dataesr/scientific-paragraphs-categorization huggingface dataset:
10 ). These estimates differ in many respects: they use different maps of surface f CO 2 , atmospheric CO 2 concentrations, wind products, and gas exchange formulations as specified in Table  A3. We refer to them as f CO 2 -based flux estimates. The measurements underlying the surface f CO 2 maps are from the Surface Ocean CO 2 Atlas version 2022 (SOCATv2022;  Bakker et al. , 2022) , which is an update of version 3  (Bakker et al. , 2016)  and contains quality-controlled data through 2021 (see data attribution Table  A5 ). Each of the estimates uses a different method to then map the SOCAT v2022 data to the global ocean. The methods include a data-driven diagnostic method combined with a multi-linear regression approach to extend back to 1957  (Rödenbeck et al. , 2022;  referred to here as Jena-MLS), three neural network models  (Landschützer et al.
Presentation of the database The database used in the present study is composed of two laboratory made soil surfaces, which were subjected to several rainfalls in order to get a variety of roughness conditions. As shown in Table  1 , a set of five successive rainfalls of two intensities and different durations was carried out. We note S 2 of these soil surface trays. The images on the middle represent the two soil surfaces S ð1Þ 1 and S ð1Þ 2 after the first rain and the images on the bottom line represent them after the last rain. Figure  2  shows a 3D view of one of these surfaces. To each pair of coordinates ðx; yÞ corresponds a single and unique elevation z. Consequently, these surfaces Sðx; yÞ ¼ zðx; yÞ are 2. 5D DEMs  (Burrough, McDonnel, & Lloyd, 1998). To make the soil surfaces, two trays of 500 Â 500 mm with a depth of 100 mm were used.
(  13 ) it can be seen that for an ellipse, rðqÞ ¼ 2 r 2 is a periodic function, of period p, the Fourier series expansion of which being: p;1 2 r v u u u t (17c) ðkÞ The determination of the tilt angle and the two correlation lengths is done in three steps. Firstly, the level curve of C ðkÞ p ðx; yÞ for the value V ðkÞ p =e is obtained by using the MATLAB ® function "contour". The contour plot is made on M ðkÞ p points whose Cartesian coordinates ðx m ; y m Þ are known. In the second step, the polar coordinates ðr m ; q m Þ of each point are defined and the periodic function rðqÞ given by Eq. (  15 ) is obtained and the Fourier coefficients a Let us ðxðtÞ;yðtÞÞ be the Cartesian coordinates of the points on the t-contour. For t ¼ 1, we obtain the ellipse given the correlation lengths. Consequently, we find that xðt¼ 1Þ ¼ l The slope of this linear regression gives the roughness exponent estimation and in theory, the y-intercept a must be equal to zero.
However, these estimates of uncertainty should be taken with caution, as recent studies  (Lagacherie et al. , 2020; Helfenstein et al. , 2021)  showed significant differences between overall uncertainties calculated from the modelling procedure and those calculated from estimated independent punctual datasets. Moreover, end-users usually focus on study areas much smaller than the spatial extents of DSM products. Gomez and Coulouma (2018)  observed large differences in uncertainty among spatial extents for soil properties predicted by spectrometry. It is therefore also expected that reduction in spatial extent strongly influences uncertainties in soil property predictions of DSM products. To estimate uncertainties, DSM model outputs are usually used. An alternative method is to perform evaluation using an independent validation dataset  (Brus et al.
Data were downloaded from https://soilgrids. org/, powered by ISRIC (last access: 12/20/2021). GSM_Fr products  (Mulder et al. , 2016)  were calculated at 90 m spatial resolution and for the six standard depth intervals. Input data were punctual field observations (23,822-57,915, depending on the soil property for the 5-15 cm depth interval) and 20 covariates for prevailing climate regimes and meteorological data, vegetation, topography, geology, soils and land management. The 90 % confidence intervals were estimated to provide uncertainties. GSM_LR products were calculated at 90 m resolution for the six standard depth intervals from a set of 2,024 legacy soil profiles associated with a set of 16 covariates freely available (at least at the national level), using a quantile random forest algorithm  (Vaysse and Lagacherie, 2017)  that also provided local uncertainty estimates.
Reference data 2. 3. 2. 1. Soil maps. The reference soil maps compared to DSM products were selected according to two criteria: i) built by experienced local soil surveyors who followed conventional pedological approaches  (Jamagne et al. , 1967)  and ii) available in a digital format. For each of the three regions studied, three soil maps were selected to explore three scales -1:250,000, 1:50,000 to 1:100,000 and 1:25,000 -focusing on study areas of decreasing size (Fig. 2 , Table  2 ). Regional (1:250,000) soil maps covered the three regions entirely. * depending on the soil property predicted. They followed specifications of the French National Soil Survey  (INRAE InfoSol, 2014) , and their soil databases were built following the national format DoneSol  (INRAE InfoSol, 2021) , which ensured that the databases for each French region had the same structure.
Soil information is spatially represented in polygons with crisp boundaries. SMUs group together one or usually several polygons and are defined as areas with homogeneous soil-forming factors, such as morphology, geology and climate. SMUs are complex, as each contains known proportions of several STUs, which are described in the semantical DoneSol database by a set of soil layers that represent vertical variation in the soil  (Laroche et al. , 2014). Intermediate-scale soil maps covered part of each region (Richer-de-Forges et al. , 2014). In Languedoc-Roussillon, the 1:100,000 pedological map of Lodève  (Bonfils, 1993)  covers 8 % of the region. In Alsace, the 1:50,000 soil map of the "Rhin-Vignoble-Grand Ballon" territory (Sauter J. , pers. comm. ) covers 7 % of the region. In Brittany, the 1:100,000 soil map of Janzé  (Rivière et al.
Punctual measurements. Punctual measurements of soil properties of interest for this study were available for the three regions. For Languedoc-Roussillon and Alsace, legacy datasets of punctual measurements (1,696 and 346, respectively), collected in the past few decades to improve pedological knowledge and map soil at multiple scales, were used. For Brittany, an independent evaluation dataset of 135 punctual measurements sampled according to a probabilistic sampling procedure  (Ellili Bargaoui et al. , 2019)  was used.
Data processing To make comparison of digital soil maps and reference data feasible, the following pre-processing procedures were applied to the datasets, if necessary: • Data cleaning to discard cells with no value in gridded maps • Standardizing units for the three soil properties in all databases • Assigning a unique Coordinate Reference System (CRS) to all vectors and rasters: WGS84 -EPSG (European Petroleum Survey Group) code: 4326 • Adjusting the spatial extents of soil maps using regional masks to ensure compatible extents To process data to compare DSM products to the reference datasets, the first step (pre-processing) consisted of extracting information about soil properties from the punctual and polygonal databases (Fig. 3 ). Soil profiles were vertically divided into pedological horizons, each of which had values for clay content, pH and SOC content.
As regional DSM products could not be compared to the punctual soil measurements that had been used as inputs to develop the products, different strategies were applied. For GSM_LR, results of crossvalidation from a previous evaluation  (Vaysse and Lagacherie, 2017)  were considered. For GSM_Br, we used the independent set of 135 punctual measurements. Areal-support comparisons consisted of comparing, for each map polygon, zonal means of a soil property derived from the DSM products to the estimated value of the property given by the map following the procedure described previously. For each region, areal-support comparisons were performed for the three soil-map scales considered. Data pre-processing and processing were performed using QGIS 3. 12 software (QGIS Development Team, 2018), along with the Python (Van Rossum and Drake, 2009) and R 3.
Statistical indicators for quantitative comparison For quantitative comparison, the similarity between datasets was assessed using several statistical indicators: the slope (SL), intercept and correlation coefficient of the linear regression between observed and predicted soil properties. In addition, the mean error (ME, Eq. (  1 )) was used to identify potential bias, and the root mean squared error (RMSE, Eq. (  2 )) measured the difference between values of two datasets. Two indicators of the overall quality of adjustment were calculated: the mean squared error skill score (SS mse , Eq. (  3 )), which represents the amount of variance explained by the prediction  (Wilks, 2011; Nussbaum et al. , 2018) , and Lin's concordance correlation coefficient  (LCCC, Eq, 4). ME = 1 n ∑ n i=1 (ŷ i -y i ) (1) RMSE = ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ 1 n ∑ n i=1 (ŷ i -y i ) 2 √ (2) SS mse = 1 - ∑ n i=1 (y i -ŷi ) 2 ∑ n i=1 ( y i -1 n ∑ n i=1 y i ) 2 (3) LCCC = 2ρσ ŷ σy σ 2 ŷ + σ 2 y + (ŷ -y) 2 (4) where n is the number of soil samples, y i the observed values, ŷi the predicted values, ŷ and y the means of the predicted and observed values, respectively, σ 2 their variance and ρ the correlation between predicted and observed values.
Drivers of GSM product performances Despite sharing a common methodological framework, the performances of DSM products differed greatly across properties, regions, scales of development and scales of application. Some possible causes of these differences include the following: • Targeted soil property: pH was generally predicted better than clay or SOC contents. This result agreed with the global and national evaluations provided by the authors of the DSM products (Table  6 ). This is also consistent with the results of a review of 244 broad-scale DSM studies published between 2003 and 2021, where pH was found to be the best predicted property among the 12 mandatory soil properties for GlobalSoilMap  (Chen et al. , 2022). Indeed, the spatial variations in pH seems to be influenced more by drivers acting over long distances, such as lithology, which are more likely to be captured by calibration datasets of low spatial density, whereas spatial distributions of clay and SOC contents seem to be influenced more by drivers acting over short distances, such as local topography and agricultural practices.
However, pH may have been predicted relatively poorly in Brittany because it usually varies little there, as most of its soils are acidic due to the bedrock, except on the northern coast, due to the presence of decarbonated Aeolian silts, which are parent materials of local marine origin, and the influence of amendments, particularly on vegetable field crops sensitive to acidity. Therefore, our results for Brittany should not be interpreted as revealing poor predictions. • Spatial density of the calibration dataset: The model for SoilGrids 2. 0 was calibrated with a less dense dataset (1 profile/600 km 2 globally and 1 profile /134 km 2 for mainland France) than that for GSM France (1 profile/15-19 km 2 ). Many recent studies have demonstrated the large impact of this spatial density on the performances of DSM models  (Somarathna et al.
, 2017; Wadoux et al. , 2019; Lagacherie et al. , 2020; Loiseau et al. , 2021). This lower density of calibration datasets may partly explain the lower performance. Thus, collecting additional soil data to densify calibration datasets is a key issue for improving DSM applications, especially if the goal is to capture local soil variations. • The scale of development of the DSM product: Calibrating models over areas larger than those at which they are subsequently analyzed generates distortions in the modelled soil-landscape rules, which become visible when comparing predicted soil patterns. For example, in pH maps of Alsace, local soil spatial structures that result from soil-landscape relationships that are specific to a mapped area, such as the presence of a narrow zone of a basic fluviosol in the Rhine Valley (Fig.
6 , blue ellipse), were not predicted by DSM products calibrated with datasets that cover larger extents. This occurs more frequently as the extent increases (global instead of national), as shown by a zone of neutral pH, which GlobalSoilMap France predicts well, but SoilGrids 2. 0 does not (Fig. 6 , black ellipse). The opposite can also occur; for example, SoilGrids 2. 0 and GlobalSoilMap France clearly delineated an acidic area that does not correspond to any soil pattern recognised at the regional level (Fig. 6 , red ellipse). This area, which corresponds to a forest, strongly influenced predictions of SoilGrids 2. 0 and GlobalSoilMap France. A soil-landscape relationship that was calibrated from soil profiles located outside of the area could have inferred a false soil pattern. Global models may not necessarily consider local variations because the variety of processes and soil-covariate relationships is too wide to model local features.
Conclusions This study evaluated DSM products obtained at global, national and regional levels over three French regions, at regional, intermediate and detailed scales. Topsoil values of pH in water, clay content and SOC content were evaluated for both point and SMU supports. The main lessons from these multiscale evaluations are the following: • Users should evaluate DSM products themselves as soon as they focus on a study area much smaller than the initial area covered by the DSM products. • Comparing DSM products to existing soil maps could greatly increase the potential of DSM product evaluations for small areas with too few soil measurements and for the consideration of areal-support uses of DSM products. • Users should select a DSM product whose coverage by the calibration soil dataset and covariates best match those of their target study area.
Acknowledgements The authors thank the  CNES (French National Centre for Space Studies)  for funding the  Centre of Scientific Expertise (CES) Théia  " Digital Soil Mapping ", to which the authors belong. They also acknowledge the  Regional Council of Brittany  for financing the project " Sols de Bretagne ", which contributed financially and technically to the study. A. R. d. F. , P. L. and D. A. are members of the research consortium GLADSOILMAP, supported by the  STUDIUM Loire Valley Institute  for advanced research studies.
Experiment B The aim of this experiment was to obtain instantaneous values of the density at each location in the tank (averaged in the direction normal to the camera view) during an experimental run. We performed measurements using the dye attenuation technique with methylene blue as the light absorption agent. The flow was recorded using a JAI CVM4+MCL 1. 3 megapixel camera equipped with a lens and a red filter. The data acquisition was performed by means of DigiFlow (see http://www. dalzielresearch. com/). The calibration was carried out using concentrations of methylene blue that varied between 0 and 1. 7 × 10 -1 ppm which was the range used for the subsequent experiments. The calibration data are provided in Appendix A. The recorded images from the camera were converted into instantaneous density maps inside the tank by means of the technique described in detail in Appendix A.
C. 1. Maximum surface velocity V max The experiments to estimate the maximum surface velocity V max of the horizontal outflow were conducted by running the bubble curtain in the channel with ρ = 0 for several values of q air and H. The velocity of the current close to the surface was observed by injecting the blue dye at the source of the bubble curtain with a syringe (see figure  20 ). We then measured the propagating horizontal velocity of the blue dye by performing the analysis of the recorded side-view videos. The results for measured V max are presented in figure  21  as a function of the scaling (g q air ) 1/3. The dispersion in the experimental data is very large and it is difficult to obtain any accurate quantitative correlations based on the crude blue dye visualisation that we used.
Acknowledgements. D. F. acknowledges support from  Fitzwilliam College and Corpus Christi College in Cambridge, UK. We would like to thank  D. Page-Croft  for the technical support with our experimental apparatus. We are grateful to three anonymous referees whose comments and suggestions have helped us to improve the manuscript. The first and the second author contributed in equal amounts to the completion of the manuscript. Funding. P. F. L. acknowledges funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation , grant no. 742480  ' Stratified Turbulence And Mixing Processes ' (STAMP). Declaration of interests. The authors report no conflict of interest.
Extending this relationship to the regional scale suggests that metacommunities with higher γ-diversity could be more compositionally variable, but empirical studies have found the lowest compositional variability at intermediate γ-diversity  (Chalcraft 2013). Compositional DSRs at both local and regional spatial scales merit additional study across ecosystems and taxonomic groups to assess their generality and transferability. Using a large compilation of long-term, spatially replicated metacommunity time series data (n=22), collected across a range of ecosystem types (e. g. , deserts, forests, coral reefs) and taxonomic groups (e. g. , birds, fish, plants, algae), we quantified diversity-stability relationships at multiple spatial scales. Specifically, we examined community variability (both aggregate and compositional) at both local (observational unit, such as a sampling plot) and regional (study scale, such as an LTER site) spatial scales, alongside changes in diversity, to address three questions.
Data acquisition, processing, archiving We acquired 22 data sets spanning a wide range of ecosystems and organismal groups represented by the Long-Term Ecological Research (LTER) Network, with data obtained from the Environmental Data Initiative (EDI) portal (https://portal. edirepository. org). We used time series of species assemblage data containing abundance information using the ecocomDP model  (O'Brien et al. 2021). We kept data sets with at least five spatial and at least five temporal replicates to ensure sufficient spatial and temporal resolution. We then filtered and aggregated each data set to ensure homogeneous sampling, consistent taxonomic identification, and to make sure that each data set represented a collection of potentially interacting species (i. e. , our data sets focus on competitive or "horizontal" metacommunities).
To ensure homogeneous sampling, we retained only the spatial replicates that were sampled at every time step. If some sites were not sampled annually, we retained only the portion of the data set with uninterrupted, annual temporal sampling while still meeting the criteria of a minimum of five sites and five time points. When a data set was sampled twice or more per year, we computed annual averages of species abundances to aid in comparison across data sets. We aggregated or filtered data to ensure homogeneous taxonomic identification. For instance, our taxonomic information was provided mostly at the species level, but some data sets contained information at the genus, family, or order level. This posed an issue only when individuals were identified as belonging to a specific genus within datasets that contained several species from the same genus.
For example, in certain datasets, some individuals were identified as simply belonging to a genus (e. g. , "Carex sp. "), while most individuals were identified as a species of said genus (e. g. , "Carex phoetida"). Such heterogeneous identification in the data suggested that species identification was inconsistent. If taxa identified at the genus level comprised a small portion of the individuals within a genus (i. e. , <5% of records were identified at the genus rather than species level), we removed the genus-level data from the data set. Conversely, if >5% of individuals were identified at the genus level, we assumed this reflected inconsistent identification. In this case, we lumped taxonomic identification at the genus level. We removed all unknown species from the data sets. We only used data sets that could represent a metacommunity by separating taxonomic groups and retaining data sets with enough shared species.
For example, when a data set contained two or more distinct taxonomic groups (e. g. , fish, sessile invertebrate, and algal assemblages in the Santa Barbara Coastal LTER), we treated these groups as separate data sets. Moreover, when a data set contained sites that shared <5% of species, we investigated these sites further and excluded them if they clearly did not appear to be part the same metacommunity as the majority of other sites. To represent the salient characteristics of each data set, we plotted species accumulation curves, time series of species abundance, spatiotemporal replication, and the number of species shared between spatial replicates (Appendix S1). The data for these analyses are publicly available at EDI and listed in Table  S1. All analyses were conducted with the R statistical computing environment, v.
, fish, zooplankton, herps) exhibited intermediate synchrony values between birds and plants. We found general support for local-scale diversity-stability relationships, such that more species rich sites in the metacommunity tended to have much lower variability in total community biomass (Fig. 2A ). This relationship did not hold for all communities (e. g. , algae and some invertebrates), but it did emerge as a general pattern across studies as well (intercept = 0. 714 ± 0. 093, t = 7. 642; slope = -0. 019 ± 0. 006, t = -2. 779). However, incorporating the random effects for each dataset strongly improved the fit of the model ( & " = 0. 0932;  ' " = 0. 848). In contrast, we found a range of relationships between compositional variability and richness (Fig. 2B ). Some metacommunities showed strong positive relationships between richness and compositional variability, while others showed strong negative relationships.
But there was no strong effect of richness on compositional variability (intercept = 0. 288 ± 0. 051, t = 5. 598; slope = 0. 0008 ± 0. 004, t = 2. 07). Again, accounting for among-dataset differences drastically improved model fit ( & " = 0. 0009;  ' " = 0. 620), showing the importance of accounting for the variance in DSR slopes among metacommunities. Metacommunities with higher sustained spatial β-diversity over time exhibited both lower aggregate (Fig. 2C ) and compositional (Fig. 2D ) spatial synchrony. We detected a stronger relationship between β-diversity and compositional synchrony (slope = -0. 125 ± 0. 028 SE, F1,20 = 19. 72, R 2 = 0. 497, p = 2. 5e-4) than aggregate synchrony (slope = -0. 093 ± 0. 030 SE, F1,20 = 9. 434, R 2 = 0. 321, p = 6. 0e-3). Therefore, β-diversity generates spatially distinct communities that vary independently in their abundance fluctuations and in their community trajectories.