dataesr/scientific-paragraphs-categorization huggingface dataset:
Currents inside the eddy and eddy rotation Estimation of the spatial distribution of currents twice per winter was done using indirect (CTD inclination and passive drifters), and direct measurements (SeaHorse and Alec current meters). Currents are anticyclonic (clockwise direction), with low speed in the center and high speed at the eddy periphery. The rotational speed of the eddy has been estimated from temperature variability measured at the ropes and direct current meter data between mid-February and end of March in 2016. This eddy made a complete rotation in about 3 d (radial speed 120 per day). While Meddies have much larger diameter (40-150 km), subsurface float measurements of 16 Meddies in the Atlantic  (Richardson et al. 2000)  show similar values for the rotational speed-their core looping period ranges between 2.
Acknowledgments This research was supported by the  ERA. NET RUS Plus S&T  # 226  " ERALECC," CNES TOSCA "LakeIce," RFBR   19-05-00522 ,  RFBR-RGO 17-05-41043 ,  CNRS PICS "BaLaLaICA," Toulouse Arctic Initiative ,  RFBR 13-05-91051 ,  GDRI  " Car-Wet-Sib ,"  IRN TTS and IDEX InHERA  projects. Corona and Landsat data are available from the  U. S. Geological Survey. A. G. Kostianoy was partially supported in the framework of the  P. P. Shirshov Institute of Oceanology RAS (Russian Academy of Sciences ) budgetary financing (Project N  0149-2019-0004 ). We would like to thank  A. Beketov  and  M. Fomenko  ( Ust' Barguzin, Russia ),  M. Ovdin  and  N. Makoveev  ( "Zapovednoye Podlemorye," Ust' Barguzin, Russia ),  P. Zavyalov  and  A. Osadchiev  ( Shirshov Institute of Oceanology RAS, Moscow ),  S.
A comprehensive evaluation of the performance of satellite-based soil moisture (SM) retrievals is undoubtedly very important to improve its quality and evaluate its potential application in hydrology, climate, and natural disasters (drought, flood, etc. ). Since the release of the SMAP (Soil Moisture Active Passive) mission data in April 2015, the associated SM retrieval algorithms have developed rapidly, and their improvement work is still in progress. However, some newly developed SM retrievals have not been fully assessed and inter-compared. One such product is the new multi-temporal dual-channel retrieval algorithm (MT-DCA) SM retrievals, which was recently retrieved using the so-called MT-DCA algorithm. To solve this, we aim to assess the MT-DCA SM retrievals along with the SMAP-enhanced level three SM products (SPL3SMP_E, version 2).
However, it should be noted that SM retrieval algorithms are rapidly developing, and work on their improvement is still being carried out using new concepts or implementing new calibration parameters  [20, 29]. Therefore, some newly developed SM products have not been fully assessed and inter-compared. One such product is the new multi-temporal dual-channel retrieval algorithm (MT-DCA) soil moisture retrievals, which were recently retrieved using the so-called MT-DCA algorithm (multi-temporal dual-channel retrieval algorithm) developed by  Konings et al. (2017)   [30]. To our knowledge, the latest MT-DCA SM product has only been directly evaluated against the baseline algorithm applied by the SMAP group  [30] , and the inter-comparison with other auxiliary datasets has not been carried out.
Furthermore, there is very little known about the performance of SMAP-enhanced level three SM products at different vegetation coverage levels. To solve all of this, the aim of our work is to assess the MT-DCA SM product along with the SMAP-enhanced level 3 SM product (SPL3SMP_E, version 2). This was carried out using the "European Centre for Medium-Range Weather Forecasts" (ECMWF) modeled SM and the "International Soil Moisture Network" (ISMN)  [31, 32]  in situ measurements from April 2015 to December 2017. Our study is also complementary to the evaluation of the SPL3SMP_E SM product by  Zhang et al. (2019)   [17]. The outline of our paper is: Datasets and methodology are introduced in Sections 2 and 3, respectively, and results and discussion are given in Section 4. Finally, concluding remarks are described in Section 5.
Datasets Datasets used in this study spanning from April 2015 to November 2017 are shown in Table  1. These include soil moisture retrieved by multi-temporal dual channel algorithm (MT-DCA), SMAP-enhanced level 3 radiometer soil moisture (SPL3SMP_E, version 2), the volumetric soil moisture content in the top layer (0-7 cm) of ECMWF, and in situ measurements obtained from the ISMN and additional datasets; details for which are given in the following subsection. After losing the radar sensor, the SMAP team is committed to using other effective methods to obtain or compensate for high-resolution observations. This initiative of obtaining high-resolution information is carried out in two different ways: i) The first method is to combine high spatial resolution radar observations from other missions with SMAP coarse-resolution passive radiometer observations  [21].
ECMWF Modeled Soil Moisture In this work, the ECMWF SM dataset is used to inter-compare with the SMAP SM retrievals on a global scale. The ECMWF product comes from the ERA-Interim reanalysis dataset, which is based on IFS-Cy31r2 (a numerical weather prediction (NWP) system) to solve for several parameters, including four-layer volumetric soil moisture  [39]. Readers are referred to  Berrisford et al. (2011)  and  Dee et al. (2011)  for more specifics about ERA-Interim modeling and the data assimilation system  [39, 40]. The ECMWF datasets obtained in this study have the sampling resolution of 25 km and temporal resolutions (1-day) as SMAP SM retrievals. Soil moisture of the shallower ECMWF soil layer (first 0-7cm layer) was used to represent the relatively low sampled soil layer of the SM retrievals obtained from SMAP radiometer sensors (0-5 cm, m 3 /m 3 ).
ISMN Ground-Based Soil Moisture SMAP SM retrievals were also evaluated on a local scale against in situ SM datasets obtained from the ISMN network (International Soil Moisture Network)  [44]. ISMN is an international initiative of GEWEX (Global Energy and Water Cycle Experiment) and ESA, aiming at the establishment and maintenance of a global in situ SM database. This database aims at promoting scientific studies on the validation and improvement of global satellite-based measurements and land surface modeling. Currently, the ISMN database hosts 2439 ground stations from ~60 networks (products are available at https://ismn. geo. tuwien. ac. at/). To ensure the accuracy of the ground-based observations and to minimize systematic discrepancies between in situ measurements and the SMAP SM retrievals, only SM observations of the top 0-5 cm soil layer flagged as "Good" were considered  [45, 46].
Additional Datasets Several additional datasets were used to interpret the results, including the International Geosphere-Biosphere Programme (IGBP) land cover classification scheme and MODIS leaf index area (LAI). Earlier studies have shown that the performance of the satellite-based SM products may vary as a function of vegetation density and land cover class  [29, 42, 47]. Here, we used the IGBP land cover classification scheme and LAI data to account for the different land cover types and vegetation conditions when comparing the SM retrievals. In this study, the global land cover classification map is a 500 m resolution dataset obtained by overlapping the 10 years (2001-2012) standard MODIS land cover type product (MCD12Q1) using the IGBP schema  [7, 48]. It is generated, for each pixel, by choosing the highest overall confidence land cover classification from 2001 to 2010; more details are given in  Broxton et al.
, 2014 [49]. The MODIS LAI product, over 2015-2017, was downloaded from NASA Earth Observations (NEO) websites (https://neo. sci. gsfc. nasa. gov/); it is a monthly LAI product calculated from MOD15A2 product and has a spatial resolution of 0. 1 degrees. The global LAI map is obtained by the maximum value composite (MVC) method proposed by Holben  [50]. All the additional data sets were rescaled to the resolution of 25 km, to ensure that all spatial data had the same spatial resolution.
e. , modeled ECMWF and in situ measurements): (Pearson) correlation coefficient (R; Equation  1 ) to assess the performance of SMAP retrievals to capture the seasonal variations of the reference SMs, bias (m 3 /m 3 ; Equation  2 ) to measure the wetness or dryness of the SMAP SM compared to the reference SMs, root mean square difference (RMSD; m 3 /m 3 ; Equation  3 ), and the ubRMSD (m 3 /m 3 ; Equation  4 )  [18]. It should be noted that R and ubRMSD were considered as first-order criteria in comparison to Bias and RMSD, as the reference soil moisture datasets do not represent the value as "observed" by the SMAP measurement, considering the different "sampling" depths of simulated, retrieved and in-situ SM data. R = n i = 1 SM est(i) -SM est SM ref(i) -SM ref n i = 1 SM est(i) -SM est 2 n i = 1 SM ref(i) -SM ref 2 , (1) Bias = (SM est -SM ref ), (2) RMSD = (SM est -SM ref ) 2 , ( 3 ) ubRMSD = RMSD 2 -Bias 2 , ( 4 ) where n is the number of SM data pairs, SM est is SMAP SM estimates (i.
e. , either SPL3SMP_E or MT-DCA SM), SM ref is the reference SM (i. e. , either ECMWF SM or ISMN in situ SM), and overbar represents the temporal mean of the entire time series. It should be noted that when comparing retrieved SM with in situ observations, the time series of satellite-based retrievals of SM were extracted from the original SMAP pixels covering each site (based on latitude and longitude of the site) to obtain values corresponding to the field measurements, and only the in situ data matching with the instantaneous overpass of the SMAP observation within a time window of 1 hour were selected. In our analysis, as done by Al-Yaari et al. (2019)  [29] , we accounted only for SM retrievals where p-value < 0. 05 and R > 0. 4 when comparing to in situ data sets (this condition only applies to the local scale evaluation).
Results In the following parts, we described the validation results for two SMAP SM products on a global scale in Section 4. 1. This involved directly interpreting the validation results compared to the ECMWF reanalysis SM and analyzing the effects of LAI and land cover types on the validation. Section 4. 2 presents the validation results using the ground-based measurements. Figure  2  shows maps of the temporal mean SM values for the three SM datasets considered in this work. As mentioned in Section 2. 3, the ECMWF modeled SM used here represents shallower soil surface (first 0-7 cm layer), and the inherent nature of this simulated SM is different from that observed by the SMAP satellite sensors. In contrast, the latter is more sensitive to soil surface depths of ~0-5 cm  [18, 23]. Hence, it should be mentioned that the ECMWF SM in Figure  2c  must be interpreted according to spatial patterns rather than in terms of absolute values.
We have confirmed this again in this study, although it is MT-DCA, an improved DCA algorithm. MT-DCA SM and SPL3SMP_E SM had biases (remotely sensed data minus in-situ data) with the same sign (either positive or negative) over all networks except over the HOBE, SCAN, USCRN, and iRON networks. It should also be noted that the comparison with in-situ is carried out on the 9 km satellite footprint that covers a wider range of land cover types over the globe, which is very close to the overall validation results of Zhang et al. (2019) for SPL3SMP_E SM using ground measurements under various landscapes, and their reporting accuracy (i. e. , unbiased RMSD) was equal to 0. 055 m 3 /m 3. As in Section 4. 1. 2, in this part, we also evaluated (mainly based on R and ubRMSD) the two SMAP SM retrievals under different vegetation conditions (based either on LAI or IGBP land cover types).
The uncertainty among climatological datasets can be characterized as the variance in space and time between various estimates of the same quantity. However, some of the current uncertainty estimates only evaluate variations in one single dimension (time or space) due to the limitation of estimation methodology as averaging variation is necessary for the other dimension. The influence on the uncertainty assessment of the ignorance of variations in one dimension is not well studied. This study introduces a new three-dimensional variance partitioning approach which avoids the averaging and provides an new uncertainty estimation (U e ) technique with consideration of both temporal and spatial variations. Comparisons of U e to classic uncertainty estimations show that the classic metrics underestimate the uncertainty because of the averaging of variation in the time or space dimension, and U e is around 20% higher than classic estimations.
The deviation between the new and classic metrics is higher for regions with strong spatial heterogeneity and where the spatial and temporal variations significantly differ. Decomposing of the new metric demonstrates that U e is a comprehensive assessment of model uncertainty which has been included the model variations identified by the classic metrics. Multiple precipitation products of different types (gauge-based, merged products and GCMs) are used to better explain and understand the peculiarity of the new methodology. The new uncertainty estimation technique is flexible in its structure and particularly suitable for a comprehensive assessment of multiple datasets over a large regions within any given period.
Introduction With the technical development for monitoring the 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. Taken the precipitation, which is the dominant variable in the land water cycle, as an example, there are point measurements as GHCN-D (global historical climatology network-daily,  Menne et al. , 2012)  , grid products based on gauge measurements and interpola-tion (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 those estimates from models (e. g. , GCMs). These products are developed using different original data, different technologies or different model settings for various purposes  (Phillips and Gleckler, 2006; Tapiador et al.
, 2012; Beck et al. , 2017; Sun et al. , 2018). Therefore, there are differences (including systemic bias and uncertainty) among the various products, and the uncertainty can be regarded as the deviation around what is believed to be the truth. Although many studies have attempted to understand the causes of the uncertainties in different products, the uncertainties are very difficult to be removed from datasets. Thus, using ensembles consisting of multiple datasets to generate a weighed average has become popular in the climate-related researches. For example, the IPCC uses 42 CMIP5 (Coupled Model Intercomparison Project Phase 5) models to show the historical temperature change and 39 CMIP5 models to average the temperature projection in future RCP 8. 5 scenario  (Figure SPM. 7 in IPCC, 2013b).
Schewe et al. (2014)  use nine global hydrological models to evaluate the 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 estimations from three independent institutes  (Landerer and Swenson, 2012). Using multiple datasets reduces the dependence on a single dataset and decreases the risk of using a single dataset which might contain undiscovered uncertainties. Extra uncertainty information has to be provided along with the ensemble means because the uncertainty influences the significance or the reliability of the ensemble result. In general, the uncertainty can be quantified as the range of maximum and minimum values (i.
e. , V max -V min ), range of values at different quantiles (e. g. , V 5% -V 95% ), the consistency of models as the ratio of models following a certain pattern to the total number of models, the variation (σ 2 ) or the standard deviation (σ), which represents different characteristics of the multiple datasets. Among the uncertainty metrics, the standard deviation (σ) is the most used because it has the same magnitude as the original dataset; it avoids influence of extreme samples and it is less sensitive to the number of datasets used for the investigation. The ratio of the standard deviation (σ) to the mean value (µ), which is called coefficient of variance (CV ), representing the dispersion or spread of the distribution of various ensemble members  (Everitt, 2013) , is a unit-less value which also shows the degree of uncertainty.
Depending on the purpose of the evaluation, the uncertainty among datasets can be displayed over space to show the spatial heterogeneity of the consistency among multiple datasets. For example, the predicted future temperature increase has a higher significance in the northern high-latitudes among different models than in the middle-latitudes (Box TS. 6 Figure  1  in  IPCC, 2013a). The other typical implementation is to evaluate the evolution of the model uncertainty across time. In general, the uncertainty range decreases in the historical period over time because more observations are accessible in recent while the uncertainty increases for future projections because the increasing spread of the model simulations  (Figure SPM. 7 in IPCC, 2013b). The increasing uncertainty range indicates the decreasing of consistency and increasing variations among various datasets.
This may result in that the uncertainty among datasets not being fully considered when estimating the uncertainties. In other words, either of the uncertainty estimates cannot represent the full differences among datasets. Therefore, the uncertainty among datasets can be underestimated and the similarity among them can be overestimated with these two procedures. However current studies have not paid attention to the ignorance of variation due to the averaging as well as its influence on the uncertainty assessment. In this study, we aim to introduce a new technique for uncertainty estimation among multiple datasets. The new uncertainty estimation technique avoids any averaging in time or space dimension thus all the information across the two dimensions can be maintained for the uncertainty assessment along with an ensemble of estimates.
Multiple precipitation products are used to explain the peculiarity of the new methodology. In section 2, the detailed methodology of the three-dimensional variance partitioning approach is introduced. The characteristics of multiple precipitation datasets and estimations of the two classic uncertainty metrics are shown in section 3. The results of the new approaches for the precipitation products are discussed in section 4. The differences between the new uncertainty estimation and the two classic metrics introduced previously are analyzed and the causes are discussed in section 5. The discussion and conclusions are followed in the end of this article.
Mathematical Derivation The multiple climatic dataset have to be organized in three dimensions of (1) time with a regular time interval (e. g. monthly or annual), (  2 ) space with regular spatial units where all the grids are re-organized in a new dimension from the original latitudelongitude grids, (3) ensemble with different ensemble datasets regarded as the third dimension. Thus, the dataset array can be reformed as Z = [z ijk ] (1) with i-th time step (i = 1, 2,. , m), j-th grid (j = 1, 2,. , n), and k-th ensemble member or ensemble model (k = 1, 2,. , l). We define the three dimensions as time, space and ensemble dimension and the means for these three dimensions are called temporal mean, spatial mean and ensemble mean, respectively. The corresponding variances are named time variance, space variance and ensemble variance, respectively.
(  9 ) is shown in Eqs. (  10 ) -(  17 ). For a specific dataset k, the grand mean µ ts [k] through space-time scale is µ ts [k] = 1 mn m i=1 n j=1 z ijk (10) The total squares for difference from the grand mean is  11)  and the grand variance σ 2 ts is SST [k] = m i=1 n j=1 (z ijk -µ ts [k]) 2 ( σ 2 ts [k] = 1 mn m i=1 n j=1 (z ijk -µ ts [k]) 2 (12) If the derivation is started from the space dimension, Eq. (  11 ) can be rewritten by incorporating the spatial mean of each time step µ s [k, i] = l j=1 z ijk /n SST [k] = m i=1 n j=1 (z ijk -µ s [k, i] + µ s [k, i] -µ ts [k]) 2 (13) It can be expanded and then rearranged as SST [k] = m i=1 n j=1 (Z ijk -µ s [k, i]) 2 + 2 × m i=1 (µ s [k, i] -µ ts [k]) × n j=1 (Z ijk -µ s [k, i]) =0 + n j=1 =n m i=1 (µ s [k, i] -µ ts [k]) 2 (14) SST [k] = m i=1 n j=1 (Z ijk -µ s [k, i]) 2 + n m i=1 (µ s [k, i] -µ ts [k]) 2 (15) SST [k] = n m i=1 σ 2 s [k, i] + nmσ 2 (µ s [k, :]) =nmσ 2 s [k, :] + mnσ 2 (µ s [k, :]) (16) 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.
Metrics definition for model uncertainty Since the temporal evolution or the spatial heterogeneity is natural in the climate variables and the purpose of this study is to evaluate the model uncertainty among datasets, we focus mainly on the variance in the ensemble dimension. The uncertainty among the ensemble member is normalized as the ratio of the square root of the ensemble variance (V e ) divided by the mean value of the datasets (µ). U e = V e /µ (27) For each basic spatial unit (grid cell in this study), we can estimate the long-term mean of the target variable for each dataset µ t [j, k], j = 1,. , n represents the space unit, and k = 1,. , l represents the number of datasets. Then for each spatial unit, we can estimate the ensemble variations across different 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 model uncertainty over space and its root σ e_t [j] is the model deviation at each space unit. The overall estimation of the model uncertainty 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) σ 2 e_t [j] has different values for each spatial unit and 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 N. s. std is normalized as the ratio of the square root of the mean of variations σ 2 e_t to the average value of all the datasets µ. Similarly, the model uncertainty can also be expressed as the normalized as the ratio of the square root of the averaged ensemble variation at all time steps σ 2 e_s to the entire means (Eq.
29). N. t. std = σ 2 e_s /µ = 1 µ 1 m m i=1 σ 2 e_s [i] ( 29 ) where the σ 2 e_s [i], i = 1,. , m is the ensemble variation of the spatial mean of each dataset across different datasets of the spatial means of each products at each time unit µ s [i, k], (i = 1,. , m, k = 1,. , l). It has different values at different time steps. The two uncertainty estimates (Eqs. 28 and 29) correspond to the two classic metrics presented in the Introduction. And we will compare the U e with the two classic metrics (N. t. std and N. s. std) to show their relations and differences.