dataesr/scientific-paragraphs-categorization huggingface dataset:
Meteorological forcing data We ran the model for 30 different 0. 5 • grid cells corresponding to each peatland site (US-Fen and US-Bog are in the same grid cell but their local meteorological data were different). Peatland fraction in each grid cell was prescribed from  Yu et al. (2010) , adapted by  Largeron et al. (2017)  to be matched with a high-resolution land cover map. For the 16 out of 30 cells without peatland (Fig. 2 , Table  2 ) in the large-scale map from  Yu et al. (2010) , a mean peatland fraction of 22 % was assigned. Time series of half-hourly air temperature, wind speed, wind direction, longwave incoming radiation, shortwave incoming radiation, specific humidity, atmospheric pressure, and precipitation were used to drive ORCHIDEE-PEAT. All variables were from measurements made at each flux tower where CO 2 and energy (latent heat: LE; sensible heat: H ) fluxes, water table position, soil temperature, and snow depth were recorded on a half-hourly time step.
The linearly interpolated 6-hourly CRU-NCEP 0. 5 • global climate forcing dataset was used to fill the gaps in the driving variables. A linear correction was applied to meteorological forcing variables (except precipitation) in the CRU-NCEP dataset to match observations before gap filling. For precipitation, no correction was applied. At CA-Wp2 and CA-Wp3, meteorological forcing data were measured only during the growing season, so CRU-NCEP data were linearly corrected using relationships derived from the available data. For some sites, several meteorological variables were not measured, such as longwave incoming radiation at NO-And, atmospheric pressure, shortwave incoming radiation, and longwave incoming radiation at CZ-Wet. In these cases, uncorrected CRU-NCEP data were used.
S3 ). After the spinup, transient simulations were conducted for each site, forced by repeated site-specific climates and rising atmospheric CO 2 concentration during the period 1901-2015. Finally, the model outputs corresponding to the respective measurement periods (all during 1999-2015) were compared to observed time series for each site. Two sets of simulations were conducted. In the first one (S1), soil water content and WT position were modeled by ORCHIDEE-PEAT, and the WT was used in the carbon module to define the fraction of oxic and anoxic decomposition in the acrotelm. S1 was performed for all the 30 sites. In the second set (S2) of simulations, we prescribed water table in the model to equal the observed values (WT obs ). That is, soil moisture at layers below the measured water table was prescribed as saturated (θ(z > WT obs ) = θ s ), while soil moisture above WT obs was simulated.
Site-specific V cmax reduces errors in carbon flux simulations Out of the 30 sites, 22 sites provided observed daily GPP (based on measured NEE). The values of optimized V cmax at each site were listed in Table  3. The optimized V cmax varied from 19 to 89 µmol m -2 s -1 (Table  3 ), with a mean value of 40 µmol m -2 s -1. The calibration of V cmax may compensate for biases in other model parameters. A brief comparison between simulated and reported (measured/estimated) LAI and aboveground biomass showed that there are no systematic errors (Fig. S1 ). Taylor diagrams were used to evaluate model results at these 22 sites (Fig. 3 ). The model had the best performance for GPP, with the correlation coefficient between simulated and observed GPP varying between 0. 66 and 0. 93, and all data points fell within the 0.
, 2015). To better understand the influence of the water table dynamics on ER and NEE in the model, we compared the second set of simulations (S2, with observed water table used in the carbon module to define the fraction of oxic and anoxic decomposition in the acrotelm) with the first set (S1, water table calculated by the model). ORCHIDEE-PEAT showed only a small improvement in reproducing ER and NEE when WT obs was used (Tables  5  and 6 ). To illustrate this effect, we took the Lompolojänkkä (FI-Lom) fen site as an example, in which WT was most severely underestimated among the 22 sites where NEE and ER measurements were available (Fig. S8 ). While modeled WT varied between 5 and 54 cm below the surface, WT obs was always above the soil surface. Figure  5a  showed that in comparison to S1, there was no aerobic respiration and larger anaerobic respiration in the acrotelm in S2.
The underestimation of the snow depth can be caused by the bias in snow processes of the model, such as underestimation of snow mass, and/or overestimation of snow density and subsequently overestimation of snow compaction, and/or overestimation of sublimation. The insulation effect of the moss layer and the top organic layer is not included in this study, which may explain why soil temperature was overestimated in summer but underestimated in winter. ORCHIDEE-PEAT calculates one energy budget for the vegetation and soil columns in one grid cell. Key parameters used for solving the heat diffusion equations in the soil, such as soil heat capacity and thermal conductivity, were prescribed by the dominant soil texture in the grid cell  (Gouttevin et al. , 2012). Nevertheless, similarly to the case of the hydrology module, the three default (coarse, medium, fine) soil textures cannot represent thermal properties of a peat soil  (Paavilainen and Päivänen, 1995; Abu-Hamdeh and Reeder, 2000).
Conclusions We developed ORCHIDEE-PEAT to simulate soil hydrology and carbon dynamics in peatlands. The model was evaluated at 30 northern peatland sites (Europe, USA, Canada, and Russia). The optimization of V cmax reduced the errors in the simulated carbon budget. The model, generally, reproduced the spatial gradient and temporal variations in GPP, ER, and NEE well. Water table depth was poorly simulated, possibly due to uncertainties in water input from non-peatland areas in the grid cell, and to a lack of representation of micro-relief, as well as the lack of consideration of peat disturbance. A significant relationship between V cmax and latitude was found. This may be attributed to the influence of temperature on growing season length and nutrient availability. For ER and NEE, the improvement brought by forcing the carbon module to use observed WT values (WT obs ), instead of being calcu-lated by the model, was small, indicating that the simulated WT was reliable to predict ER and NEE properly.
Acknowledgements. This study was supported by the  European Research Council Synergy  grant  ERC-2013-SyG-610028 IMBALANCE-P. We would like to thank all the  PIs  for giving us permission to use the flux and ancillary data and for all the help and advice they provided while we were preparing the manuscript. We thank the  Polish National Science Centre  which provided funds for site Kopytkowo (PL-Kpt) under projects  UMO-2011/01/B/ST10/07550  and  UMO-2015/17/B/ST10/02187 , and the  Department of Energy  for supporting measurements at  Lost Creek fen (US-Los)  through the  AmeriFlux Network Management Project. We gratefully acknowledge the financial support provided for the La Guette site under the  Labex VOLTAIRE  ( ANR-10-LABX-100-01 ) and the  PIVOTS  project of the  Région Centre -Val de Loire  ( ARD 2020 program  and  CPER 2015-2020 ).
Data from the Greenlandic sites (DK-ZaF and DK-NuF) were provided by the  Greenland Ecosystem Monitoring Programme. The US-Bes tower is funded by  NSF  (award nos. 1204263  and  1702797 ),  NASA ABoVE  ( NNX15AT74A ;  NNX16AF94A ),  EU   Horizon 2020 INTAROS  (under grant agreement no. 727890 ), and the  NERC   UAMS grant  ( NE/P002552/1 ). Edited by: Carlos Sierra Reviewed by: two anonymous referees.
Code availability. The access to the source code is available online via (http://forge. ipsl. jussieu. fr/orchidee/browser/perso/ chunjing. qiu/ORCHIDEE, but its access is restricted. Readers interested in running the model should follow the instructions at http://orchidee. ipsl. fr/index. php/you-orchidee and contact the corresponding author for a username and password. Data availability. Measured eddy-covariance fluxes and related meteorological data can be obtained from the FLUXNET database (http://fluxnet. ornl. gov/), the AmeriFlux database (http://ameriflux. lbl. gov/), and from investigators upon request. Model outputs are available at https://files. lsce. ipsl. fr/public. php?service=files&t= 0f319ede335dc37d43edf617c94f83d0. The Supplement related to this article is available online at https://doi.
Contributions In this paper, we leverage recent advances in phase retrieval, nonlinear physical models, and modern regularization. We propose a unified framework that can cope with forward models at various levels of sophistication (e. g. , Born  [4] , beam-propagation method  [44] , Lippmann-Schwinger  [45] ) and with various sparse regularizers (e. g. , TV  [46] , Hessian-based  [47] ). This is possible because of the modularity of the proposed approach, which comes from an adequate splitting of the initial problem into simpler subproblems. Moreover, our method can be easily adapted to different types of noise by the way of specific data-fidelity terms for which an explicit expression of the proximity operator is available. Finally, we validate the proposed method on several simulated and real datasets using both the beam-propagation method (BPM) and the Lippmann-Schwinger forward model (LSm) together with a total-variation (TV) regularizer.
Validation on experimental data We validate our framework using the publicly available experimental datasets of the Institut Fresnel  [59]. In this experiment, the sensors were circularly distributed around the objects at a distance of 1. 67 m from their centers with 1 • step (see Fig. 3 ). Eight sources (E 1-8 ), uniformly distributed around the object, were activated sequentially. At each activation, the total field was measured using 241 sensors (S 241 ), excluding the sensors closer than 60 • from the source. We reconstructed the three targets FoamDielExt, FoamDielInt, and FoamTwinDiel using the TM polarization at 3 GHz (i. e. , λ = 10 cm). Each two-dimensional inhomogeneous sample is depicted in Fig. 4  (top row). The indicated permittivities were experimentally measured and are subject to uncertainties  [59].
Acquisition setup for the Fresnel dataset. The sensors (dots in the inner circle) correspond to the illumination angle of 0 • (i. e. , E 1 ). The measurements are restricted either by reducing the number of sensors (sensors sets S 241 ,. , S 91 ) or the number of acquired views (emitters E 1 ,. , E 8 ). S 181 S 151 S 121 S 241 S 91 sc 1 1 Fig. 3.
Our method relies on maximising the likelihood of a fixed number of panmictic populations, using a combination of geometric approach and fast likelihood optimisation, using the Expectation-Maximisation (EM) algorithm. It can be used for assigning genotypes to populations and optionally identify various types of hybrids between two parental populations. Several goodness-of-fit statistics can also be used to guide the choice of the retained number of clusters. 3. Using extensive simulations, we show that snapclust performs comparably to current gold standards for genetic clustering as well as hybrid detection, with some advantages for identifying hybrids after several backcrosses, while being orders of magnitude faster than other model-based methods. We also illustrate how snapclust can be used for identifying the optimal number of clusters, and subsequently assign individuals to various hybrid classes simulated from an empirical microsatellite dataset.
We also provide a worked example based on the analysis of a simulated dataset to illustrate typical results provided by the method. Here, snapclust is implemented in the package adegenet  (Jombart, 2008; Jombart & Ahmed, 2011)  for the R software (R Core Team 2017), thus being readily compatible with a wealth of tools for genetic data analysis in R  (Goudet, 2005; Jombart et al. , 2017; Kamvar, Tabima, & Grünwald, 2014; Paradis, 2010; Popescu, Huber, & Paradis, 2012).
| Model likelihood We consider a dataset of allelic profiles x = {x i,j } where i indexes individuals (i = 1, …, N) and j indexes loci (j = 1, …, J), so that x i,j is a vector of allele counts for individual i at locus j. The likelihood of our model is defined as the probability of observing these data given a clustering solution g = {g(i)}, where g(i) defines the group of individual i, with groups indexed by k = 1, …, K. Under the HW model, this likelihood is defined as: where M is the probability mass function of the multinomial distribution, f g(i),j is the vector of allele frequencies in group g(i) at locus j, and π is the ploidy of the organism considered. Allele frequencies within a group are directly computed as the relative frequencies of each allele in this group. Assuming independence between loci, the likelihood term for the genotype i is given by the following: where f g(i) = {f g(i),1 ,…, f g(i),J } and x i = {x i,1 , …, x i,J }.
| Starting point The EM algorithm typically converges very fast, generally within 10 iterations in the simulated and empirical datasets described here. Unlike some other optimisation procedures and MCMC, it is a deterministic algorithm, so that it always converges to the same solution for a given starting point (step 1). As a consequence, it is unfortunately also prone to being trapped in local maxima, yielding suboptimal results for some starting points. To avoid this issue, we implemented several options to define the initial clusters used as starting point of the algorithm. The first strategy, borrowed from the original implementation of K-means in R (R Core Team, 2017), is a "brute force" approach in which the algorithm is run multiple p(x i,j |f g(i),j , Π) = M(x i,j , f g(i),j , π) p(x i |f g(i) , π) = Π j p(x i,j |f g(i),j , π) p(x|f, g,π) = Π i p(x i |f g(i) , π) LL(g) = ∑ i ∑ j M(x i,j , f g(i),j ,π) p(g(i) = k) = p(x i |g(i) = k, f k , π)∕ ∑ q p(x i |g(i) = q, f q , π) f H,j (w) = wf A,j + (1 -w)f B,j p(x i |g(i) = H, f A , f B , w, π) = Π j p(x i,j |f H,j , π) times, using each time a randomly defined group assignment, and retaining the solution with the highest likelihood.
The second strategy which we introduce here is to use fast geometric approaches such as Ward's clustering  (Legendre & Legendre, 2012)  or K-means after dimension reduction  (Jombart et al. , 2010)  to set up the initial clusters. Based on our simulated datasets, random initial groups with 50 independent replicates, K-means, and Ward initialisation all gave similar results. By default, we recommend using Ward as it will be faster for most datasets. The three methods are available in the implementation of the algorithm, as well as any other user-defined initial clusters.
| Finding the optimal number of clusters The advantage of using a ML approach is that different models can be compared using classical goodness-of-fit statistics. While a full comparison of model selection techniques for genetic clustering is beyond the scope of the present paper, we have implemented four different information criteria shown to be useful for selecting the true number of clusters in the case of mixtures of distributions  (Akogul & Erisoglu, 2016). These statistics all rely on measuring the lack of fit of the model (deviance), and use different penalties for the complexity of the model (number of free parameters). The first, AIC  (Akaike, 1998) , is probably the most frequently used for models comparison. Noting L' the estimated maxima of LL(g), the AIC of our model is computed as: where the first term is the deviance of the model, and the second term corresponds to the complexity of the model, with P being the total number of alleles in the dataset across J loci.
| Implementation and availability snapclust is implemented in the R package adegenet  (Jombart, 2008; Jombart & Ahmed, 2011)  version 2. 1. 0, available via R's native package installation system as well as on github (https://github. com/thibautjombart/adegenet). The function snapclust. em implements the basic method, including different options for defining the initial state of the EM algorithm and the model for hybrids classification. The functions AIC, AICc, BIC and KIC implement the respective goodness-of-fit statistics. The function snapclust. em. choose. k derives clustering solutions for increasing numbers of clusters and computes the associated goodness-of-fit statistics, so that it can guide the choice of the optimal number of clusters. The method is documented in a dedicated online tutorial available by typing adegenet::adegenetTutorial('snapclust') in a R session.
| Simulated datasets without hybrids The datasets were simulated using QuantiNEMO  (Neuenschwander, Hospital, Guillaume, & Goudet, 2008)  with the parameters indicated in Table  1. We chose to simulate single nucleotide polymorphism (SNP) markers and explored a wide range of possible configurations by varying four simulation parameters: the number of loci, the dispersal model, the rate of dispersion, and the number of populations. The different rates of dispersal led to different levels of differentiation between populations. All combinations of dispersal rate and number of loci were tested as the number of loci and the differentiation level T A B L E 1 Parameters used in the simulations using the computer program QuantiNEMO are expected to define jointly the resolution of a panel of genetic markers  (Vähä & Primmer, 2006).
This led to 36 combinations of parameters. Ten independent random replicates were obtained for each combination leading to 360 simulated datasets. To avoid prohibitive computational times, we allowed the number of populations and the dispersal model to vary randomly across replicate, rather than adding systematically new combinations of parameters to the pool of data to simulate. The number of individuals per population was fixed to 100. AIC = -2L � + 2(K(P -J)) AIC c = -2L � + 2(K(P -J)N)∕(N -KP + KJ -1))) BIC = -2L � + ln(N)(K(P -J)) KIC = -2L � + 3(K(P -J) + 1).
| Simulated datasets with hybrids The simulated datasets used for the clustering of hybrids were derived from the previous simulations, by sampling two parental populations (P1, P2) at random in each of the 360 simulated datasets described before. For each, hybrids were simulated using the function While arbitrary, these sample sizes yielded a sufficient number of hybrids to analyse while retaining enough individuals to characterize the genetic makeup of parental populations.
| Analyses of simulated datasets without hybrids Our simulation study focussed on comparing snapclust to existing standard for the assignment of individual genotypes to groups (rather than inferring the true number of clusters). Therefore, the number of clusters was fixed to the known number of populations within the simulated dataset for all presented analyses. The clustering of individuals in absence of hybrids was performed using the snapclust, structure 2. 3. 4  (Falush et al. , 2003; Hubisz, Falush, Stephens, & Pritchard, 2009; Pritchard et al. , 2000) , BAPS 5. 4  (Cheng, Connor, Sirén, Aanensen, & Corander, 2013; Corander et al. , 2003; Tang, Hanage, Fraser, & Corander, 2009) , and adegenet's find. clusters (Jombart et al. , 2010). The snapclust analysis was carried out using default parameters (group assignment initialisation using the "ward" option).
We used two complementary measures to do so calculated on each of the 360 simulated dataset analysed. The true positive rate (TPR) was defined as the proportion of individuals belonging to the same population which were indeed clustered together by the method. The true negative rate (TNR) was defined as the proportion of individuals which did not belong to the same population and were adequately placed in different groups by the method. Note that the Rand index  (Rand, 1971) , which can be used for comparing unlabelled clusters, is proportional to (TPR + TNR), so that the present analyses should give a more detailed account of clustering results than the Rand index alone. The impact of the different simulation parameters on TPR and TNR was assessed using separate multivariate linear regressions.
As classical linear regression is designed to predict a response variable which can take any positive or negative values, a logit transformation was applied to the proportions, so that log(TPR/1 -TPR) and log(TNR/1 -TNR) were used as response variables. We preferred a linear regression on these rates to a binomial generalized linear model (GLM) for practical reasons. The calculation of TPR and TNR being based on all pairwise comparisons of individuals within simulated datasets, a binomial GLM would have required millions of observations to be included, leading to prohibitive computations. Instead, 360 TPR and TNR values were analysed, that is, one per simulation. We tested for the effects of the number of loci, the dispersal model, the overall F st between simulated populations, the number of populations, and the clustering method.
| Analyses of simulated datasets with hybrids The clustering of individuals in the presence of hybrids was carried out using snapclust and the computer program newhybrids  (Anderson & Thompson, 2002). The snapclust analysis was carried out, using the default parameters and specifying hybridisation coefficients for F1, first (BC1) and second (BC2)-generation backcrosses (hybrid. coef values: 0. 5, 0. 25, 0. 125). The NEWHYBRIDS analysis was carried out, using Jeffreys's prior and setting the burn-in period to 100,000, with a MCMC length of 500,000 iterations. Ten repetitions were carried out for each simulated dataset. Unlike the previous comparison, parental and hybrid classes are labelled, so that it was possible to compare the methods by directly examining how well they assigned individuals to their actual hybrid group, using the mean correct group assignment, computed as the proportion of individuals whose type (parental, F1, BC1 and BC2) was correctly identified.
| Illustration using microsatellite data To complement the simulation study which assessed the overall performances of our method, we illustrated its practical application by reproducing a typical analysis of microsatellite markers data, starting with the identification of the most likely number of clusters, followed by the assignment of individuals to groups, and the description of relationships between groups. We simulated hybrids from an empirical dataset of 30 microsatellite markers typed for 15 breeds  (Laloë, Jombart, Dufour, & Moazami-Goudarzi, 2007) , distributed as the "microbov" dataset in adegenet. Parental populations were obtained by sampling 30 individuals from the Lagunaire and 30 from the Salers populations. Hybrids were simulated using the function hybridize, to obtain 30 F1 hybrids, and then 30 of each first and second backcrosses, resulting in 210 individuals.
While arbitrary, these numbers replicate a situation where hybrids are more numerous than parental populations, as could be the case in nature when studying large hybridisation zones. We first carried out a global clustering analysis on this dataset, looking for the optimal number of clusters, using AIC (function snapclust. em. choose. k) in order to confirm that K = 2 parental populations was the optimal solution. We then looked for potential hybrids (function snapclust. em), using hybridisation coefficients corresponding to F1 (0. 5), first-generation backcross (0. 25, 0. 75) and second-generation backcross individuals (0. 125, 0. 875). Group membership probabilities were visualised using the function compoplot. As a complement, we also explored the diversity between hybrid classes using a discriminant analysis of principal components (DAPC;  Jombart et al.