dataesr/scientific-paragraphs-categorization huggingface dataset:
Study area and data descriptions China is large in its area, and different climate types are encountered in the mainland  (Kottek et al. , 2006). To facilitate the comparisons and analyses that have spatial variations, ten different subregions are defined in Figure  3  as the (1) Songhua River Basin, (2) Liao River Basin, (3) Hai River Basin, (4) Yellow River Basin, (5) Huai River Basin, (6) Yangtze River Basin, (7) Southeast China, (8) South China, (9) Southwest China, (10) Northwest China. The entire Chinese mainland is numbered as the 11 st region. Most of the regions are natural river basins, and this definition is more natural when considering water resources analysis than definitions using longitude-latitude grids or that are based on administrative regions. Thirteen precipitation datasets from different sources are collected for comparison (Table  1 ).
These datasets are categorized Among the merged precipitation products, the CMAP, GPCP and MSWEP use different sources of precipitation data (e. g. , gauge observations, satellite remote sensing, atmospheric model re-analysis). These different precipitation sources are averaged using different weights. Thus the differences among the three merged products are associated with the precipitation sources and the weight of the gauge observations. ERA-Interim is a re-analysis product, while it uses near-real-time assimilation with data from global observations  (Dee et al. , 2011). Thus the forecasting model is constrained by observations and forced to follow the real system to some degree. Because of the usage of observations, ERA-interim is also belonging to the merged products. GCM precipitation is model estimation, therefore, the physical and numerical choices will affect the accuracy of model results.
In addition, observations are not used to constrain the simulations. The lack of constraints on the GCMs will cause them not following the actual synoptic variability and explore other trajectories in the solution space. Kay et al. (2015)  repeatedly run the same GCM with a very small difference in the initial conditions, and there is a spread of the model outputs after a number of time steps of running (see Figure  2  in  Kay et al. , 2015). Therefore, the uncertainty estimated is due to the differences in the model settings and the initial conditions. There are more than 20 datasets of GCMs, while only four are randomly taken to match the number of gauge-based products and merged products. All the datasets have been interpolated to 0. 5 o spatial resolution to unify the spatial units and the overlap time span of all the datasets is from 1979 to 2005 for the maximum coverage of all products.
Spatial patterns of ensemble annual precipitation The ensemble means of the long-term annual precipitation , obtained by averaging the multiple datasets in the corresponding precipitation group, are mapped in Figure  4. The long-term annual mean precipitation obtained from the CMA data is 589. 8 mm yr -1 (1. 6 mm day -1 ) over mainland China. The gauge-based precipitation has the least bias (-4. 1mm yr -1 , -0. 7% in proportion) compared to the CMA precipitation. Precipitation in the merged products and GCMs is larger than CMA by 63. 1 and 232. 0 mm yr -1 (with the bias as +20. 4% and +41. 3%), respectively. The spatial pattern of the annual precipitation shows a decreasing gradient from the southeastern China (>1600 mm yr -1 ) to the northwestern China (<400 mm yr -1 ). All the ensemble means of the three precipitation groups capture the spatial gradient, while they have different ability to express in some details.
Spatial distribution of model uncertainties In addition to differences of the long-term annual precipitation, differences are found among datasets within the same precipitation group. The spatial distribution of the model uncertainty, which is expressed as the ensemble deviation across multiple products of the annual precipitation, is calculated for each group and mapped in Figure  5. Among the datasets based on gauge observations (Figure  5-a ), the ensemble deviation value is small in most land area of China (<50 mm yr -1 ). It is higher in the south of China (50-100 mm yr -1 ) but the area is not continuous in space. The highest deviation occurs along the Himalayas, indicating a high variation among datasets. Regarding the merged precipitation products, the deviation shows high values (>200 mm yr -1 , Figure  5-c  The magnitude of the ensemble deviation demonstrates the model uncertainty among different precipitation products in the same precipitation group and it shows the ability of the precipitation estimation with different methodologies.
The temporal evolution of the gauge-based products and merged products agree well with that of the CMA dataset, while the temporal evolution of GCMs ensemble is weaker and not well correlated with that of the CMA. The main reason is that GCMs are not constrained in their synoptic variability and the sequence of the wet and dry years can be very different from that of the observations. So a smoother result can be obtained when we build the ensemble means from the GCMs. While this is different for the gauge-based and merged products, as they have a strong co-variance and the ensemble mean preserves this co-variance. For the entire mainland of China (Figure  6 -k), the ensemble deviation remains stable for different precipitation groups. In contrast, the annual precipitation spans the largest spatial heterogeneity in the mainland compared to those divided subregions (Figure  4 ).
Variations in the time and space dimensions The precipitation varies in time and space, however, it is averaged either in the time dimension to obtain the spatial patterns of model uncertainty (Figure  5 ) or in the space dimension to obtain the temporal evolution of the model uncertainty (Figure  6 ). But the deviations in the time and space dimensions are indeed very rarely compared. Herein, the standard deviation of the temporal and spatial variations in the precipitation datasets are compared in Figure  7  in ten subregions and the Chinese mainland for different precipitation groups. The gauge-based products provide similar annual regional precipitation to CMA over the China mainland and ten specific regions except for the region 7-southeast China (Figure  7 -g) and region 9-southwest China (7-i).
It might indicate the decreased ability of remote sensing, the important data source in the merged products, to estimate the precipitation amount in storms as the storms mainly contribute to the total precipitation for the two subregions. The regional precipitation is larger in merged products than that of observations and the magnitude of the deviation in GCMs is even larger except in the region 8-south China (Figure  7-h ). These results indicate the reduced ability of merged products and GCMs in reproducing the total value of the annual precipitation. Regarding the variations in time and space dimensions, the regions 9, 10 and 11 have the largest ratio of the spatial standard deviation (to the mean), indicating the most significant spatial heterogeneity over the regions. The 7-southeast and the 3-Hai River have the smallest variations either because of the small area or because of the homogeneity in the subregion as the Ratio of the spatial standard deviation to the mean Ratio of the temporal standard deviation to the mean The P values in the left bottom is the annual precipitation of CMA.
spatial correlation is high in the area. The relative ratio of the temporal standard deviation to the spatial standard deviation is among the smallest in the regions 9, 10 and 11 (k=0. 1, 0. 12 and 0. 05, respectively. k is the ratio of the temporal deviation to the spatial deviation), showing an apparent difference between the variation in the time and space dimensions. While, the difference between variation in two dimensions is small in the 3-Hai River basin (k=1. 15) and 7-southeast China (k=0. 90), mainly because the relatively strong variability of the annual precipitation in different years. In addition to the differences across regions, the variations in different precipitation groups are also different. Excluding the CMA dataset which only consists of one single product, the variations in the gauge-based products are higher than that of the other two groups.
V s is higher in the precipitation of GCMs especially in the 9-southwest China, indicating the strong spatial heterogeneity in the GCM models over the Himalayas (Figure  8-i ). The ensemble variance (V e ) is relatively small in most regions in gauge-based products (Figure  8 -j), with the In conclusion, the grand variance and individual variance for each of the three different dimensions are generally larger in the dataset group consisting of GCMs. The variations for the gauge-based products and merged products are similar in values and spatial distribution. However, in addition to the variances, the uncertainty defined as the ratio of the square root of the variance to the mean (i. e. , U , U t , U s , U e ) contains extra information of the regional means, and will be discussed in the next section.
These two components are related to the two classic metrics N. s. std (Eq. 28) and N. t. std (Eq. 29), respectively. By decomposing the Eq. (  30 ), the contributions of the four components to the ensemble variance (V e ) are shown in Figure  11. For all three precipitation groups, σ 2 e is the dominant component simply because all the information on variations among the original datasets is retained in the uncertainty estimation. While, the other three components are estimations after averaging is performed in time, space or the full spatiotemporal dimensions, which indicates a loss of information. The contribution of the σ 2 e_t and σ 2 e_s is approximating 0. 15 for regions from 1 to 8. While the σ 2 e_t increases for the region 9, 10 and 11, indicating that the spatial heterogeneity is significant for these regions.
On the contrary, σ 2 e_s decreases because the spatial averaging has collapsed the spatial variations. The very small contribution of σ 2 e_s related to N. t. std is the cause for larger deviations between N. t. std and U e (Figure  10-b ). Although all the components can be used as metrics for evaluating the variations among multiple datasets, there are limitations for each of the variations. For the variation of temporal mean σ 2 e_t and spatial mean σ 2 e_s , the collapse of a dimension has ignored part of the information (also introduced in the Introduction). Moreover, the variation of the grand mean σ 2 e (µ ts ) has ignored both the temporal variability and spatial heterogeneity, which further decreases its applicability in uncertainty assessment. The variation σ 2 e is estimated based on the original data without averaging, and thus represents the most information.
In the extreme cases, U e is larger than twice N. t. std (Figure  12-b ). The results show that the known uncertainty estimated by the two classic metrics, which have been widely applied to climatic analysis, have underestimated the uncertainty among different models / datasets, which has been assumed when introducing the peculiarity of the new method. The underestimation may especially occur for assessment of temporal evolution of the uncertainties (N. t. std), which is very commonly seen in scientific reports and articles to illustrate the temporal evolution of the variables of interest. 6 Discussion and Conclusion.
Features and applicability of the approach The proposed variance partitioning approach works in three dimensions, and it is able to use all of the information in the time and the space dimensions among the multiple ensemble members. The proposed U e estimation technique is especially suitable for the overall assessment of the variations among multiple datasets over a certain period and over a specific space. Though, the compensation is that the U e technique cannot provide the temporal evolution or spatial heterogeneity for users' consideration. However, in most cases we would like to know the general performance of the ensemble models with single estimate. The two classic metrics (eqs. 28 and 29) are also single values but their estimation has averaged the variations which means a loss of informations.
Figure2. The illustration of the partitioning time-space-ensemble variance method. The original dataset is reorganized into three dimensions of time, space and ensemble. The denotations of the zones are listed to the right. The grand variance is defined as σ 2 and the grand mean as µ. The subscripts t, s, and e represent time, space and ensemble, respectively. Zone A (µi) indicates the means of the i dimension; zone B (σ 2 i ) indicates the variation for i dimension; zone C (σ 2 i_j ) indicates the variation across i dimension of the means of µj; zone D (µij) indicates the means across i and j dimensions; zone E (σ 2 ij ) indicates the variation across i and j dimensions; zone F (σ 2 i (µ jk )) indicates the variation across i dimension of the means across j and k dimensions. The detailed definitions of these denotations can be found in Appendix A.
into three groups according to the methodologies used to generate the products, i. e. , gauge-based products, merged products and General Circulation Models (GCMs). The gauge-based products (i. e. , GPCC, CRU, CPC and UDEL) use observed data 9 Hydrol. Earth Syst. Sci. Discuss. , https://doi. org/10. 5194/hess-2019-49 Manuscript under review for journal Hydrol. Earth Syst. Sci. Discussion started: 5 February 2019 c Author(s) 2019. CC BY 4. 0 License. from global atmospheric gauges, while the density of ground observation gauges, the representatives of the gauges and the interpolation algorithms for converting the gauge observations to grids dataset vary from product to product. CMA (provided by China Meteorological Administration) dataset uses the densest gauges and probably has the best quality to capture the spatiotemporal variations of the precipitation.
Figure6. The temporal evolution of the model uncertainty, which is expressed as the normalized ensemble deviation of annual precipitation across datasets in each precipitation group for specific subregions. The value on the top right of each panel is the annual regional precipitation estimated in CMA dataset. The annual precipitation is normalized as the ratio to the CMA long-term annual precipitation. The shaded area represents the standard deviation of the annual precipitation in each year among the datasets within that group (divided by the annual precipitation of the corresponding group).
datasets. The new uncertainty metric (U e ) is estimated with an overall consideration of temporal and spatial variations among the ensemble products. Results show that U e is generally larger than the classical uncertainty metrics N. s. std and N. t. std which require a collapse in either of the time or space dimension. The deviation occurs where the spatial variations are significant but being averaged in N. t. std estimation. The decomposing of the V e shows the complementary relation of the two classic metrics and therefore the new uncertainty estimation (U e , derived from V e ) technique is a more comprehensive estimation way of uncertainty for multiple datasets. Thirteen precipitation datasets generated by different methodologies are categorized into three groups (i. e. , gauge-based products, merged products and GCMs) and the model uncertainty in the ensemble products in the same group is analyzed with the new and two classic uncertainty metrics.
Acknowledgements. This study was supported by the  National Natural Science Foundation of China  (grant nos. 41561134016  and  51879068 ); the  CHINA-TREND-STREAM French national project (ANR grant  no. ANR-15-CE01-00L1-0L ); the  National Key Research and Development Program  ( 2018YFC0407900 ) and the  China Scholarship Council  (CSC, 201506710042). The work was supported by computing resource of the  IPSL ClimServ cluster at École Polytechnique, France.
Data availability. The CMA dataset is available through website http://data. cma. cn/data/detail/dataCode/SURF_CLI_CHN_PRE_MON_ GRID_0. 5/ (Zhao et al. , 2018) ; The GPCC dataset is available at https://doi. org/10. 5676/DWD_GPCC/FD_M_V2018_050 (Schneider et al. , 2018)  ; The CRU dataset is available at https://doi. org/10. 5285/edf8febfdaad48abb2cbaf7d7e846a86 (University of East Anglia Climatic Research Unit et al. , 2017); The CPC dataset is available at http://ftp. cpc. ncep. noaa. gov/precip/CPC_UNI_PRCP/ (Xie et al. , 2007) ; The UDEL datasets is available at http://climate. udel. edu/data (Willmott and Matsuura, 2012) ; The CMAP dataset is available at https://www. esrl. noaa. gov/psd/data/gridded/data. cmap. html (Xie et al. , 2003) ; The GPCP dataset is available at https://www. esrl.
noaa. gov/psd/data/gridded/ data. gpcp. html (Adler et al. , 2018) ; The MSWEP dataset is available at http://gloh2o. org (Beck et al. , 2017); The ERA-I dataset is available at https://www. ecmwf. int/en/forecasts/datasets/archive-datasets/reanalysis-datasets/era-interim (Dee et al. , 2011) ; The CMIP5 GCMs products are available at https://esgf-node. llnl. gov/projects/esgf-llnl/.
Acknowledgements This work was supported by funding from the  European Research Council  under the  Seventh Framework Programme  ( FP7) ,  ERC  grant  N°290424 -RheoMan. J. M. J. is thankful for support from the  National Science Foundation (NSF)  under  EAR-CSEDI-1316362  and W. M. Keck Institute for Space Studies. J. S. P. was supported by  NSF   EAR-PF #14-52545. We are thankful to the  CIDER program  set at the  Kavli Institute for Theoretical Physics, University of California, Santa Barbara  ( NSF EAR-1135452 , funded under the  FESD Program ).
Acknowledgments. The authors are gratefull to  Philippe Courville  and  Damien Gendry  ( University of Rennes 1, Rennes, France ),  Sandra Delaunay  and  Thibault Keinerknecht  ( Musée Aquarium, Nancy, France ),  Annelise Folie  ( Institut Royal des Sciences naturelles de Belgique, Bruxelles, Belgium )  Claire Mellish  ( Natural History Museum, London, United Kingdom ),  Christian Neumann  and  Andreas Abele  ( Museum für Naturkunde, Berlin, Germany ),  Günter Schweigert  ( Staatliches Museum für Naturkunde, Stuttgart, Germany ),  Ingmar Werneburg  ( Eberhard Karls Universität, Tübingen, Germany ) and  Walter Etter  ( Naturhistorisches Museum, Basel, Switzerland ) for the access to the fossils housed in the collections of their respective institutions. We also greatly thank  Alessandro Garassino  ( Museo di Storia Naturale di Milano, Milan, Italy ),  Christian Klug  ( University of Zurich, Zurich, Switzerland ) and  Neil Landman ,  Bushra Hussaini  and  Stephen Thurston  ( American Museum of Natural History, New York, United States ) for searching and supplying photographs of the specimens stored in the collections of their institutions.
In Situ Data Thanks to international programs such as GEOTRACES (www. geotraces. org), several recent cruises allowed further documentation of dissolved and particulate iron concentrations, among other trace elements. In addition to the modeling results, we used in this paper an updated compilation of measurements gathered in a database of DFe for the global ocean (http://pcwww. liv. ac. uk/~atagliab) that has been published in  Tagliabue et al. (2012). The original database gathered >13,000 measurements to which 9,612 recent observations have been added for the purpose of this study. Despite these observational efforts, Figure  3  shows that the spatial distribution of DFe data remains quite sparse. Nevertheless, some large-scale patterns can be identified, such as (i) the high surface DFe concentration in the Atlantic ocean due to the Saharan dust inputs, (ii) an overall increase from the surface toward greater depths, and (iii) a well-marked coastal to offshore regions gradient.
Characterization of the dissolution rates for each types of sediment present at global scale would then need to be gathered from experiments that have yet to take place. Moreover, the dependence of those dissolution rates to abiotic (e. g. , light, temperature) and biotic (bacterial activity) environmental factors have to be assessed in order to refine the model. Indeed, those processes may explain the differences between the slow dissolution rates derived from the experimental data and the higher indirect estimation computed from in situ observations in  Slemons et al. (2012). This study does not aim at improving, at this stage of our knowledge, the simulated dissolved iron distribution through the addition of a PFe Inorg compartment. Such a validation would require a global database distinguishing and quantifying for each sample the particulate iron from different origins (eolian, hydrothermal, sedimentary, or biogenic).
Acknowledgments This work was supported by the  CNRS LEFE-CYBER   MOBIDIC , the  ANR-BIIM  ( ANR-18-CE01-0006-01 ), and by the  LabexMER  ( ANR-10-LABX-19-01 ) projects. The present work was also supported by the  Instituto Milenio de Oceanografia (IMO-Chile) , funded by the  Iniciativa Cientifica Milenio  ( ICM-Chile ), and by  FONDECYT  project  11160801  for  P. A. Auger. Models outputs used in this study are available at http://data. umr-lops. fr/pub/Iron/PFEI.
The width-to-length ratio (hereafter WL ratio) has been used to differentiate fuel sources, since grasses produce thinner and longer particles than woody vegetation  [42, 43] , which is especially useful in the grass-savanna environment where low-intensity, high frequency fires are thought to have been common  [44]. The width and length of each charcoal particle was measured using the image analysis software WinSeedle (Regular version 2016, Regent Inc. Instrument). Local fire episodes were inferred from the macrocharcoal record using the decomposition approach, which separates charcoal peaks (CHARpeak), indicative of local fire episodes, and charcoal background (CHARbackground) component, that is indicative for regional area burned , following the method described by Higuera et al. [45]. To decompose the CHAR series, we separated the CHARbackground and CHARpeak components by fitting the data with a LOWESS regression, and identifying outstanding events as those that surpass the locally defined threshold type.
meanvar() of the package changepoint of R software. This function is used to find changes in mean and variance for data using an exact multiple changepoints (Segment Neighbourhoods) method. To confirm that the change points revealed were not biased by the change of accumulation rate, or the age-depth model, a change point analysis was done on 100 random resamplings of charcoal influx paired on the same time period and resolution, following the method of W. Finsinger (available online on github. com/wfinsinger; last access 11 April 2019). Superposed epoch analyses (SEA) were performed for retained fire events on the annually resolved regional moisture index (PDSI,  [49] ). For the tree scar-derived fire events, the SEA spans the period 1810-1935 CE, corresponding to the length from the oldest to the youngest tree scars (Figure  3 ).
The innermost ring for most of these cores ranged from 1898-1927 CE, with a subset of all cores that intersected pith or were estimated to be within five years dating to 1898-1916 CE. These age data suggest that the living tree population is largely an even aged cohort that recruited within the 27-year fire-free window from 1882-1909 CE and may be, in part, a result of human-caused fire suppression. The occurrence of fire scarring and a lack of other stumps in the stand make it unlikely that this stand had been logged, and no red pine clearcutting activities were reported for the area, though there are reports of widespread timber harvesting of white pine in the region  [36]. The distribution of intervals between tree-ring recorded fire episodes provided a median of 15 years for the active burning period (1822-1924 CE).