dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction models (http://www. baci-h2020. eu/). This loss in information content should, however, be balanced against the associated benefits of re-using data in terms of time gain and resource savings. When tree rings are to be used as benchmarks for land surface models, the models will need the skill to mechanistically simulate tree-ring width (TRW). In the past decades, the major physiological and ecological processes that are responsible for annual tree-ring growth became sufficiently well-understood to be formalized in mathematical models with different levels of details and complexities. The first TRW models  (Wilson and Howard, 1968 ) described processes at the cell level: cell division, cell enlargement, and cell wall thickening. Later, the carbon and water balance of trees was added  (Fritts et al.
, 2004; Merganičová et al. , 2019)  rather than cell dynamics, the latter being computationally too expensive for large scale vegetation models  (Li et al. , 2014; Misson et al. , 2004; Sato et al. , 2007). Hence, a variety of approaches are now available to describe TRW growth in forest models, dynamic vegetation models and landsurface models, but to the best of our knowledge there is yet no land surface component of an Earth system model with such capability. This study articulates an improved conceptual framework for benchmarking simulated radial growth against ITRDB tree-ring data, addressing limitations in the models, the data and the methods to compare models and data. The aims are to: (1) use current understanding of tree-ring growth to derive the minimal requirements for benchmarking land-surface models against https://doi.
(v) The final term in the aggregate tree growth model constitutes all processes and interactions between processes not previously accounted for in the land-surface model, and will make up the model error. This aggregate tree growth model provides the conceptual basis for tree-ring standardization and climate signal extraction methods used in dendrochronology  (Briffa and Melvin, 2011; Cook and Kairiukstis, 1990) , which rely on the assumptions that the sampled trees capture the relevant growth variability of the stand and that the contribution of each major driver can be statistically identified as either signal or noise. If tree-rings are formed, observed TRW records cannot, however, be fully decomposed in the absence of metadata because several drivers do not leave a unique fingerprint in the tree-ring record.
Challenges of using ITRDB data as a long-term benchmark Despite of known biases in the ITRDB, it can be used to extract information useful for LSMs. The predominant sampling design in the ITRDB targets the presumably oldest trees, which should give the longest time series and are therefore be most useful to reconstruct the climate variability prior to instrumental records. The ITRDB is thus likely to overrepresent large trees  (Brienen et al. , 2012; Nehrbass-Ahles et al. , 2014)  relative to the population demographics at time of sampling. This big-tree bias makes the ITRDB unsuitable to upscale growth of individual trees to larger spatial domains, i. e. , stand, forest or the region  (Babst et al. , 2014a; Nehrbass-Ahles et al. , 2014)  but does not affect the value of the ITRDB archive for documenting individual tree growth as long as tree size and dominance effects are explicitly considered.
, 2012). The other challenge of using ITRDB data is rooted in the difference between the observed and simulated forest structure. Treering datasets are composed by cores of individuals from different cohorts (Fig. 3b ). Comparing these data against simulations requires the model to be individual based or to align TRW records by age (Fig. 3a ). Given the above, only part of the information contained in TRW records can be used for benchmarking if their sampling protocol is poorly described or not rigorously enforced. A model-data comparison cannot correct for these biases but consistency between modelled and observed tree-rings for a stand under study can be improved by making use of virtual trees. As the output of LSMs must be coupled to realistic models for TRW, careful post-processing of the ITRDB data may be required to become suitable benchmarks for land surface models.
In this study we use a climate data product from a merged and homogenized gridded dataset developed for modelling purpose over the 20 th century, i. e. , CRU-NCEP (Viovy, 2016), such that observed tree-ring widths for the past century can be used to evaluate the skill of the land-surface model ORCHIDEE r5698 to simulate radial tree growth. A detailed overview of earlier developments  (Krinner et al. , 2005; Naudts et al. , 2015; Vuichard et al. , 2019)  that resulted in the emerging capability of ORCHIDEE r5698 to match the aggregate tree growth model (Fig. 2 ) is given in the supplementary material (Text S1).
Reference data of ecologically sampled TRW data A "fixed-plot approach" TRW database was established under the BACI project (http://www. baci-h2020. eu/) by archiving 48 datasets from multiple research efforts in Europe  (Klesse et al. , 2018). To be retained and archived, all trees larger than 5. 6 cm in diameter had to be sampled in a 10 to 40 m radius plot of which the exact radius depended on stand density  (Babst et al. , 2014). The BACI archive is, therefore, considered to be free from the big-tree selection bias which is present in the ITRDB. The records from BACI were used to evaluate the validity of using virtual trees constructed from ITRDB records to combat the aforementioned sampling biases. For all four benchmarks each reflecting a different usage of the information contained in the ITRDB, the virtual trees were constructed by making use of only the top 15% of the trees based on their diameter.
Test case As the test case aimed at illustrating the four benchmarks rather than evaluating the ORCHIDEE model itself, the main objective of the test case is confirming that each benchmark indeed tests different aspects of the model's performance and that the proposed benchmarks can, therefore, be considered complementary to each other. The four benchmarks presented above were applied to a test case consisting of ten Pinus sylvestris L. sites across Europe. For each site the dataset consisted of 11 to 304 cores (Table  S2 ); a leave-one-out approach was used to evaluate the sensitivity of the benchmark to individual tree records. For the simulations, the land-surface model ORCHIDEE r5698 was used. This model versions accounts for the aforementioned minimum requirements for land surface models to mechanistically simulate TRW.
, 2018; Nickless et al. , 2011) , as well as sampling biases  (Babst et al. , 2014a) , can be better accounted for. Whereas previous studies had to rely on a single qualitative benchmark, i. e. , interannual variability, our method shows that at least four benchmarks, each of them defined by two metrics, are available for models that meet the minimal requirements to simulate TRW determined by Cook's aggregate tree growth model (Fig. 2 ). Irrespective of the model approach, the largest archive of tree-ring records that is freely available to the land-surface community, i. e. , the ITRDB, is notorious for its sample biases  (Klesse et al. , 2018; Zhao et al. , 2019). Although it may be difficult to correct the data for these biases, we propose two solutions for comparing LSM output to biased observations.
Simulating a size-structured population of trees enables comparing the observations relative to a benchmark tall simulated tree, which compensates for the tendency of dendroclimatic samplers to select the oldest trees in a stand (which often turn out to be the larger trees). Although the ITRDB does not contain the site metadata that would be required to make this comparison exact, i. e. , the diameter and true age distribution of the sampled stand, it protects against comparing extreme samples to mean simulations. The second solution relies on the observation that the variation due to size-related growth by far exceeds the variation due to environmental changes and helps to constrain the survivor bias which is derived from the growth of young fast-growing trees that died a long time ago and are therefore absent from records made from present day sampling of old growth forests.
It is also unstable in longrange LD regions such as the human leukocyte antigen (HLA) region of chromosome 6. This issue has led to the removal of such regions from analyses  (Marquez-Luna et al. 2020; Lloyd-Jones et al. 2019) , which is unfortunate since this region of the genome contains many known disease-associated variants, particularly with autoimmune diseases and psychiatric disorders  (Mokhtari and Lachman 2016; Matzaraki et al. 2017). Here, we present LDpred2, a new version of LDpred that addresses these issues while markedly improving its computational efficiency, allowing exploring a larger grid of parameters in the same computational time as LDpred1. We provide this faster and more robust implementation of LDpred in R package bigsnpr  (Privé et al. 2018). We also provide two new options in LDpred2.
Simulations Figure  1  presents the simulation results comparing LDpred1 (v1. 0. 0 as implemented by  Vilhjálmsson et al. (2015) ) with the new LDpred2 (as implemented in R package bigsnpr). Seven simulation scenarios are used, each repeated 10 times. 300,000 individuals are used for computing the GWAS summary statistics, 10,000 for computing the LD matrix and choosing the best-performing hyper-parameters, and the remaining 52,320 individuals for testing. In the first four simulation scenarios, a heritability h 2 of 40% and a prevalence of 15% are used. We simulate 300, 3000, 30,000 or 300,000 causal variants anywhere on the genome. In these scenarios, infinitesimal models perform similarly. When testing a grid of hyper-parameters, LDpred2 performs substantially better than LDpred1 in the cases where the number of causal variants is small, i.
Real data Figure  3  presents the results of real data applications comparing LDpred1 (v1. 0. 0 as implemented by  Vilhjálmsson et al. (2015) ) with the new LDpred2 (as implemented in R package bigsnpr) when run genomewide. Eight case-control phenotypes are used, summarized in table 2. For BRCA, CAD, MDD, PRCA, T1D and T2D, LDpred2-inf and LDpred2-grid perform much better than LDpred1-inf and LDpred1-grid respectively. For example, for BRCA, AUC improves from 58. 9% with LDpred1-grid to 65. 5% with LDpred2-grid, and from 57. 4% to 78. 4% for T1D. For Asthma and RA, predictive performance of LDpred1 and LDpred2 are similar. As in simulations, the sparse version of LDpred2-grid performs as well as the non-sparse version. Sparsity of resulting effects ranges from 19. 3% for RA to 54. 4% for Asthma (Table  S5 ).
We also use a larger window size for computing correlations between variants (see above), yet LDpred2 is still as fast as LDpred1. The efficiency of LDpred2 is achieved through an efficient parallel implementation in C++. Efficient parallelization over the grid of hyper-parameters is possible because we use an on-disk sparse matrix format accessed using memory mapping. This new data format is available in R package bigsparser, which has been developed for this paper. It takes between 12 and 36 hours to run all the LDpred2 models over 1. 1 million HapMap3 variants at once (genome-wide) using 30 cores; LDpred1 takes a similar time (note that LDpred1 cannot be easily run in parallel). It takes a little more than two hours to pre-compute the LD matrix for 10,000 individuals and 1. 1 million HapMap3 variants (using 16 cores).
LDpred2-auto is an attractive option in many applications, especially since we also provide an LD reference that can be used directly (Section "Software and code availability"). LDpred2-auto almost always performs equally well as LDpred2-grid in simulations as well as in real data applications. However, LDpred2-auto requires that some quality control is performed on summary statistics (see Methods section "Quality control of summary statistics"). This quality control aims at ensuring that effects are transferable from the external GWAS summary statistics to the data where PGS are computed. Note that this quality control is also beneficial for other methods such as lassosum (data not shown). Even when this quality control is performed, LDpred2-auto can slightly underperform in some situations, e.
Simulation analyses We use the UK Biobank imputed data for both real data analyses and simulations  (Bycroft et al. 2018 ). We use dosage data for LDpred2, which we read from BGEN files using function snp_readBGEN from R package bigsnpr  (Privé et al. 2018). For the other software that require a PLINK bed file as input, we use function snp_writeBed that round dosages to write genotype data in bed format. We restrict individuals to the ones used for computing the principal components (PCs) in the UK Biobank (Field 22020). These individuals are unrelated and have passed some quality control including removing samples with a missing rate on autosomes larger than 0. 02, having a mismatch between inferred sex and self-reported sex, and outliers based on heterozygosity (more details can be found in section S3 of  Bycroft et al.
Such simulation of phenotypes based on real genotypes is implemented in function snp_simuPheno of R package bigsnpr. We also vary the sample size to compute GWAS summary statistics in the scenario with 3000 causal variants; in addition to a GWAS sample size of 300,000, we also use 10,000, 20,000, 50,000 and 120,000. We design two other simulation scenarios with 300 or 3000 causal variants randomly chosen in the HLA region (chromosome 6, 25. 5-33. 5 Mb). In these two scenarios, we use h 2 = 0. 3 instead of h 2 = 0. 4 because the total heritability is gathered in one chromosome only. Finally, we design a seventh simulation scenario as a mixture of previous scenarios; we simulate 300 causal variants in the HLA region explaining 20% of the variance in liability, and 10,000 causal variants anywhere on the genome explaining another 20% (h 2 = 0.
Real data analyses We use the same data as in the simulation analyses. We use the same 10,000 individuals as validation set, and use the remaining 352,320 individuals as test set. We use external published GWAS summary statistics listed in table 2. We defined phenotypes as in  Privé et al. (2019). Briefly, we use self-reported illness codes (field 20001 for cancers and 20002 otherwise) and ICD10 codes (fields 40001, 40002, 41202 and 41204 for all diseases and field 40006 specifically for cancers). Some quality control is applied to summary statistics (see Method section "Quality control of summary statistics" below). For more details, please refer to our R code (Software and code availability section). In real data applications, we first compare all four LDpred2 models to the two LDpred1 models.
We use the Area Under the ROC Curve (AUC) to compare methods. We sample 10,000 bootstrap replicates of the individuals in the test set and compute the AUC for each of these. We then report the mean of these 10,000 values, along with their quantile at 2. 5% and at 97. 5% to act as the 95% confidence interval (CI) for the AUC. This is implemented in function AUCBoot of R package bigstatsr.
Then we get γjoint = S -1 R -1 Sγ marg. (1) In practice, the correlation matrix R is usually not available but is computed from another dataset. Also note that γ are the effects on the allele scale while we denote by β = Sγ the effects of the scaled genotypes. For the marginal effect γj of variant j, let us denote by y and Gj the vectors of phenotypes and genotypes for variant j residualized from K covariates, e. g. centering them. Then, (se(γ j )) 2 = (y -γj Gj ) T (y -γj Gj ) (n -K -1) Gj T Gj ≈ yT y n Gj T Gj ≈ var(y) n var(G j ). The first approximation is possible because γj is expected to be small, while the second approximation assumes that the effects from covariates are small. Thus we can derive sd(G j ) ≈ sd(y) se(γ j ) √ n (2) and then (sd(G j ) γj ) ≈ γj se(γ j ) sd(y) √ n. Let us go back to equation 1.
Quality control of summary statistics For summary statistics of binary traits derived from a logistic regression, instead of equation (  2 ), we have sd(G j ) ≈ 2 se(γ j ) √ n eff , (3) where n eff = 4 1/n case + 1/n control. We strongly recommend to verify this assumption and to perform some quality control. Indeed, in simulations, the approximation of equation (3) seems valid (Figure  S6 ). However, in real data applications, where summary statistics come from a meta-analysis of many external datasets, this approximation can be invalidated (Figure  S7 ). Let us denote by SD ss the standard deviations derived from the summary statistics (right-hand side of equation (  2 ) or (  3 )) and by SD val the standard deviations of genotypes of individuals in the validation set (left-hand side). Note that, in order to compute SD ss in the case of summary statistics from a linear regression, sd(y) from equation (  2 ) can be estimated e.
New LDpred2 models LDpred2 comes with two extensions of the LDpred model. The first extension consists in estimating p and h 2 within the model, as opposed to testing several values of p and estimating h 2 using constrained LD score regression  (Bulik-Sullivan et al. 2015). This makes LDpred2-auto a method free of hyper-parameters which can therefore be applied directly to data without the need of a validation dataset to choose best-performing hyper-parameters. To estimate p in the Gibbs sampler, we count the number of non-zero variants (i. e. M c = j (β j = 0) in equation 7). We can assume that M c ∼ Binom(M, p), so if we place a prior p ∼ Beta(1, 1) ≡ U(0, 1), we can sample p from the posterior p ∼ Beta(1 + M c , 1 + M -M c ). Due to complexity reasons, we could not derive a Bayesian estimator of h 2.
We provide function snp_asGeneticPos in package bignspr to easily interpolate physical positions (in bp) to genetic positions (in cM). We recommend to use genetic positions and to use a size parameter of 3 cM when computing the correlation between variants for LDpred2. Note that, in the code, we use 'size = 3 / 1000' since parameter size is internally multiplied by 1000 in the bigsnpr functions.
Providing an LD reference We provide an LD reference for European ancestry to be used by researchers who cannot compute their own. We use the 362,320 UKBB individuals as used here, with some further quality control based on allele frequencies. Indeed, some large allele frequency mismatches have been reported recently in the UKBB when comparing to other datasets, which are apparently due to mismappings  (Kunert-Graf et al. 2020). Note that most of these errors should be captured by the quality control we propose in this paper. Using 503 European individuals from the 1000 Genomes (1000G) data, we remove variants with allele frequency differences between UKBB and 1000G at p < 10 -5 (Figure  S10 ). We also remove variants with minor allele frequencies less than 1% in the 1000G or less than 0. 5% in the UKBB.
Acknowledgements Authors would like to thank the four reviewers of this paper for their relevant comments and valuable suggestions,  Naomi Wray  and  Alkes Price  for pointing to issues due to long-range LD regions in LDpred1,  Yixuan Qiu  for pointing to matrix-free solvers,  Doug Speed  and others for early testing of the software and for providing useful feedback, GenomeDK and  Aarhus University  for providing computational resources and support that contributed to these research results. This research has been conducted using the UK Biobank Resource under Application Number  41181.
Hence, this author showed that a Voigt circuit including n RC elements could exactly represent any linear circuit at n experimental impedance points although no discussion of the values of the circuit parameters was provided. As pointed out by a referee of this article, "Boukamp wrote a KK test program that carries out exact approximation in all the frequency points of the data file (to check KK transforms). The program KKtest. exe might be found on the Boukamp Web page and it is also included in the free Extra Material to the EIS book  [7]. The above program deals with both diffusion and kinetic-diffusion impedances". More recently, Schönleber and Ivers-Tiffée  [8]  questioned about the approximability of impedance spectra by serially connected RC elements, and its implications for impedance analysis.
(2019) , which also provides a python implementation of  Yadav and Michalak (2013)  and can also avoid most of the work when performing a multiple inversions where only the prior mean estimates differ. CarbonTracker-Lagrange additionally applies sparse matrix methods to reduce the memory requirements. The inversion framework presented here is tested in a series of pseudo-data experiments over North America, demonstrating the potential of this approach to solve for subdaily surface CO 2 fluxes at 27 km resolution, similar to the resolution of the mesoscale atmospheric simulations used to drive the transport. The present framework is a step toward ensembles of multi-year inversions at sub-daily temporal resolution with limited memory requirements.
e. LPDM particle release locations). Fluxes are aggregated over Influence functions for nine selected tower locations (available from  Wesloh & Lauvaux, 2019)  are presented in figure  1 ; a description of that network is given in section 2. 5. The inversion provides the most potential for improvement where the fluxes have the greatest influence on the measurement towers. For this combination of month and tower network, much of the Rockies, Mexico, and southeastern Canada do not strongly influence the observations, and so can not be effectively constrained by the inversion. Most corrections in these regions will be due to correlations with corrections in regions better constrained by the tower network. LPDM gridding software was written to keep computational demands low while post-processing continental-scale simulations.
Details on where to find this code are available in appendix Appendix A. LPDM has been used in multiple previous inversion studies  (Lauvaux, Schuh, Uliasz, et al. , 2012; Schuh et al. , 2013; Wu et al. , 2013; Lauvaux & Davis, 2014; Lauvaux et al. , 2016). A recent comparison of WRF-and LPDM-calculated mole fractions is presented in  Karion et al. (2019) , an older comparison of Lagrangian dispersion models is presented in  Potempski et al. (2008) , and both studies additionally compare both WRF and LPDM to observations. A similar comparison of WRF-calculated to LPDM-calculated mole fractions for the towers used in this study showed model-model agreement within a few ppm and good correlation when there were strong signals in the data.
Observation Network This paper considers a network of pseudo-observations corresponding to permanent tall towers from the National Oceanic and Atmospheric Administration (NOAA) network. The Global Monitoring Division (GMD) has deployed and maintained a network of eight towers over the last 15 years offering a continuous and high-accuracy measurement network to perform continental-scale inversions of greenhouse gases  (Andrews et al. , 2014). Seven of the eight towers were selected for our experiments covering different regions of North America: the Great Lakes (LEF), the upper Midwest (WBI), the southeastern US (SCT), the southern Great Plains (WKT), New England (AMT), the Mid-Atlantic (SNP), and the Rocky Mountains (BAO). The selected tower locations are marked by circles in figure  1. These seven towers are enough to demonstrate the system, and would be expanded to include more of the North American network of calibrated CO 2 mole fraction observations in a real-data inversion.