downscale the basin-scale closure constraint to the pixel scale. This new framework is applied to the Mediterranean basin to provide an updated WC budget. Section 2 presents the study domain and introduces the datasets used in the following. The integration approaches are described together with the other combination techniques in Sect. 3. Section 4 presents the evaluation metrics for the integrated product: its ability to close the WC and its validation with in situ data at the sub-basin or pixel scale.
Original EO datasets The datasets presented in this section will be used in the integration process. Most of them are satellite products and are commonly used for studying the WC. In order to integrate them, the datasets have been projected onto a common 0. 25 • spatial resolution grid and re-sampled at the monthly scale. Precipitation (P ) -four satellite-based datasets have been selected. Two are gauge-calibrated products: the Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis (TMPA, 3B42 V7) presented in  Huffman et al. (2007)  and the Global Precipitation Climatology Project (GPCP, v2) introduced by  Adler et al. (2003). Two are uncalibrated products:  Joyce et al. (2004)  have unveiled the NOAA CPC Morphing Technique (CMORPH, v1) and  Ashouri et al. (2015)  developed the Precipitation Estimation from Remote Sensing Information using Artificial Neural Network  v1).
In this study, we use a mix of gauged/ungaugedcalibrated precipitation datasets. This choice is motivated by Hydrol. Earth Syst. Sci. ,  23, 2019  www. hydrol-earth-syst-sci. net/23/465/2019/ the goal of preserving the original EO spatial pattern where limited gauge density in some areas may corrupt the signal during the gauge-calibration process (in TMPA and GPCP products). Evapotranspiration (E) -three satellite-based products were chosen to describe evapotranspiration over land: the Global Land Evaporation Amsterdam Model (GLEAM-V3B,  Martens et al. , 2017; Miralles et al. , 2011) ; the MODIS Global Evapotranspiration Project (MOD16,  Mu et al. , 2011) ; and the Numerical Terradynamic Simulation Group product (NSTG,  Zhang et al. , 2010). Two products were chosen for the evaporation over the sea: the Objectively Analyzed air-sea Fluxes for Global Oceans (OAflux,  Sun et al.
, 2003) ; and The Global Energy and Water Cycle Exchanges Project product (GEWEX-Seaflux,  Curry et al. , 2004). Water storage change ( S) -the terrestrial and seawater storage datasets are all derived from the GRACE mission. The estimates of water storage implicitly include the underground water. Four satellite datasets are based on the spherical decomposition of GRACE measurement: the Jet Propulsion Laboratory (JPL, Watkins and Yuan, 2014) product; the Centre for Space Research (CSR,  Bettadpur, 2012)  product; the German Research Centre for Geoscience (GFZ,  Dahle et al. , 2013)  product; and the land-only product from the Groupe de Recherche de Géodésie Spatiale (GRGS,  Biancale et al. , 2005). One extra solution based on the JPL-MASCONS decomposition of GRACE measurement  (Watkins et al.
, 2015)  is also used in this work. In order to compute the monthly change in water storage, we applied a centered derivative smoothing filter: [5/24 3/8 -3/8 -5/24]  (Pellet et al. , 2017). The filter is a slightly smoother version of the filter [1/8 1/4 -1/4 -1/8] presented by  Eicker et al. (2016). It has been compared with several other filters (results not shown). The chosen filter is a good compromise between its smoothing (that suppresses information) and its ability to de-noise the time series. Discharge (R l ) -no satellite-based product is available for the discharge with sufficient temporal extent and only a few rivers are still monitored by public or private networks for the Global Runoff Data Centre (GRDC) that collects discharge data at the global scale. The two discharge datasets used in the following are described in  Pellet et al.
(2017). Groundwater discharge is neglected and considered as an uncertainty source. The CEFREM-V2 dataset of coastal annual discharge into the Mediterranean Sea  (Ludwig et al. , 2009)  is based on in situ observations and some indirect estimates using the Pike formula  (Pike, 1964). In addition, the Laboratoire de Météorologie Dynamique developed the Organising Carbon and Hydrology In Dynamic Ecosystems (OR-CHIDEE,  Polcher et al. , 1998; Ducharne et al. , 2003)  land surface model chosen here to describe the monthly dynamics of the discharge. Two coastal discharges are available from its routing scheme with two different precipitation forcings: GPCC and Climatic Research Unit (CRU) products. We therefore projected the monthly dynamical patterns from ORCHIDEE towards the CEFREM grid. We then scaled the monthly values of ORCHIDEE to match the CE-FREM annual values.
For comparison purposes, CEFREM total freshwater inflow into the Mediterranean (without the Black Sea) is 400 km 3 yr -1 , while ORCHIDEE gives a value of 380 km 3 yr -1. The scaling is then a simple way to take into account the anthropogenic impact that is not modeled at the annual scale and the 0. 5 • resolution. The final product then has the spatial resolution and the annual cumulative value of CEFREM, but with the monthly dynamics of the ORCHIDEE model. Precipitable water change ( W ) -we considered two datasets for the precipitable water: the ESA Globvapor dataset  (Schneider et al. , 2013)  and the 6 h reanalysis product from the ECMWF reanalyses (ERA-I,  Dee et al. , 2011). The ERA-I reanalysis has been considered here because precipitable water, although model-based, is largely constrained by satellite observations.
Validation datasets The ENSEMBLES observation dataset (EOBS) -in order to validate the precipitation, an additional dataset is used: the EOBS dataset developed by EU-FP6 project ENSEMBLES  (Haylock et al. , 2008). It was a regional, well-documented and validated in situ gridded daily dataset at the 0. 25 • spatial resolution, covering the 1950-2007 period. FLUXNET -ground-based FLUXNET data  (Falge et al. , 2017)  were used to validate the evapotranspiration and precipitation over several sites in Europe 1. These flux measurements were based on a eddy covariance technique. All stations available in Europe for the 2004-2009 period have been selected. In order to avoid coastal contamination, the three seaside towers IT-Ro2, IT-Noe and ES-Amo have been suppressed. Total and thermosteric sea-level databases -to validate the sea-level output from the integration technique, we use an independent estimate of the Mediterranean water content.
EO uncertainty assumptions Some studies aimed to characterize the uncertainty of satellite-retrieved products: estimating the relative uncertainty of numerous datasets by the distance to the average product  (Pan et al. , 2012; Zhang et al. , 2016)  or using nonsatellite datasets  (Sahoo et al. , 2011). Nevertheless, such characterizations are generally product-and site-specific, and for some products used in this work, no uncertainty characterization can be found in the literature. For these reasons we considered the same uncertainty as in  Aires (2014). Table  2  summarizes the uncertainty used in the various integration techniques. The uncertainty is associated with a weight which is the ratio of the sum of all the uncertainties in the WC equation and the uncertainty of the considered 1 FLUXNET2015 datasets; https://fluxnet.
fluxdata. org (last access: 24 January 2019). 2 CMEMS http://www. marine. copernicus. eu (last access: 24 January 2019). variable (computed as σ 2 i / i σ 2 and expressed in percentage). Note that uncertainties in Table  2  stand for the merged product and not for a particular satellite dataset (see Eq. 6). The uncertainties are prescribed by the literature, but they are slightly modified from  Munier et al. (2014)  to handle the special case of the Mediterranean region. Munier et al. (2014)  used uncertainty values of 10 mm month -1 for each of the four P products and the three E products (leading to 5 and 5. 8 mm month -1 for the merged P and E estimate), 5 mm month -1 for each of the three S products (leading to 2. 9 mm month -1 for the merged product) and 1 mm month -1 for only one R. The choice of these values was motivated by results of the studies cited in Sect.
1. In order to be closer to  Rodell et al. (2015) , on the one hand, we decide to reduce P uncertainty to 4 mm month -1. This is justified since the de-biasing was done toward the gauge-calibrated TMPA dataset (see  Pellet et al. , 2017, for details). On the other hand, we increased E uncertainty up to 6 mm month -1. The uncertainty of the merged S is estimated to be broadly the same since it is mainly driven by the large pixel resolution of GRACE. Finally, the uncertainty of the discharge R has been increased since the product is partially based on model simulations and the groundwater discharge is not included in the analysis (see Sect. 2). For the atmospheric variables, we consider an uncertainty proportional to the range of variability for the precipitable water change: 1 mm month -1. Following the suggestion from  Seager and Henderson (2013) , the reanalysis moisture divergence uncertainty has been set to 6 mm month -1 due to its large range of variability and timescale.
Simple weighting (SW) A general approach to deal with EO datasets in the analysis of the WC is to choose the best individual dataset for each water component. This is the approach developed, for example, in the GEWEX project. In  Pellet et al. (2017) , an optimal selection (OS) was based on the minimization of the water budget residuals to select the best combination of individual datasets. Using the OS principle facilitates finding datasets coherent to each other and with independent errors  (Rodell et al. , 2015). But this kind of strategy limits the use of several sources of information to reduce the uncertainties. On the other hand, the SW approach benefits from the multiplicity of the observations. EO products, and more generally any estimation of a variable via observations, present two types of errors.
(1) Systematic errors related, for instance, to the absolute calibration of the sensor. These can be represented by a bias and/or a scaling factor. (2) Random errors related to retrieval algorithm uncertainties or to missing or inaccurate auxiliary information (e. g. , cloud mask) or to the sensor itself. These are often characterized by a standard deviation using a Gaussian hypothesis. From a statistical point of view, using the average of several estimates reduces the random errors of the estimation if no bias errors are present in the estimates. The merging process such as in Eq. (  4 ) requires unbiased estimates  (Aires, 2014). The difficulty is that, as for uncertainties (Sect. 2. 4), it is rather difficult to obtain bias estimates from the literature for every dataset used in this approach.
A pragmatic strategy is to set the reference as the mean state for each component. Then, all the sources of information for this component are bias-corrected toward this reference  (Munier and Aires, 2017). A slightly modified version of the bias correction is to choose one reference among the datasets and apply the bias correction. We opted for the modified version and de-biased the EO using the climatological season of the TMPA product as a reference  (Pellet et al. , 2017). Therefore, our SW methodology is first based on a seasonal bias correction to reduce the systematic biases and is then followed by a weighted average of the corrected estimates to reduce the random errors. After the seasonal debiasing, all the precipitation products will have a similar seasonality, but their inter-annual trend or monthly variations will still be different.
In particular, the seasonal de-biasing will not change the trend of the EO products. The SW methodology uses the diversity of datasets to reduce the random errors. Let us consider the p precipitation observations P i associated with Gaussian errors i ∼ N (O, σ i ). σ i is the standard deviation of the ith estimate. The SW precipitation estimate P SW is given by the weighted average: P SW = 1 p -1 p i=1 k =i (σ k ) 2 k (σ k ) 2 P i. ( ) 5 This equation is valid when there is no bias error in the P i s (thanks to the preliminary bias correction) and is optimal when the errors i are statistically independent of each other. This expression is valid for the other water components. The variance of the P SW uncertainties is then given by σ P SW = 1 (p -1) 2 p i=1    k =i (σ k ) 2 k (σ k ) 2    2 σ 2 i.
No cross terms in B lo and are included, meaning that there is no dependency of the first guess and closure errors between the months. This SW + PF technique is able to deal only with time series (average value over the considered sub-basins), not with maps (pixel), since the discharge is not available at this resolution. Therefore, in order to obtain a multi-component dataset that closes the WC budget and has spatial patterns at the pixel level, another technique needs to be used.
2  for precipitation and evaporation, for a particular month. In this analysis, we consider only the Mediterranean sub-basins and their close neighborhood, so a simple spatial interpolation of the closure correction is assumed to be sufficient. The SW + PF method (Fig. 2 , second row) provides a WC budget closure over the six sub-basins, for each month m = 1, • • •, 72 of the 2004-2009 period. The INT method requires a scaling factor to go from the SW to the SW + PF solution at the sub-basin scale. We define β (i) (m) = P (i) PF (m)/P (i) SW (m) (for precipitation here), the ratio between the SW and the SW + PF solution, for each sub-basin i and month m. This ratio can be used to scale the SW dataset towards the SW + PF solution at the basin scale, for a particular month m, in the following way: P (i) INT (m) = β (i) (m) • P (i) SW (m) = P (i) PF (m).
-Interpolation -a region of 200 km on either side of the frontier between two sub-basins i 1 and i 2 is defined, and a smooth interpolation is performed between the two scaling factors β (i 1 ) (m) and β (i 2 ) (m) based on the distance to the frontier. This interpolation of the scaling factors α between two sub-basins can introduce errors (closure residuals can slightly increase), but it will be shown that this effect is limited and that the bottom equations (in parenthesis) in Eqs. (  16 )-(  17 ) stand overall. -Extrapolation -an extrapolation of the α maps is then performed to have a scaling factor α outside of the subbasin domain. This extrapolation is weighted according to the respective distances to the two closest sub-basins. The INT product is the convolution between the SW dataset with the resulting scaling map α that constrains the WC budget closure.
CALibration (CAL) To obtain the INT solution, many EO datasets were combined: multiple datasets for each water component (the SW part), and for the various WC components (the PF part). However, if one of the datasets is missing, the INT solution cannot be estimated and this will result in a gap in the time record, and shorter time series of the integrated database. In  Munier et al. (2014) , a "Closure Correction Model" (CCM) was introduced to correct each dataset independently, based on the results of the SW + PF integration. The CCM is defined as a simple linear transformation with a scaling factor a and an offset b, such that X cal = a • X obs + b. The CCM parameters a and b were calibrated by computing a linear regression between the original observation datasets and the SW + PF components.