dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction With the technical developments in monitoring natural climate variables and the increasing knowledge of the physical mechanisms in the climate system, many institutes have the ability to provide different kinds of climate datasets. Taking precipitation, which is the dominant variable in the land water cycle, as an example, there are point measurements, such as GHCN-D (global historical climatology network-daily,  Menne et al. , 2012) , gridded products based on gauge measurements and interpolation (e. g. CRU,  Harris et al. , 2014) , products derived from remote sensing (e. g. the Tropical Rainfall Measuring Mission -TRMM), reanalysis datasets (e. g. NCEP) and estimates from models (e. g. GCMs). These products have been developed using different original data, technologies and model settings for vari-Published by Copernicus Publications on behalf of the European Geosciences Union.
ous purposes  (Phillips and Gleckler, 2006; Tapiador et al. , 2012; Beck et al. , 2017; Sun et al. , 2018). As a result, there are differences between the various products due to measurement errors, model biases, or chaotic noise. The uncertainty is thus regarded as the deviation of these model results from their real values. However, the real values are difficult to measure and the uncertainties are difficult to remove from the datasets. Thus, using ensembles consisting of multiple datasets to generate a weighted average has become very popular in climate-related research. The ensemble means of multiple datasets are considered more reliable estimates than a single dataset. For example, IPCC uses 42 CMIP5 (Coupled Model Intercomparison Project Phase 5) models to show historical temperature changes and 39 CMIP5 models to average future temperature projections in a RCP 8.
5 scenario (Fig. SPM. 7 in IPCC, 2013b). Schewe et al. (2014)  use nine global hydrological models to evaluate global water scarcity under climate change. GLDAS (Global Land Data Assimilation System) involves four different land surface models  (Rodell et al. , 2004)  and GRACE (Gravity Recovery and Climate Experiment) provides estimates from three independent institutes  (Landerer and Swenson, 2012). Using multiple datasets reduces the dependence on a single dataset and eliminates the random variations associated with biases or noise in each single model estimate. Along with the ensemble means, uncertainty information is recommended to be presented because the level of uncertainty determines the reliability of the ensemble results. In general, uncertainties can be quantified as the range of maximum and minimum values (i.
e. V max -V min ), the value difference at different quantiles (e. g. V 5 % -V 95 % ), the consistency of models (ratio of models following a certain pattern to the total number of models), the variation (σ 2 ) or the standard deviation (σ ) of multiple model estimations. These metrics describe the differences between multiple model estimates in different aspects. Among the metrics, the standard deviation (σ ) is the most used because it has the same unit as the original dataset. Moreover, it is less sensitive to extreme samples and to the number of datasets used for the investigation. The ratio of the standard deviation (σ ) to the mean value (µ), the so-called coefficient of variance (CV), representing the dispersion or spread of the distribution of various ensemble members  (Everitt, 2013) , is a unitless value which also shows the degree of uncertainty efficiently.
Depending on the purpose of data evaluation, the uncertainty between the datasets can be displayed or visualized in space to show the spatial heterogeneity. For example, the predicted future temperature increase has a higher significance in different models in the northern high latitudes than in the middle latitudes  (Box TS. 6 Fig. 1 in IPCC, 2013a). Another typical implementation is to evaluate the evolution of the uncertainty over time. In general, the range of the uncertainty decreases in the historical period over time because more observations have been accessible recently. But the uncer- The two kinds of ways can easily show the spatial distribution or the temporal evolution of the uncertainty. But a shortcoming is apparent, as the variation along one dimension (time or space) has to be collapsed to generate the mean values when we attempt to assess the uncertainty for the other dimension (space or time).
For example, the averaging over a specific region to obtain the spatial mean is estimated at each time step before obtaining the temporal evolution of the model uncertainty (red flowcharts in Fig. 1 ). In contrast, averaging over a certain temporal period to obtain the temporal mean is necessary for each grid cell when estimating the spatial variations of model uncertainties (blue flowcharts in Fig. 1 ). The averaging, in either dimension, means a loss of information about the variation in the data. Any changes in the variation that leave the mean values unchanged will not be propagated to the global uncertainty estimation. The result of this is that the variations between datasets are not fully considered when estimating the uncertainties. In other words, neither of the uncertainty estimates can represent the whole of the differences between multiple datasets.
The uncertainty can be underestimated, and the similarity of the datasets thus overestimated. Indeed, the current literature has not paid attention to the neglect of variation after averaging as well as its influence on the assessment of the uncertainty. The total variation across multiple datasets is contributed by the spatial heterogeneity, temporal variability and the model uncertainties. To some degree, the model uncertainty is similar to other dimensions as a variation along a third dimension (ensemble dimension). The key to evaluating the model uncertainty is to decompose the variation caused by differences between the datasets from the other two contributors. Although decomposing the variation by means of ANalysis Of VAriance (ANOVA) is often seen in hydrometeorological studies, this is designed to separate the process uncertainties generated in different model processes that propagate to the final variation.
However, their approach is only valid for one single dataset and is thus not able to evaluate the uncertainties if multiple datasets describe the same variable. But a generalized approach should be based on Sun's work, as one more dimension can be added for a specific analysis of the uncertainties. In the present study, we aim to introduce a new approach to estimating uncertainty of multiple datasets. The new uncertainty metric should avoid any averaging over time or space, so that all information along each of these two dimensions can be maintained for the assessment of the uncertainty. Multiple precipitation products will be used to display the results and explain the specifics of the new approach. In Sect. 2, the details of the three-dimensional variance partitioning approach are introduced.
Mathematical derivation Multiple datasets recording the same climatic variable should be reorganized into a three-dimensional database, using the dimensions of (1) time with a regular time interval (e. g. monthly or annual), (2) space with regular spatial units, with all the grids re-organized into one dimension from the original longitude-latitude grids, and (3) ensemble as the third dimension describing the different ensemble datasets. Thus, the dataset array can be re-organized to be Z = [z ij k ], (1) with the ith time step (i = 1, 2,. , m), j th grid (j = 1, 2,. , n), and kth ensemble member or ensemble model (k = 1, 2,. , l). We define the three dimensions to be time, space and ensemble dimension, and the means for these three dimensions to be the temporal mean, spatial mean and ensemble mean.
The corresponding variances are referred to as the temporal variance, spatial variance, and ensemble variance. We also define the grand mean (µ), grand variance (σ 2 ) and total sum of squares (SST) (or total variation) across the entire database: µ = m i=1 n j =1 l k=1 z ij k /(mnl) (2) σ 2 = SST mnl (3) SST = m i=1 n j =1 l k=1 (z ij k -µ) 2. (4) The total variation receives contributions from the variations along all three dimensions (Eq. 4). It can be reformulated as an expression in terms of the variations along each of the three different dimensions. For instance, the derivation of the total variation can start from the third ensemble dimension. For a specific kth ensemble member, the grand mean is formulated as µ ts [k] = m i=1 n j =1 z ij k /(mn), leading to the total sum of squares being rewritten as SST = m i=1 n j =1 l k=1 (z ij k -µ ts [k] + µ ts [k] -µ) 2.
(5) The SST can be further expanded and rearranged as SST = m i=1 n j =1 l k=1 (z ij k -µ ts [k]) 2 + 2 × l k=1 (µ ts [k] -µ) m i=1 n j =1 (z ij k -µ ts [k]) =0 + m i=1 n j =1 =mn l k=1 (µ ts [k] -µ) 2 , ( 6 ) SST = m i=1 n j =1 l k=1 (z ij k -µ ts [k]) 2 + mn l k=1 (µ ts [k] -µ) where σ 2 (µ ts ) is the variation of the grand mean for each ensemble member and σ 2 ts [k] is the grand variance in the spatial and temporal dimensions for the ensemble member k. Moreover, σ 2 ts [k] can be split using the mean of the spatial variation at each time step σ 2 s [k, :] and the variation of the spatial mean σ 2 (µ s [k, :]), denoted as in Eq. (  9 ) with its derivation given in Eqs. (  10 )-(  17 ). σ 2 ts [k] = σ 2 s [k, :] + σ 2 (µ s [k, :]). (9) For a specific dataset k, the grand mean µ ts [k] at the spatiotemporal scale is µ ts [k] = 1 mn m i=1 n j =1 z ij k.
(16) The grand variance of this specific dataset is Eq. (  17 ) (identical to Eq. 9). σ 2 ts [k] = SST[k] mn = σ 2 s [k, :] + σ 2 (µ s [k, :]) (17) Here, σ 2 s [k, :] is the mean of the spatial variation at each time step and σ 2 (µ s [k, :]) is the variation of the spatial mean, or if we started the derivation from the time dimension, the grand variance can be split using the average of the temporal variation from all regions σ 2 t [:, k] and the spatial variation of the temporal mean σ 2 (µ t [:, k]): σ 2 ts [k] = σ 2 t [:, k] + σ 2 (µ t [:, k]). (18) With Eqs. (  9 ) or (  17 ) and (  18 ), we obtain σ 2 ts [k] = 1 2 [σ 2 (µ t [:, k]) + σ 2 s [k, :]] + [σ 2 (µ s [k, :]) + σ 2 t [:, k]]. (19) Substituting Eq. (  19 ) into (8) results in SST = mn 2 l k=1 [σ 2 (µ t [:, k]) + σ 2 s [k, :]] + mn 2 l k=1 [σ 2 (µ s [k, :]) + σ 2 t [:, k]] + mnlσ 2 (µ ts ).
An illustration of the present approach is shown in Fig. 2  to facilitate the understanding of the partitioning results. The original database, consisting of multiple datasets, is re-organized into three dimensions (grey in the centre). Zones with different colours represent different processes of the original database from different dimensions (see the details in the caption of Fig. 2  and Appendix A ). Note that the ensemble variance V e in Eq. (  26 ) is a combination of several variations across the ensemble members. The four components are the variations of temporal and spatial values (σ 2 e , zone B3), temporal mean (σ 2 e_t , zone C5), spa-tial mean (σ 2 e_s , zone C6) and the grand variance of the spatiotemporal mean for a single ensemble member (σ 2 e (µ ts ), zone F3). Similarly, the other variances only rely on the variances in the corresponding dimension, which shows the independence of the three dimensions.
Definitions of the metrics for model uncertainty Although the total variation is a result of contributions from the spatial heterogeneity, temporal variability and the uncertainties across different datasets, we mainly focus on the variance in the ensemble dimension because the spatial or temporal variation is natural for climatic variables. The uncertainty of ensemble members is normalized as the ratio of the square root of the ensemble variance (V e ) to the grand mean value of the datasets (µ). U e = V e /µ (27) Two classic metrics used for uncertainty estimates are also introduced for comparison. For each basic spatial unit (in the present study this means a grid cell), we can estimate the temporal mean of the target variable in each ensemble dataset as µ t [j, k], j = 1,. , n represents the spatial unit and k = 1,.
, l represents the index of the dataset. Then we can estimate the variations across different ensemble datasets of the mean values as σ 2 (µ t [j, :]) (expressed as σ 2 e_t  [j ]  in this study). The spatial distribution of the σ 2 e_t shows the magnitude of the model uncertainty over space and its root σ e_t  [j ]  is the model deviation at each spatial unit. The estimate of this model deviation over the entire region can be expressed as N. s. std = σ 2 e_t /µ = 1 µ 1 n n j =1 σ 2 e_t [j ]. (28) For each spatial unit, σ 2 e_t [j ] (j = 1,. , n) can take a different value. The values for all the grid cells are averaged to obtain σ 2 e_t , which shows the general magnitude of the ensemble variation over space. The quantity N. s. std is normalized as the ratio of the square root of the averaged variations σ 2 e_t to the grand mean of all the datasets µ.
Similarly, the model uncertainty can be normalized as the ratio of the square root of the averaged ensemble variation but at different time steps σ 2 e_s to the entire means: N. t. std = σ 2 e_s /µ = 1 µ 1 m m i=1 σ 2 e_s [i], (29) where σ 2 e_s [i] (i = 1,. , m) is the variation across different datasets of the spatial means of each product at each time unit µ s [i, k], (i = 1,. , m, k = 1,. , l). www. hydrol-earth-syst-sci. net/24/2061/2020/ Hydrol. Earth Syst. Sci. , 24, 2061-2081, 2020 The two uncertainty estimates (Eqs. 28 and 29) correspond to the two classic metrics presented in the Introduction. We will compare U e estimated by the newly proposed approach with these two classic metrics (N. t. std and N. s. std) to show their relations and differences.
Thirteen different precipitation datasets from various sources have been collected for comparison (Table  1 ). These datasets have been categorized into three groups according to the methods they used for generating the products, namely, gauge-based products, merged products and general circulation models (GCMs). The gauge-based products (namely, CMA, GPCC, CRU, CPC and UDEL) use data observed from global precipitation gauges. The density of the ground observation gauges, the representativeness of the gauges, and the interpolation algorithms for converting the gauge observations to a gridded dataset differ from product to product. The CMA (China Meteorological Administration) dataset has the densest distribution of gauges and probably has the best quality to capture the spatiotemporal variations of the precipitation over the study area.
The CMA dataset is excluded when estimating the uncertainty of the gauge-based products: it is chosen as the reference dataset for comparison. As for the merged precipitation products, the CMAP, GPCP and MSWEP use different sources of precipitation data (namely, gauge observations, satellite remote sensing, and atmospheric model re-analysis). These different precipitation sources are averaged using different weights. Thus, the differences between the three merged products are associated with the precipitation sources and the weight of the gauge observations. ERA-Interim is a re-analysis product: it uses near-real-time assimilation with data from global observations  (Dee et al. , 2011). Thus, the forecasting model is constrained by the observations and forced to follow the real system to some degree.
There are more than 20 kinds of different GCMs; only 4 of them have been chosen, randomly, to maintain the same number of datasets using the gauge-based products as those using merged products. All the products of the three precipitation types, including CMA, are in gridded format. Although they differ in their original spatial resolution, all the products have been interpolated to a 0. 5 • spatial resolution to unify the spatial units. Annual average values are summed based on their original time steps (daily or monthly) and the overlap time span of all the datasets is from 1979 to 2005 for all the products.
Spatial patterns of annual precipitation The long-term annual mean precipitation  obtained by averaging the precipitation from multiple datasets in the corresponding precipitation group is mapped in Fig. 4. The annual mean precipitation obtained from the CMA dataset is 589. 8 mm yr -1 (1. 6 mm d -1 ) over the entire Chinese mainland. The gauge-based precipitation has the least bias (-4. 1 mm yr -1 , -0. 7 % in percentage) compared to the CMA precipitation. The precipitation in the merged products and GCMs is larger than that of the CMA by 63. 1 and 232. 0 mm yr -1 (with the bias equal to +10. 7 % and +39. 3 %), respectively. The spatial pattern of the annual precipitation shows a decreasing gradient from Southeast China (> 1600 mm yr -1 ) to Northwest China (< 400 mm yr -1 ) in CMA and all other three precipitation groups.
Spatial distribution of model uncertainties In addition to the precipitation differences in its long-term annual means, differences can be found between datasets within the same precipitation group. The spatial distribution of the model uncertainty for each precipitation group, which is expressed as the ensemble deviation of the annual precipitation from different precipitation products, is mapped in Fig. 5. The ensemble deviation of the datasets based on gauge observations is small in most of the land area of China (< 50 mm yr -1 , Fig. 5a ). Although the deviation is higher in the south of China (50-100 mm yr -1 ), the area is not continuous in space. The highest deviation occurs along the Himalayas, indicating a high variation across the observed datasets. Regarding the merged precipitation products, the deviation shows high values (> 200 mm yr -1 , Fig.
Temporal evolution of the model uncertainty. The uncertainty is expressed as the normalized ensemble deviation of annual precipitation across ensemble datasets in each precipitation group for specific subregions. The value on the top right of each panel is the annual regional precipitation estimated in the CMA dataset. The annual precipitation is normalized as the ratio to the CMA long-term annual precipitation. The solid curve represents the ensemble mean of precipitation in each precipitation data group over the subregion. The width of the shaded area represents the standard deviation of the annual precipitation estimated from the datasets within that group for each year (divided by the annual precipitation of the corresponding group). The shaded area is equally distributed in the two sides of the ensemble mean values for the corresponding precipitation group.
precipitation is among the lowest. The model deviation of GCMs varies between regions as it is at its smallest in 1-Songhua River Basin (Fig. 6a ) and 6-Yangtze River Basin (Fig. 6f ), while it is among the highest in 8-South China and West China (9, 10), agreeing with the deviation maps in Fig. 5. Despite their mean values and magnitudes of deviation, the temporal evolutions of the gauge-based products and merged products agree well with those of the CMA dataset, while the temporal evolution of the members of the category of GCMs 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 wet and dry years can be very different from that of the observations. A smoother result is thus obtained when we build the ensemble mean from the GCMs.
Unlike the weak variation in GCMs, the gaugebased and merged products have a strong co-variance, and the ensemble mean preserves this co-variance. For the entire Chinese mainland (Fig. 6k ), the ensemble deviation remains stable in different precipitation groups. In contrast, the annual precipitation spans the strongest spatial heterogeneity in the mainland compared to those divided by subregions (Fig. 4 ). However, the spatial variation has been collapsed because the regional precipitation has to be obtained before the temporal analysis. It is therefore interesting to evaluate how the uncertainty changes when the variations Hydrol. Earth Syst. Sci. ,  24, 2020  www. hydrol-earth-syst-sci. net/24/2061/2020/ along both the time dimension and the spatial dimension are considered in the precipitation datasets.
Variations along the temporal and spatial dimensions Previous subsections provide the deviation analysis in either temporal scale or spatial scale. However, the two are seldom compared with each other. Herein, the standard deviations of the temporal and spatial variations in the precipitation datasets are compared in Fig. 7  in 10 subregions and the China mainland for different precipitation groups. The gauge-based products provide similar annual regional precipitation to CMA over the China mainland and the 10 specific subregions except for the region 7-Southeast China (Fig. 7g ) and region 9-Southwest China (Fig. 7i ), while the merged products provide larger precipitation estimations for most of the regions. It might indicate the degraded ability of remote sensing, one of the important data sources in the merged products, to estimate the precipitation amount in storms as the storms mainly contribute to the total precipitation for the two subregions.
15) and 7-Southeast China (k = 0. 90), mainly due to the relatively strong variability of the annual precipitation in different years. In addition to the differences between regions, the variations in different precipitation groups also vary in magnitude. Excluding the CMA dataset, which consists of only one single product, the total variation (the sum of the spatial and temporal variations) across the gauge-based products is higher than that of the other two groups. This difference demonstrates that the gauge-based products may have the largest spatial variation, and the correlations between the different gauge-based products are high, so that this variation is preserved when passing to the ensemble. In contrast, variations across the GCMs are the smallest, either because the precipitation estimated in the GCMs is more spatially homogenous than that of other precipitation products or be- cause the precipitation estimations in different GCMs are not consistent in time or space since there are no constraints on the GCM simulation.
6h, i. Similar patterns of the spatial variance V s are found in the gauge-based products and merged products (Fig. 8g, h ). The largest V s is found in regions 7-Southeast River basin and 9-Southwest China because the precipitation significantly varies in space in these two subregions: it is higher in GCM precipitation especially in 9-Southwest China, indicating the strong spatial heterogeneity in the GCM models over the Himalayas (Fig. 8i ). The ensemble variance V e is relatively small in most regions for gauge-based products (Fig. 8j ), indicating that the model variation across datasets in the observation group is small. A similarly small V e is found in the northern regions of the merged products as well as in the GCMs for the regions in North China, while the intraensemble variations are large in the GCMs, especially in the south, especially 9-Southwest China and 8-South China (Fig.
4 ). The averaging process before estimating the classic metrics will cause a significant smoothing of the datasets when the spatial heterogeneity of the datasets is very strong, because the spatial variation is significantly higher than the temporal variation, as shown in Fig. 7. The estimation of N. t. std, which needs an averaging over the spatial dimension, will lose more information than that in the time dimension. The deviation between N. t. std and U e (Fig. 10b ) is larger than that between N. s. std and U e (Fig. 10a ). The priority of the precipitation types also changes, from model dominated (the model uncertainties in GCMs are larger than the others) to region dominated (the uncertainties in the specific regions 9, 10, and 11 are larger than in the other regions no matter which precipitation data are used).