dataesr/scientific-paragraphs-categorization huggingface dataset:
The annual RAPID trend is currently not statistically significant (-0. 11 Sv yr -1 , p > 0. 05). Plain Language Summary There are ongoing discussions in the scientific community about whether the Atlantic Meridional Overturning Circulation transport is slowing down. This is of interest due to the importance of this circulation in transporting heat from the tropics to the northern latitudes. A consensus about its decline is hard to reach due to the limited direct observational data available; with the longest continuous data being 14 years long from 2004 to 2018. We therefore conduct a simulation experiment to examine how many years of data are required to detect a decline in the circulation. We create simulations of the North Atlantic transport based on statistical properties from 20 general circulation models with future climate change projections (until 2100) and from the RAPID array observations (since 2004).
g. , variance and autocorrelation, or short-term memory), and the trend detection technique used  (Beaulieu et al. , 2013; Henson et al. , 2010; Tiao et al. , 1990; Weatherhead et al. , 1998). To explore these factors, we use the 14-year RAPID observations and 93-year CMIP5 future scenario model AMOC data which exhibit a range of trends and variability. We also compare four approaches for trend detection to assess sensitivity to the presence of autocorrelation and technique choice. Previous studies have largely focused on time of emergence of an anthropogenically forced AMOC decline; that is, when a trend falls outside the range of its natural variability  (Baehr et al. , 2007 (Baehr et al. , , 2008;; Jackson & Wood, 2020; Keller, Deutsch, et al. , 2007; Keller, Kim, et al. , 2007; Roberts & Palmer, 2012; Roberts et al.
Three different powers of detection are used in this study, meaning that the minimum sample size with significant trends in 80%, 90%, or 95% of the 100 time series is identified as the length of data required to detect a declining trend (n * ). This is repeated for each of the 1,000 simulations, and the results are represented as a probability density function (PDF); and summarized as a median n * and the 5th-95th percentile interval representing the uncertainty, which we also call a "detection window. ".
c ) are results from simCMIP5var (generated using 1,000 values from the pCDFs of the CMIP5 trends, AR(1) coefficients, and variances in Figure  2 ). Panels (d)-(f) are results from simRAPIDvar (generated with the same trends as in simCMIP5var but RAPID's AR(1) coefficient, 0. 29, and variance, 2. 33 Sv 2 ). The four linear regressions used are displayed: ordinary least squares ("ols") in green, OLS with effective number of degrees of freedom ("neff") in blue, prewhitening ("pw") in red, and generalized least squares ("gls") in black. All methods produce similar results, when comparing the medians of the PDFs. The power of detection increases from 80% in (a) and (d), to 90% in (b) and (e), and to 95% in (c) and (f). See section 4 for further details on the simulation experiment setup. We also quantify the effect of different start months to compute a year of data on the n * using the approximation from  Weatherhead et al.
The form of Eqs. 12-13 makes it straightforward to verify that if Eq. 13 is verified and if α s,i-1 2 lies between α s,i-1 and α s,i (and if α s,i+ 1 2 lies between α s,i and α s,i+1 ) then the resulting advection scheme guarantees monotonicity of mixing ratios, which is physically desirable and is the reason why chemistry-transport models usually resolve advection of trace species using an approach based on Eq. 12 rather than a straightforward resolution of Eq. 6. Regarding chemistry-transport models, in practice, approximated values of F i-1 2 are inferred from the wind and density fields provided by the forcing meteorological dataset. Here we will avoid the typical problem of mass-wind inconsistenciesdiscussed in, e. g. ,  Jöckel et al. (2001) ;  Emery et al. (2011) ;  Lachatre et al. (2020) , by working with analytically-defined non-divergent mass fluxes, and constant and uniform air density, so that Eq.
In more general words, this result suggest that the Després and Lagoutière (1999) scheme may be expected to perform better than classical schemes in chemistry-transport models for advection of polluted plume thinner study  (Mailler and Pennel, 2020)  is available permanently in the HAL repository at https://hal. archives-ouvertes. fr/hal-02933095. The latest stable version of toyCTM is available from: https://gitlab. in2p3. fr/ipsl/lmd/intro/toyctm/-/archive/master/toyctm-master. tar. gz.
Acknowledgements. We are thankful to  Walter Joyce  ( University of Fribourg ) for his support and for reading an earlier draft of this paper. We thank  Chris Mah  and the anonymous reviewer for their comments that helped improve the manuscript. Financial support. This work was supported by a grant from  Synthesys  ( GB-TAF-6581 ) to  Marine Fau  for visiting the  Natural History Museum (London)  in June 2017 and by funds from the  Department of Geosciences of the University of Fribourg. Review statement. This paper was edited by  Florian Witzmann  and reviewed by  Chris Mah  and one anonymous referee.
This suggests that the signal is due to freestreaming particles within the vacuum gap rather than particles transporting through the wedge. For the case with a cone spanning the gap (c), the effect was further enhanced, Fig. 2 (f), with 10× higher peak signal and 18× higher integrated signal compared to the freestanding case, Fig. 2(g ). These data indicate confinement of the proton beam in one dimension by the wedge and in two dimensions by the cone. The proton beam spectrum from all targets was collected with the TPIE which was apertured with a pinhole in the forward direction with solid angle ~10 -7 sr. Extrapolation of the full proton beam was made by multiplying the measured solid angle on layers of RCF in a separate shot day. The beam angular distribution was similar shot-to-shot. For a shot with a free hemi with no structure and no foil, the spectrum had a characteristic slope temperature of =.
Acknowledgements This material is based upon work supported by the  U. S. Department of Energy National Nuclear Security Agency  under the  National Laser User Facility (NLUF) program  with Award Number  DE-NA0002034  and the  High Energy Density Laboratory Plasmas program  with Award Number  DE-NA0003876. The support of  DOE  does not constitute an endorsement by  DOE  of the views expressed in this article. The authors would like to acknowledge excellent support provided by the  OMEGA EP Laser Facility  staff including  D. Canning  and  D. Mastrosimone  and General Atomics target fabrication by  Michelle Evans. We thank  B. Qiao  for serving as NLUF PI while at  UCSD. S. N. C is supported by  Extreme Light Infrastructure Nuclear Physics  ( ELI-NP) Phase II , a project co-financed by the  Romanian Government and European Union  through the  European Regional Development Fund.
Oceanic and Atmospheric Datasets Phytoplankton needs light and nutrients to grow. Physical processes strongly control spatial distribution and time-variability of nutrient inputs in the upper-sunlit layer, and thus of phytoplankton over a large part of the global ocean. Thus, we make use of this physical (bottom-up) control to derive statistical models that relate several physical variables (predictors) to satellite Chl (output) as detailed in Table  1. Chl was retrieved from the Ocean Colour-Climate Change Initiative (OC-CCI) from the European Space Agency (ESA,  [32] ). This product has generated global, ocean-colour products for climate research by merging observations from different sensors while attempting to reduce inter-sensor biases  [33]. The V4. 2 product was extracted on a 1 • grid and with a monthly temporal resolution over 1998-2015.
Neural Networks Deep learning models and neural networks (NNs) are at the core of the state-of-the-art in machine learning and artificial intelligence for a large range of applications  [43]. NNs are particularly appealing due to their capacity to learn complex relationships from raw data better than other models, when data are abundant. Though the concept of NNs has been around for a long time, these state-of-the-art approaches recently obtained impressive results for many supervised or unsupervised learning problems thanks to the availability of very large datasets, and the increase in computational power in the last few decades  [44]. NNs learn complex patterns through the composition of simple elementary operations forming a global highly-nonlinear input/output relationships, whose parameters can be efficiently trained using the back-propagation algorithm.
These recent advances motivate an increasing number of applications in spatial oceanography, (e. g. ,  [45, 46] ). In this context, physics-informed and theory-guided NNs  [47]  are of key interest as new means to exploit the computational and learning efficiency of NNs, while exploiting prior knowledge and making easier model interpretation. Here, we follow such an approach with a MLP architecture, which uses the same physical features and geospatial information as inputs as the SVR. NN frameworks exploit mini-batch gradient descent schemes during the training phase. This can allow us to exploit the entire dataset contrary to the SVR model. Indeed, SVR is known not to scale up well with large training datasets. The considered MLP architecture exploits LeakyReLU activation functions after each dense layer (Figure  S1 ).
Dropout layers  [48]  are added to the last 3 layers to reduce overfitting. Since we are dealing with a regression task, the last layer is linear. Thanks to its benefit of penalizing large errors, MSE is used as the loss function for the MLP. The MLP is set up with python and the Keras library. Configurations details are provided in Table  S1. As for the SVR, we first train a MLP on 9% of the training dataset, randomly selected. The reconstructed Chl is hereafter referred to as Chl MLP-9%. The aim is to provide a first consistent comparison with Chl SVR using the same training setting. Then, we take advantage of the MLP ability to be trained on larger database and a second MLP is trained on 80% of the dataset. Reconstructed Chl is referred to as Chl MLP. The two learning curves are provided in Figure  S2.
Data Preprocessing and Procedure Predictors and log(Chl) are normalized by removing their respective average and dividing them by their standard deviations. The SVR and the two MLP are trained from 1998 (the first complete year of the satellite Chl OC-CCI time-series) to 2015 between 50 • S and 50 • N (Step 1 in Figure  1 ). Thus, the resulting SVR and NN schemes are applied on the physical predictors over 1998-2015, and the annual means and standard deviations initially removed are applied to perform the back transformation and reconstruct Chl values, namely either Chl SVR , Chl MLP-9% and Chl MLP outputs (Step 2 in Figure  1 ). These three Chl reconstructed whole datasets are then compared to Chl OC-CCI to evaluate their skills in reconstructing satellite observations (Step 3 in Figure  1 ).
scale up well with large training datasets. The considered MLP architecture exploits LeakyReLU activation functions after each dense layer (Figure  S1 ). Dropout layers  [48]  are added to the last 3 layers to reduce overfitting. Since we are dealing with a regression task, the last layer is linear. Thanks to its benefit of penalizing large errors, MSE is used as the loss function for the MLP. The MLP is set up with python and the Keras library. Configurations details are provided in Table  S1. As for the SVR, we first train a MLP on 9% of the training dataset, randomly selected. The reconstructed Chl is hereafter referred to as ChlMLP-9%. The aim is to provide a first consistent comparison with ChlSVR using the same training setting. Then, we take advantage of the MLP ability to be trained on larger database and a second MLP is trained on 80% of the dataset.
Data Preprocessing and Procedure Predictors and log(Chl) are normalized by removing their respective average and dividing them by their standard deviations. The SVR and the two MLP are trained from 1998 (the first complete year of the satellite ChlOC-CCI time-series) to 2015 between 50° S and 50° N (Step 1 in Figure  1 ). Thus, the resulting SVR and NN schemes are applied on the physical predictors over 1998-2015, and the annual means and standard deviations initially removed are applied to perform the back transformation and reconstruct Chl values, namely either ChlSVR, ChlMLP-9% and ChlMLP outputs (Step 2 in Figure  1 ). These three Chl reconstructed whole datasets are then compared to ChlOC-CCI to evaluate their skills in reconstructing satellite observations (Step 3 in Figure  1 ). Empirical orthogonal function (EOF) analysis is performed to investigate the model's ability to reconstruct Chl seasonal and interannual variability.
First, centered seasonal and interannual Chl OC-CCI are obtained by removing their annual and monthly means over 1998-2015, respectively, and by dividing them by their standard deviations. Then, the so-called reference EOF analysis is performed on these centered seasonal and interannual Chl OC-CCI anomalies to avoid an overly dominant contribution of high values on the analysis  [49]. Thus, Chl SVR and Chl MLP outputs are projected onto the seasonal and interannual Chl OC-CCI spatial patterns to obtain their associated time components (i. e. , principal component-PC). Seasonal and interannual PCs for each dataset are then compared.
Statistical Performances A first evaluation of the Chl SVR vs. Chl OC-CCI is provided over 1998-2015 at basin scales and for the whole dataset (Figure  2 , upper row). Determination coefficients between both datasets are below 0. 5 and even get down to 0. 26 in the Indian Ocean, while RMSE is about 0. 6 in the three basins. The MLP trained on the same amount of data than the SVR is more skillful than the SVR to reconstruct Chl OC-CCI (Figure  2 , middle row). The regression lines between the log of Chl MLP-9% vs. Chl OC-CCI are closer to the 1:1 line for each oceanic basin with determination coefficients higher than 0. 63 and up to 0. 73 in the Atlantic Ocean. Increasing from 9% to a usual 80% the MLP training dataset further increase the skills of the NN approach to reconstruct Chl OC-CCI with a relative gain of about 10% (Figure  2 , lower row).
Nevertheless, Chl MLP still underestimates Chl OC-CCI , more specifically in the Pacific. Some of these differences may be related to changes in Chl, which may due for instance to photo acclimation (e. g. ,  [50, 51] ) or by other components that are not Chl such as suspended particulate matter (SPM) or colored dissolved organic matter (CDOM;  [52] ). Interestingly, the use of a MLP not only removes computational restrictions imposed by the SVR (i. e. , size of the training samples), but it also appears to be more efficient in reconstructing surface Chl from oceanic and atmospheric variables. Thereafter, Chl OC-CCI and Chl SVR are compared to the best NN product, Chl MLP (i. e. , trained on 80% of the dataset). Consistently with the scatterplots, Chl OC-CCI correlations with Chl SVR are significantly lower than with Chl MLP (Figure  3A ,C; r = 0.
As expected, the SST and short-wave radiations are the most important predictors (Table  2 ). Interestingly, the zonal surface wind stress component seems of particular importance while sea level anomaly is far behind. Indeed, redundant indirect information's about the ocean circulation can be derived from those predictors, with potentially more information "embedded" within the wind stress that may also be linked to a meaningful parameter for phytoplankton growth: the mixed layer depth. Spatial coordinates (latitude and longitude) are less important for the reconstructions suggesting that the MLP can extract geospatially-dependent features from other predictors than the coordinates themselves. Thus, a complementary run was performed, still using 80% of the dataset to train the MLP but based only on the five main predictors with a relative importance higher than 0.
Discussion To our knowledge, the only study that has been performed to reconstruct satellite surface Chl on a global scale used a SVR approach  [16]. In this former study, we also used Chl OC-CCI and the same physical predictors than in the present study, but the predictors were originating from a numerical model (vs. satellite observations and numerical atmospheric reanalysis here). The SVR accurately reproduced most aspects of the satellite Chl variability (although underestimated by half) and spatial patterns. Here, we show that the SVR, trained on satellite data and atmospheric reanalysis, also encounters difficulties to well reproduce the Chl signal. The MLP demonstrates the ability of deep learning schemes to reproduce satellite Chl with far better skill than the SVR, not only to capture the general patterns of Chl seasonal and interannual signals and trends, but also their amplitude.
Particulate backscattering (as a proxy of the Particulate Organic Carbon) retrieved from satellite also deserves to be considered in addition to Chl in the training/reconstruction process. Indeed, it would allow us to investigate the extent to which the Chl variability reflects changes in phytoplankton biomass vs. cellular changes in response to light  [51, 61, 62] , which is of particular importance in oligotrophic gyres. If, in this study, we demonstrate the better potential of NNs to accurately represent Chl seasonal and interannual signals, compared to the SVR, so far, only a MLP was used. MLP is known to not explicitly consider the spatial and temporal correlations in the dataset. Specific architectures to handle spatially or temporally structured data, i. e. , convolutional neural networks and recurrent neural networks (such as long short-term memory networks) are currently under investigation and are expected to further improve the Chl reconstruction performance, in particular for the Chl seasonal cycle amplitude.
Supplementary Materials: The following are available online at http://www. mdpi. com/2072-4292/12/24/4156/s1, Figure  S1 : MLP architecture. Table  1 : MLP configuration. Figure  S2 : Learning curves of Chl MLP-9% and Chl MLP. Figure  S3 : Scatter plots of Chl MLP trained only for predictors with a relative importance higher than 0. 1 in Table  2. Figure  S4 : Correlation and NRMSE of Chl OC-CCI vs. Chl MLP trained only for predictors with a relative importance higher than 0. 1 in Table  2. Funding: Funding for the internship of A. Brini and GPU was provided by the CNES/TOSCA call (Grant n • 160515/00) PhytoDeV project. The J. Roussillon PhD grant was funded by the ISblue project, Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015) and co-funded by a grant from the French government under the program "Investissements d'Avenir".
We use the package Arpack 2  , which is devoted to solve large sparse eigenvalue problems using iterative methods. More precisely, it uses implicitly restarted Lanczos or Arnoldi methods, respectively for symmetric and non-symmetric matrices,  Lehoucq & Sorensen (1996). Several options are available in the package, including the maximum number of iterations allowed, or a tolerance parameter for the accuracy of acceptable solution 3. Remark 9 (Eigenvectors associated with the lowest eigenvalues). The Lanczos and Arnoldi methods are particularly efficient to compute the largest eigenvalues and associated eigenvectors of the matrix, and only require matrix vector multiplication. However, we are interested in the lowest eigenvalues for our decomposition. The idea is simply to use that the lowest eigenvalues of the discretized diffusion matrix, say A, are simply the largest eigenvalues of the matrix A -1.
Then, the matrix-vector multiplication, say Av for a vector v, becomes a resolution of a linear system A -1 v. It may appear computationally expensive but it is not thanks to the use of the direct solver Mumps (see above), which, once the factorization is obtained, is very efficient for the resolution procedure. Hence, the computation follows the steps 4  : 1. compute the (sparse) matrix discretization of the selected diffusion operator: A; 2. compute the factorization of the matrix A using Mumps, 3. use the package Arpack to compute the largest eigenvalues of A -1 , by replacing the matrix-vector multiplication step in the iterations by the resolution of a linear system using Mumps. Finally, the last step is to retrieve the appropriate coefficients α k in (  14 ) for the decomposition. It basically consists in the resolution of a dense linear system (from least squares method).
Acknowledgments The authors would like to thank  Prof. Marcus Grote  for thoughtful comments and discussions. The research of FF is supported by the Inria-TOTAL strategic action DIP. FF acknowledges funding from the  Austrian Science Fund (FWF)  under the Lise Meitner fellowship M 2791-N. OS is supported by the  FWF , with  SFB   F68 , project  F6807-N36  (Tomography with Uncertainties). OS also acknowledges support from the  FWF  via the project  I3661-N27  ( Novel Error Measures and Source Conditions of Regularization Methods for Inverse Problems ). HB acknowledges funding from the  European Union 's  Horizon 2020 research and innovation program  under the  Marie Sklodowska-Curie  grant agreement Number  777778  ( Rise action Mathrocks ) and with the  E2S-UPPA CHICkPEA  project.
The decrease of electrical resistance observed at this step corresponds to the removal of the absorbed moisture in the sample capsule and the surrounding area, which could be incorporated into the sample at higher temperatures  (Manthilake et al. , 2015). During the measurements, sample resistance was determined in several heating and cooling cycles until the electrical resistance of heating and cooling paths become reproducible. For the discussion, we have used the data from the last cooling cycle, which minimizes the uncertainty in electrical conductivity. The sample resistance can be obtained by fitting the impedance spectra with an appropriate equivalent circuit. For polycrystalline samples, as we use in this study, the equivalent circuit can be illustrated by a combination of resistor-capacitor/constant phase element (R-C/CPE) components, connected in parallel, series, or a series-parallel combination.
The PXRD was obtained for ~1 mm 3 of crushed samples that were placed on zerobackground Si sample holders. The PXRD was recorded using a Philipps X-Pert Pro diffractometer with CuKα radiation source (λ = 0. 15405 nm). The PXRD patterns were recorded over the 10-90° (2θ) range in steps of 0. 0167° with a counting time of 700 s per step. Lattice parameters were obtained from LeBail fits using the FULLPROF program  (Rodriguez-Carvajal, 1993). The background can be obtained by linear interpolation between twenty-six points, and the peak profiles were modeled using a pseudo-Voigt function. Raman spectroscopy was used to identify liebermannite and the minor mineral phases present in the experimental run products. Raman spectra were collected in a back-scattered geometry using an InVia confocal Raman micro-spectrometer, equipped with a 532 nm diode laser, a Peltier-cooled CCD detector, a Rayleigh rejection edge filter  (Schiavi et al.
Acknowledgments We thank  Nathalie Bolfan-Casanova  and  Maud Boyet  for constructive discussion,  J-L. Devidal  for his assistance with electron microprobe analyses and  Emmy Voyer  for her assistance with SEM analyses. The constructive and in-depth reviews by the associate Editor, and two reviewers:  Lidong Dai  and  Hongzhan Fei  substantially improved the quality of the manuscript. G. M. acknowledges funding from the (INSU-CNRS. M. M. is supported by the  US National Science Foundation  grants,  EAR 1753125 ,  1763215. This research was financed by the  French Government Laboratory of Excellence  initiative  n°ANR-10-LABX-0006 , the  Région Auvergne , and the  European Regional Development Fund  (ClerVolc contribution number xx). The authors comply with AGU's data policy, and the data of this study are available in Figshare.