dataesr/scientific-paragraphs-categorization huggingface dataset:
The larger spatiotemporal coverage of the dataset considered here enabled one to take into consideration more statistical variables for a bet- ter description of the troposphere while studying more thoroughly different aspects that had not been taken into account previously, such as sensitivity to both temporal and spatial samplings of the training dataset, consistency with the number of clusters or comparison with a k-means algorithm. A decision tree is also proposed as a tool for interpreting the different classes, highlighting the relative importance of temperature and humidity in the classification process. The article is organized as follows. Section 2 presents the data to classify, the pre-processing data compression step, the classification method and the choice of the optimal configuration of the model.
Data and methods Figure  1  outlines the methodology used in this paper. The goal is first to build air mass clusters from atmospheric situations characterized by temperature and humidity probabilistic data only, along with probabilities of the situations belonging to each cluster. The clusters have to be as coherent as possible in terms of temperature and humidity (e. g. hot and wet, or cold and dry air masses) and as different as possible from each other. To achieve this, a representative training dataset of thermodynamic profiles is first turned into a manageable set of CDF values. The latter are used as input into the EM algorithm to obtain a partition of the atmospheric sit-uations as well as a probabilistic description of each group (cluster) of the partition, without having any prior reference classification (a process called unsupervised classification, clustering or cluster analysis).
Thermodynamic description of the atmosphere The atmospheric dataset used in this study is based on ERA-Interim global atmospheric reanalyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) covering the period from 1 January 2000 to 31 December 2009  (Dee et al. , 2011). The different daily products (e. g. surface pressure, surface temperature, temperature and specific humidity profiles) are available on a 0. 75 • by 0. 75 • latitudelongitude global grid (241 × 480 data points) every 6 h for 4 synoptic hours, i. e. 00:00, 06:00, 12:00 and 18:00 (Coordinated Universal Time). Vertical profiles are described on 60 pressure (or altitude) coordinates called "sigma levels" from the surface to 0. 1 hPa (about 65 km in altitude on sea). Unless explicitly mentioned, the set of observed data corresponding to 00:00 and 12:00 UTC of the 15th day of January, April, July and October from 2005 to 2009 will be used in this article and referred to as "training dataset".
Each synoptic hour gathers 241 × 480 = 115 680 atmospheric situations spatially distributed over the Earth corresponding to However, keeping all these situations may not be necessary to get the intended atmospheric partition. The influence of the temporal and spatial sampling of the dataset on the classification will be studied in Sect. 3. 2. Humidity can be measured by various variables. Here, specific humidity, dew point temperature as well as total column water vapour will be considered. They correspond to the ratio of the mass of water vapour to the mass of dry air plus water vapour (expressed in kg kg -1 ), the temperature at which air is saturated with water vapour (in K) and the amount of vertical integrated water vapour in the whole atmospheric column (expressed here as the height of an equivalent column of liquid water in precipitable centimetres) respectively.
The selected part of the profiles is converted into a PDF first and then into a CDF from which a discrete set of key CDF values is selected as being the most representative information of the temperature (or dew point temperature) vertical profiles (data aggregation step). Here, since the general shape of temperature and humidity distributions is not known a priori, the conversion into PDF is performed using the non-parametric Rosenblatt-Parzen kernel density estimation (KDE) method  (Rosenblatt, 1956; Parzen, 1962) , which can be seen as a weighted sum of p parametric normal distributions centered at each value of the sample (e. g. the p = 38 values of interest of a given temperature profile here). More details can be found in  Vrac et al. (2005 Vrac et al. ( , 2011)). A priori knowledge is often essential to choose the relevant variables (here, the CDF values) able to distinguish the intrinsic groups in a given dataset.
Such a problem is known as "feature selection" or "variable selection". Some numerical techniques exist in the literature to help make a choice (e. g. Diday and Vrac, 2005; Vrac et al. , 2011; Pudil et al. , 1994; Raftery and Dean, 2006) , but they remain not really relevant for the datasets studied here. Looking at the diversity of the profiles leads one to select subjectively CDF values at several temperature values from 200 to 290 K, and the same for dew point temperature. A set of 10 values within this interval, every 10 K, seems a good compromise between keeping enough information and reducing as much as possible the number of dimensions. Finally, the database used as input data into the clustering algorithms (EM or k-means) is an array of size N × D, where N is the number of selected atmospheric situations (e.
The Gaussian mixture model and the EM algorithm Model-based clustering relies on the assumption that a given observed dataset contains several sub-populations and that the overall population can therefore be modelled as a finite mixture model. Usually, and as done here, a Gaussian mixture model is used, that is, a mixture of weighted Gaussian PDFs, each one associated with a given cluster related to a sub-population. Let x = { x i ∈ R D |i = 1,. , N} be a population of N observed data, each one represented by a D-dimensional vector x i , containing K sub-populations modelled by multivariate Gaussian PDFs parameterized by their mean vector µ k and covariance matrix k. With θ k = (θ 1 k ,. , θ D k ) = ( µ k , k ) , the PDF g of x takes the following form: g(x |φ) = K k=1 π k f k (x|θ k ), (2) where φ = (π 1 ,.
Initialization strategy In order not to use arbitrary a priori information, the initialization strategy used in this paper consists in repeating r (here, r = 50) random draws of the component means in the dataset with short runs of EM, that is, until the number of iterations has reached a pre-defined maximum number of iterations (here, 10) if convergence has not been reached before. The resulting mixture model parameters corresponding to the random partition that maximizes the log-likelihood among the r runs are then provided as initial parameters to the normal EM procedure. This method, which was introduced by  Biernacki et al. (2003) , is often considered as a reference strategy since it is a trade-off between avoiding suboptimal solutions, often obtained with a single run of EM with a random initialization partition, and reducing the number of iterations to reach convergence.
The expressions of the k eigenvalue decomposition for these two models are respectively the diagonal matrices λ k I and λI , where I is the identity matrix, λ is a scalar and the presence of the subscript k implies that λ can vary between the clusters. For illustrative purposes, Fig. 4  shows the projection in a two-dimensional subspace of the result of an unsupervised classification into seven clusters with EM-VII (EM and model VII) applied to the D = 20 CDF values corresponding to 10 % of the observations coming from the training dataset (for 2005, 00:00 UTC only). The central figure shows the F T (230 K) and F T (260 K) CDF values for the N atmospheric situations as well as their corresponding cluster, where the four representative temperature profiles of Fig. 3  are also represented. Here, the projected hyperspherical isocontours are reduced to circles whose radius equals the standard deviation of the samples within each cluster.
Partition and cluster features In this section, unsupervised classification is applied to the training dataset with no spatial sampling. The situations associated with elevations above sea level higher than 1 km will be referred to as air mass 0 from now on to indicate that they have been discarded (Sect. 2. 1). The seven resulting clusters are ordered from the average hottest surface temperature to the average coldest one, that is, globally from a tropical air mass (1) to a polar one (7), and can be thermodynamically correlated with the maps shown in Fig. 2. The features of each cluster can be represented for example by their mean and standard deviation profiles for temperature and dew point temperature shown in Fig. 5 , and also by the total column water vapour mean and mid-tropospheric layer average temperature (here, 800-320 hPa) listed in Table  1.
Sensitivity to the temporal sampling Depending on the choice of the spatial sampling step on which the atmospheric situations are selected for the clustering process, air masses may be significantly different. In order to know how many years, how many months a year, and so on, should be used, a sensitivity study must be performed. Studies within the period 2000 to 2009 show that resulting partitions are similar as soon as 4 months representative of each season are used. However, there is an exception for 2003, for which the features of air masses 3 and 4 are significantly different from those corresponding to the other years (not shown). In a more general framework, in order to avoid possible singular partitions due to specific thermodynamical features over the years, the training dataset will contain 2 synoptic hours, 1 day, 4 months and 5 years, hence the choice of the training dataset mentioned in Sect.
Here, the two partitions correspond to the training dataset with no spatial sampling and have been obtained through two different ways: first, via unsupervised classification, and second, via supervised classification from each of the S 2 possible training datasets corresponding to the S 2 possible spatial grids. The box-and-whisker plots represented in Fig. 8  show the distribution of the misclassification rates with the spatial sampling step S for both EM-EII and EM-VII. In both plots, the bottom, middle and top of the blue boxes are respectively the first quartile (25 %), the second one (the median, i. e. 50 %) and the third one (75 %), whereas the whiskers indicate the minimum and maximum of the sample consisting in the S 2 misclassification rates for a given spatial sampling step S. For EM-VII, spatial sensitivity is low until S = 5, since misclassification values are lower than 2 % in the worst case and lower than 1 % for at least 75 % of the possible cases.
For S = 6 and 7, sensitivity slightly increases, but the misclassification rates are not higher than 4 %, which are still relatively low values. For S ≥ 8, there are significant differences among the partitions. The red dashed curve shows the misclassification rate for each spatial sampling step S when random starting grid points are selected, which is what will be used in practice. This curve is generally below the curve which would link the median values, meaning that randomly drawing the starting grid point for each synoptic hour selected appears to reduce even more the misclassification rate. However, EM-EII is much more sensitive to the spatial grid than its counterpart. In the following, S is set to 5 (thus 3. 75 • in longitude and latitude) for building the training dataset since it is a good trade-off between reducing the size of the training database and avoiding differences in terms of clustering.
Supervised classification In the following sections, the supervised classification of the atmospheric situations corresponding to a given synoptic hour is obtained by using the mixture model parameters estimated via unsupervised classification of the training dataset   with a spatial sampling step of 3. 75 • in both longitude and latitude and random starting grid points. Figure  11a  shows examples of supervised classification maps for the 15th day of January and July at 00:00 UTC for 1 year outside the 5-year time period of the training dataset, that is, 2002, for which the subtraction between supervised classification and unsupervised classification (using in that case the period 2000-2004 instead of 2005-2009 for the training dataset) is also shown. It is important to notice that air mass patterns are similar to the ones resulting from unsupervised classification at the same day, which is expected since air masses retain their essential features when they are not sensitive to the choice of the spatial and temporal richness of the training dataset.
Cluster interpretation with a decision tree Another interesting way to interpret a partition is to build a decision tree, that is, a supervised classification method in the form of a tree structure separating a dataset into smaller and smaller subsets through some decision rules given a partition known a priori. The goal of such a tree is to predict the value of the variable to be explained (here, the class to which a given observation belongs) given a subset of input explanatory variables (here, the D = 20 CDF values) corresponding to observations whose partition is already known. For this purpose, R package "rpart"  (Therneau and Atkinson, 2015)  has been used, based mainly on  Breiman et al. (1984)  and on binary trees: each node has at most two children. In this section, the terms "cluster" and "class" will refer respectively to the unsupervised classification and supervised classification results.
Separations between the nodes have been performed via maximal impurity reduction, with the use of the Gini index as an impurity function. That means that the tree tries to build nodes containing as few clusters from the reference partition as possible. In order to compare the classes obtained from the decision tree to the reference partition, the tree has been pruned to seven terminal nodes. It is done by setting a complexity parameter measuring the "cost" of adding another explanatory variable among the 20 possible ones in the model underlying the decision tree. For more technical details, see  Therneau and Atkinson (2015). Pruning the tree implies that we may not have the same set of explanatory variables as used previously in the EM algorithm. Figure  13  shows the classification tree obtained by considering as a priori probabilities of belonging to each cluster the mixture proportions of the reference partition obtained via unsupervised classification with EM-VII on the training dataset.
Summary and conclusions In this paper, a methodology for unsupervised and supervised classifications of various and large atmospheric databases into distinct air masses has been proposed and applied to thermodynamic profiles (temperature and dew point temperature) from ECMWF reanalyses. These three-dimensional data are gridded in latitude, longitude and vertical layers, homogeneously distributed over the Earth, and span the period 2000-2009. This methodology follows a similar probabilistic point of view considered by  Vrac et al. (2005 Vrac et al. ( , 2011) )  through a different approach to the problem of mixture models (estimation approach against clustering one previously). It relies (i) on a probabilistic classification method based on a multivariate Gaussian mixture model whose parameters are estimated via maximum likelihood estimation by the expectation-maximization (EM) algorithm; and (ii) on the use of probabilistic data: classical thermodynamic values at different pressure levels are converted into a set of cumulative distribution function (CDF) values whose number represents the number of statistical variables needed to characterize each atmospheric situation.
This data compression step implies a description of the data different from the common ones, giving information on the vertical distribution of the temperature and dew point temperature values regardless of the successive pressure levels. In  Vrac et al. (2005 Vrac et al. ( , 2011)) , (i) a limited set of observations consisting of only 1 winter day was used as a training dataset for classifying new data through projections not exceeding 1 month; (ii) only four statistical variables were used to characterize each atmospheric situation; (iii) an initial partition based on seven subjective zonal clusters homogeneous in temperature and humidity was used. Such choices were not enough to steadily characterize air masses at any time and any location on large temporal scales. To overcome this problem, several updates have been implemented.
First, a much larger set of observations has been selected as a training dataset in order to take into account their high variability, that is, 2 synoptic hours of the central day of 4 months representative of each season for a period covering 5 years. Second, each atmospheric situation has been characterized by a substantially higher number of statistical variables for a better thermodynamical description of the profiles: 10 CDF values for temperature, and 10 for dew point temperature. And third, an initialization strategy for EM based on the use of a suitable random initial partition has been adopted to avoid the use of arbitrarily chosen prior information. Furthermore, 14 models adding different constraints (or not) to the structure of the covariance matrices and thus to the dispersion of the observations have been studied, since dealing with the unconstrained model does not provide representative partitions.
The latter is more physically expected and leads to a classification which depicts more accurate tropical air masses due to a stronger influence of humidity on the classification. These results show that EM generalizes k-means by providing, in addition, the probabilities of belonging to each class for each atmospheric situation and thus the corresponding uncertainties as well. The proposed method shows low temporal and spatial sensitivity to the choice of the training dataset. Within the period 2000-2009, we have not only shown that the partitions are similar as soon as the training dataset contains 1 day of 4 months representative of each season and spans several years, but also that a 3. 75 • by 3. 75 • spatial sampling delivers partitions similar to those obtained with no spatial sampling.
This low sensitivity provides the ability to classify new data through long-range projections (more than 3 years). Our method complies with the five properties introduced by  Huth (1996)  and  Huth et al. (2008)  to assess the quality of a classification: (i) the method reproduces expected patterns known to exist in the data, as low-pressure systems or the traditional winter continental polar (cP) air mass; (ii) it shows little sensitivity in time and space to the choice of the training dataset, both in terms of observation selection and size; (iii) it shows neither high equability (clusters tending to be equal in size) nor low equability (a huge cluster accompanied by small ones, called the snowballing effect); (iv) it makes a good distinction between clusters since the boundary regions separating the air masses, associated with high uncertainty, present narrow extents not exceeding 3 • in longitude and latitude, despite the difficulties induced by the continuous nature and the high variability of the atmosphere; and (v) it is in fact quite consistent with the number of clusters, meaning adding successively one cluster does not drastically change most of the clusters.
Based on temperature and dew point temperature variables, the proposed classification method is applicable to most atmospheric datasets used by the atmospheric science community, such as radiosonde measurements, meteorological reanalyses or satellite data. Depending on the intended objective, other variables could also be considered, especially dynamic variables to help monitor air mass movement, such as potential vorticity, which is commonly used for weather analysis (e. g. Emanuel, 2008). An important feature of this method consists in providing probabilistic information, which can be used to provide the uncertainties associated with the classes or improving a priori information in many atmospheric applications such as in remote sensing. Finally, through the evolution of the classes and their associated probabilities along several decades, the method could be easily adapted to evaluate general circulation models and study climate variability and potential changes at different spatial and temporal scales.
Data availability The temperature and specific humidity profiles as well as the surface temperatures and pressures used in this study come from ERA-Interim global atmospheric reanalyses  (ECMWF, 2016)  and can be downloaded for example from http://apps. ecmwf. int/datasets/data/interim-full-daily/levtype=sfc/. The elevations above sea level are from the 1 / 6 • global elevation dataset compiled by the U. S. Navy Fleet Numerical Oceanography Center (2016) (which can be downloaded from http://rda. ucar. edu/datasets/ds754. 0/). The EM algorithm has been implemented using the Rmixmod S4 package  (Mixmod Team, 2008; Lebret et al. , 2015) , which is available at https://cran. r-project. org/web/packages/ Rmixmod/index. html  (CRAN, 2016a). As for the decision tree, it has been implemented using R package rpart, which can be downloaded from https://cran.
We detail our observations and data reduction procedures in ( §2), the theoretical basis and the numerical methods in ( §3), broadband (white) light curve modelling in ( §4), transmission spectroscopy in ( §5), and finally conclude with a discussion of the results ( §6). The analysis and the raw data are publicly available on Github, 1 as an easy-to-follow set of IPython notebooks and Python codes, to help with reproducibility of the study.
The analysis relies on Python-and Fortran-based code utilising SciPy, NumPy (van der Walt et al. 2011), IPython  (Perez & Granger 2007) , Pandas  (Mckinney 2010) , matplotlib  (Hunter 2007) , seaborn, 4  PyFITS, 5  and F2PY  (Peterson 2009). The tran-  Parviainen, H. et al. :  The GTC exoplanet transit spectroscopy survey II Table  2. Parametrisation and priors. The uninformative priors are uniform and wide enough not to affect the posteriors. N(µ, σ) stands for a normal prior with mean µ and standard deviation σ. The colour dependent parameters are per passband.
Likelihood for the stellar limb darkening profile Instead of relying on the tabulated limb darkening coefficients, we model stellar intensity profiles calculated for TrES-3 and our passbands using the PHOENIX stellar atmosphere code jointly with the photometric data. This allows us to marginalise over the whole limb darkening coefficient space that can explain the theoretical stellar intensity (limb darkening) profile, and may yield more robust parameter estimates than by using fitted limb darkening coefficients directly. The stellar limb darkening profile data, D LD , is constructed from stellar limb darkening profiles calculated using the PHOENIX code for 27 stellar parameter sets over 16 passbands (corresponding to the ones in our basic spectroscopic analysis) and 75 values of µ (where µ = cos γ = √ 1z 2 , γ is the foreshortening angle, and z is the projected distance from the centre of the stellar disk divided by the stellar radius).
Systematic errors from limb darkening The stellar limb darkening is one of the main factors affecting the radius ratio estimates, especially with grazing orbits. Our approach uses the PHOENIX-generated limb darkening profiles as input information, and if the code were to feature systematic deviations from the reality (for example, exaggerated limb darkening towards blue), this would directly affect the θ k estimates. We tested whether the θ k difference of 0. 01 between the 542. 5 nm and 642. 5 nm centred passbands (1st and 5th, starting from the bluest) could be explained by systematic errors in limb darkening by first generating a transit light curve corresponding to other passband, and then fitting a transit model to this with free limb darkening coefficients and θ k set to the other passband value.