dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2011b). The consumption-based emissions have the same global total but reflect the trade-driven movement of emissions across the Earth's surface in response to human activities. We estimate consumption-based emissions from 1990-2020 by enumerating the global supply chain using a global model of the economic relationships between economic sectors within and between every country (Andrew and  Peters, 2013; Peters et al. , 2011a). Our analysis is based on the economic and trade data from the Global Trade and Analysis Project (GTAP;  Narayanan et al. , 2015) , and we make detailed estimates for the years 1997 (GTAP version 5); 2001 (GTAP6)  ; and 2004 and , 2007 and , 2011 and , and 2014 (GTAP10. 0a) (GTAP10. 0a) , covering 57 sectors and 141 countries and re-gions. The detailed results are then extended into an annual time series from 1990 to the latest year of the gross domestic product (GDP) data (2020 in this budget) using GDP data by expenditure in current exchange rate of US dollars (USD; from the UN National Accounts main aggregates database; UN, 2021) and time series of trade data from GTAP (based on the methodology in  Peters et al.
, 2011a). We estimate the sector-level CO 2 emissions using the GTAP data and methodology, add the flaring and cement emissions from our fossil CO 2 dataset, and then scale the national totals (excluding bunker fuels) to match the emission estimates from the carbon budget. We do not provide a separate uncertainty estimate for the consumption-based emissions; however, based on model comparisons and sensitivity analysis, they are unlikely to be significantly different than for the territorial emission estimates  (Peters et al. , 2012a).
To correct for this, we add peat fire emissions based on the Global Fire Emission Database (GFED4s;  van der Werf et al. , 2017)  to the bookkeeping models' output. Emissions are calculated by multiplying the mass of dry matter emitted by peat fires with the C emission factor for peat fires indicated in the GFED4s database. Emissions from deforestation fires used to derive E LUC projections for 2022 are calculated analogously. As these satellitederived estimates of peat fire emissions start in 1997 only, we follow the approach by  Houghton and Nassikas (2017)  for earlier years, which ramps up from zero emissions in 1980 to 0. 04 Pg C yr -1 in 1996, reflecting the onset of major clearing of peatlands in equatorial Southeast Asia in the 1980s. Similarly, we add estimates of peat drainage emissions.
In recent years, more peat drainage estimates that provide spatially explicit data have become available, and we thus extended the number of peat drainage datasets considered. We employ FAO peat drainage emissions 1990-2019 from croplands and grasslands  (Conchedda and Tubiello, 2020) , peat drainage emissions 1700-2010 from simulations with the DGVM ORCHIDEE-PEAT  (Qiu et al. , 2021) , and peat drainage emissions 1701-2021 from simulations with the DGVM LPX-Bern  (Lienert and Joos, 2018; Müller and Joos, 2021) , applying the updated LUH2 forcing as also used by BLUE, OSCAR, and the DGVMs. We extrapolate the FAO data to 1850-2021 by keeping the post-2019 emissions constant at 2019 levels, by linearly increasing tropical drainage emissions between 1980 and 1990 starting from 0 GtC yr -1 in 1980, consistent with H&N2017's assumption  (Houghton and Nassikas, 2017) , and by keeping pre-1990 emissions from the often old drained areas of the extratropics constant at 1990 emission levels.
ORCHIDEE-PEAT data are extrapolated to 2011-2021 by replicating the average emissions in  2000 -2010 (Chunjing Qiu" personal communication, 2022). Further, ORCHIDEE-PEAT only provides peat drainage emissions north of 30 • N, and thus we fill the regions south of 30 • N using the average peat drainage emissions from FAO and LPX-Bern. The average of the carbon emission estimates by the three different peat drainage datasets is added to the bookkeeping models to obtain net E LUC and gross sources. The three bookkeeping estimates used in this study differ with respect to the land-use change data used to drive the models. The updated H&N2017 bases its estimates directly on the Forest Resource Assessment of the FAO, which pro-vides statistics on forest area change and management at intervals of 5 years and is currently updated until 2020  (FAO, 2020).
The data are based on country reporting to FAO and may include remote-sensing information in more recent assessments. Changes in land-use other than forests are based on annual, national changes in cropland and pasture areas reported by  FAO (FAOSTAT, 2021). On the other hand, BLUE uses the harmonized land-use change data LUH2-GCB2022 covering the entire 850-2021 period (an update to the previously released LUH2 v2h dataset;  Hurtt et al. , 2017; Hurtt et al. , 2020) , which was also used as input to the DGVMs (Appendix C2. 2). It describes land-use change, also based on the FAO data as described in Appendix C2. 2 and the HYDE3. 3 dataset  (Klein Goldewijk et al. , 2017a, b) , but provided at a quarter-degree spatial resolution, considering subgrid-scale transitions between primary forest, secondary forest, primary non-forest, secondary non-forest, cropland, pasture, rangeland, and urban land  (Hurtt et al.
All DGVMs use the LUH2-GCB2022 dataset as input, which includes the HYDE cropland/grazing land dataset  (Klein Goldewijk et al. , 2017a, b) , and additional information on land-cover transitions and wood harvest. DGVMs use annual, half-degree (regridded from 5 min resolution) fractional data on cropland and pasture from HYDE3. 3. DGVMs that do not simulate subgrid-scale transitions (i. e. net land-use emissions; see Table  A1 ) used the HYDE information on agricultural area change. For all countries, with the exception of Brazil and the Democratic Republic of the P. Friedlingstein et al. : Global Carbon Budget 2022  Congo, these data are based on the available annual FAO statistics of change in agricultural land area available from 1961 up to and including 2017. The FAO retrospectively revised their reporting for the Democratic Republic of the Congo, which was newly available until 2020.
In addition to FAO country-level statistics, the HYDE3. 3 cropland/grazing land dataset is constrained spatially based on multi-year satellite land cover maps from ESA CCI LC (see below). After the year 2017, LUH2 extrapolates, on a grid cell basis, the cropland, pasture, and urban data linearly based on the trend over the previous 5 years to generate data until the year 2021. This extrapolation methodology is not appropriate for countries that have experienced recent rapid changes in the rate of land-use change, e. g. Brazil, which has experienced a recent upturn in deforestation. Hence, for Brazil we replace FAO state-level data for cropland and grazing land in HYDE by those from in-country land cover dataset MapBiomas (collection 6) for 1985-2020  (Souza et al. , 2020). ESA-CCI is used to spatially disaggregate as described below.
We use the same FAO wood harvest data as last year for all dataset years from 1961 to 2019 and extrapolate to the year 2022. The HYDE3. 3 population data are also used to extend the wood harvest time se-ries back in time. Other wood harvest inputs (for years prior to 1961) remain the same in LUH2. These updates in the land-use forcing are shown in comparison to the more pronounced version change from the GCB2020  (Friedlingstein et al. , 2020)  to GCB2021, which was discussed in  Friedlingstein et al. (2022a)  in Fig. B6 , and their relevance for landuse emissions is discussed in Sect. 3. 2. 2. DGVMs implement land-use change differently (e. g. an increased cropland fraction in a grid cell can either be at the expense of grassland, shrubs, or forest, the latter resulting in deforestation; land cover fractions of the non-agricultural land differ between models).
This sum is expected to be conceptually more comparable to LU-LUCF than E LUC. E LUC data are taken from bookkeeping models, in line with the global carbon budget approach. To determine S LAND on managed forest, the following steps were taken: spatially gridded data of "natural" forest net biome productivity (NBP) (S LAND , i. e. due to environmental change and excluding land-use change fluxes) were obtained with S2 runs from DGVMs up to 2021 from the TRENDY v11 dataset. Results were first masked with a forest map that is based on Hansen  (Hansen et al. , 2013)  tree cover data. To do this conversion ("tree" cover to "forest" cover), we exclude grid cells with less than 20 % tree cover and isolated pixels with maximum connectivity less than 0. 5 ha following the FAO definition of forest. Forest NBPs are then further masked with the "intact" forest map for the year 2013, i.
8 GtC yr -1 , BLUE-OSCAR of 0. 4 GtC yr -1 , OSCAR-updated H&N2017 of 0. 3 GtC yr -1 ), and between the updated estimate of H&N2017 and its previous model version  (Houghton et al. , 2012). A factorial analysis of differences between BLUE and H&N2017 attributed them particularly to differences in carbon densities between natural and managed vegetation or primary and secondary vegetation  (Bastos et al. , 2021). Earlier studies additionally showed the relevance of the different land-use forcing as applied (in updated versions) also in the current study  (Gasser et al. , 2020). Ganzenmüller et al. (2022)  recently showed that E LUC estimates with BLUE are substantially smaller when the model is driven by a new high-resolution land-use dataset (HILDA+). They identified shifting cultivation and the way it is implemented in LUH2 as a main reason for this divergence.
C3. 3 GOBM evaluation and uncertainty assessment for S OCEAN The ocean CO 2 sink for all GOBMs and the ensemble mean falls within 90 % confidence of the observed range, or 1. 5 to 2. 9 GtC yr -1 , for the 1990s  (Ciais et al. , 2013)  before and after applying adjustments. An exception is the MPI model, which simulates a low ocean carbon sink of 1. 38 GtC yr -1 for the 1990s in simulation A owing to the inclusion of riverine carbon flux. After adjusting to the GCB's definition of S OCEAN by subtracting simulation B, the MPI model falls into the observed range with an estimated sink of 1. 69 GtC yr -1. The GOBMs and data products have been further evaluated using the fugacity of sea surface CO 2 (f CO 2 ) from the SOCAT v2022 database  (Bakker et al. , 2016 (Bakker et al. , , 2022)). We focused this evaluation on the root-mean-squared error (RMSE) between observed and modelled f CO 2 and on a measure of the amplitude of the interannual variability of the flux (modified after  Rödenbeck et al.
The diffuse fraction dataset offers 6-hourly distributions of the diffuse fraction of surface short-wave fluxes over the period 1901-2021. Radiative transfer calculations are based on monthly averaged distributions of tropospheric and stratospheric aerosol optical depth and 6-hourly distributions of cloud fraction. Methods follow those described in the Methods section of  Mercado et al. (2009)  but with updated input datasets. The time series of speciated tropospheric aerosol optical depth is taken from the historical and RCP8. 5 simulations by the HadGEM2-ES climate model  (Bellouin et al. , 2011). To correct for biases in HadGEM2-ES, tropospheric aerosol optical depths are scaled over the whole period to match the global and monthly averages obtained over the period 2003-2020 by the CAMS reanalysis of atmospheric composition  (Inness et al.
, 2019) , which assimilates satellite retrievals of aerosol optical depth. The time series of stratospheric aerosol optical depth is taken from the climatology of  Sato et al. (1993) , which has been updated to 2012. The years 2013-2020 are assumed to be background years and thus replicate the background year 2010. That assumption is supported by the Global Spacebased Stratospheric Aerosol Climatology time series  (1979 -2016; Thomason et al. , 2018). The time series of cloud fraction is obtained by scaling the 6-hourly distributions simulated in the Japanese Reanalysis  (Kobayashi et al. , 2015)  to match the monthly averaged cloud cover in the CRU TS v4. 06 dataset  (Harris et al. , 2020). Surface radiative fluxes account for aerosol-radiation interactions from both tropospheric and stratospheric aerosols and for aerosol-cloud interactions from tropospheric aerosols (except mineral dust).
ILAMB variables cover key processes that are relevant for the quantification of S LAND and resulting aggregated outcomes. The selected variables are vegetation biomass, gross primary productivity, leaf area index, net ecosystem exchange, ecosystem respiration, evapotranspiration, soil carbon, and runoff (see Fig. B3  for the results and for the list of observed databases). Results are shown in Fig. B3  and discussed in Sect. 3. 6. 5. For the uncertainty for S LAND , we use the standard deviation of the annual CO 2 sink across the DGVMs, averaging to about ±0. 6 GtC yr -1 for the period 1959 to 2021. We attach a medium confidence level to the annual land CO 2 sink and its uncertainty because the estimates from the residual budget and averaged DGVMs match well within their respective uncertainties (Table  5 ).
Each system uses a different transport model, which was demonstrated to be a driving factor behind differences in atmospheric inversion-based flux estimates and specifically their distribution across latitudinal bands  (Gaubert et al. , 2019; Schuh et al. , 2019). The inversion systems all prescribe similar global fossil fuel emissions for E FOS ; specifically, the GCP's Gridded Fossil Emissions Dataset version 2022 (GCP-GridFEDv2022. 2; Jones et al. , 2022) , which is an update through 2021 of the first version of GCP-GridFED presented by  Jones et al. (2021) , or another recent version of GCP-GridFED (Table  A4 ). All GCP-GridFED versions scale gridded estimates of CO 2 emissions from EDGARv4. 3. 2  (Janssens-Maenhout et al. , 2019)  within national territories to match national emissions estimates provided by the GCP for the years 1959-2021, which are compiled following the methodology described in Appendix C1.
D2 Contribution of other carbonates to CO 2 emissions Although we do account for cement carbonation (a carbon sink), the contribution of emissions of fossil carbonates (carbon sources) other than cement production is not systematically included in estimates of E FOS , except for Annex I countries and lime production in China  (Andrew and Peters, 2021). The missing processes include CO 2 emissions associated with the calcination of lime and limestone outside of cement production. Carbonates are also used in various industries, including in iron and steel manufacture and in agriculture. They are found naturally in some coals. CO 2 emissions from fossil carbonates other than cement not included in our dataset are estimated to amount to about 0. 3 % of E FOS (estimated based on  Crippa et al. , 2019).
Jones of the Ocean Thematic Centre of the EU Integrated Carbon Observation System (ICOS) Research Infrastructure; Eugene Burger of NOAA's Pacific Marine Environmental Laboratory; and Alex Kozyr of NOAA's National Centers for Environmental Information for their contribution to surface ocean CO 2 data and metadata management. This is PMEL contribution 5434. We thank the scientists, institutions, and funding agencies responsible for the collection and quality control of the data in SOCAT and the International Ocean Carbon Coordination Project (IOCCP), the Surface Ocean Lower Atmosphere Study (SOLAS), and the Integrated Marine Biosphere Research (IMBeR) program for their support. We thank data providers ObsPack GLOBALVIEWplus v7. 0 and NRT v7. 2 for atmospheric CO 2 observations. We thank the individuals and institutions that provided the databases used for the model evaluations used here.
Jones et al. (2021)are updates through the year 2021 of the GCP-GridFED dataset presented byJones et al. (2021). d Ocean prior is not optimized. Variational Ensemble Kalman filter Non-linear least squares four- dimensional variation (NLS-4DVar) Variational Optimization Variational Ensemble Kalman fil-Conjugate Ensemble Kalman fil-Variational GCP-GridFED v2021. 2, v2021. 3, v2022. 1, and v2022. 2 (Thomas G. Thompson ter gradient (re-ortho-normalization) d ter https://doi. org/10. 25925/20220624 (Schuldt et al. , 2022). c North Atlantic, tropical Atlantic, North Pa-cific, tropical Pacific, coastal 47 073 Alin, S. R. ; Feely, R. A. Trans Future 5 Southern Ocean, North Pacific, tropical Pa-cific, coastal 257 424 Nakaoka, S. -I. ; Takao, S. Tukuma Arctica North Atlantic, coastal 70 033 Becker, M.
: CO 2 emissions from land-use, land-use change, and forestry (E LUC ) The net CO 2 flux from land-use, land-use change, and forestry (E LUC , called land-use change emissions in the rest of the text) includes CO 2 fluxes from deforestation, afforesta- tion, logging, and forest degradation (including harvest ac- tivity); shifting cultivation (cycle of cutting forest for agri- culture, then abandoning); and regrowth of forests following wood harvest or abandonment of agriculture. Emissions from peat burning and drainage are added from external datasets (see Appendix C2. 1 below). Only some land-management activities are included in our land-use change emissions es- timates (Table.
the auto-regressive integrated moving average model (ARIMA) and its multivariate treatment or state-space models such as the Kalman filter and generalised autoregressive conditional heteroskedasticity (GARCH) process that are additive  [1]. These methods are well suited for modelling time series when the data are uniformly sampled. However, as the number of time series in a dataset increases, these methods do not scale well because each time series must be trained individually. Moreover, it is difficult to model the shared temporal patterns across various time series in the whole dataset during training and forecasting. Modelling real-world healthcare related time series for forecasting is often difficult owing to the limited availability of data due to practical constraints. For example, if a study is conducted only with a small number of participants, then the dataset might not always be a complete representation of a given task.
We experiment with two real-life time-series datasets from healthcare to prove the efficacy of the proposed solution in multi-step time series forecasting. We further demonstrate the implications of limited individual data on training by varying the availability of data in time and assessing the prediction error. We empirically show that our approach not only reliably predicts in the case of missing observations but also accurately predicts multiple steps ahead in time in the case of limited personal data. The main contributions of this paper are: r Finally, we empirically show that the SS-GP approach outperforms state-of-the-art approaches on two real-world healthcare datasets where there is a need to predict early and where missing data are inevitable.
III. NOTATION Let us assume, N subjects are studied and the training data consists of time series data of K predictor variables denoted by x at time t for each subject 1 ≤ j ≤ N : x j 1 (t),. , x j K (t). Our goal is to make predictions about a response variable y j (t) based on such feature data. For each subject however the time series are sampled at i different times, t j i , such that, t j 1 < t j 2 < • • • < t j m j , where m j denotes the number of measurements of the feature x j k (1 ≤ k ≤ K) that are available for the j th subject. Remark that, for a given subject j, all predictor variables are measured at the same time instances. In what follows, the feature data is denoted in matrix notation: X j = [x j k (t j i ) ] ik denoting a m j × K matrix of which the k th column contains the data of the k th feature of the j th subject over all the time instances.
The measurements of the responses of a subject are collected in a vector: y j = [y j (t j 1 ). y j (t j m j )]. Note that the response variable for subject j is sampled at the same time instances as the predictor variables of subject j. There are two ways that data in time series might go missing: r missing observations within a time-series: time series in the j th instance of training or target data might not be evenly spaced, i. e. , t j (i+1)t j i = λ, ∀i ∈ {1, 2,. , m j -1}, where λ > 0 is some constant. r missing observations in different time instants within all time-series: Time series data of predictor variables are not sampled at the same times across different subjects, i. e. , t j i is not necessarily equal to t j i , ∀j, j ∈ {1,. , N}, i ∈ {1,. , m j } Suppose, we are interested in predictions for a target subject (indexed with '+') based on the measurements of the predictor variables X + and the measurements of the response variable available up to some time t + d : y + = [y + (t + 1 ) y + (t + 2 ) • • • y + (t + d )], where we assume that t + d << t j m j , ∀j ∈ {1,.
2(b ) that has a Euclidean distance of 5. 1 compared to a reference time series. 1) Distance Measurement: Remember that our goal is to make predictions of the response variable y + (t) for t > t + d. Our aim in this section is to find a subset of response variables y j (t) (1 ≤ j ≤ M ) that show similar temporal characteristics with y + (t) for t < t + d. This will lead to a subset X = {(X 1 , y 1 ),. , (X M , y M )} with M << N of the training dataset {Xs, ys} that is used in a non-parametric GP approach for predicting y + (t). For this purpose, we start by calculating the distances between target response time series data y + = [y + (t + 1 ) y + (t + 2 ) • • • y + (t + d )] and training data's response variable (nearest to the allowed time point, i. e. '≤ t + d '). Let's denote this distance vector as Ω + = [ω 1+ ω 2+ • • • ω N + ] T , where ω j+ = dist([y j (t j 1 ) • • • y j (t j d )], [y + (t + 1 ) • • • y + (t + d )] ).
Similarly, multiple such turning points exist that can be used as thresholds represented with the prime ( ) symbol. Intuitively, ω th U can be considered as another appropriate choice for threshold. However, the first value of turning point, ω th L is chosen as the preferred threshold. It selects the "smallest" most informative subset from the training data to capture the trend while keeping the variability among the selected subset to a minimum as compared to other thresholds. For the sake of simplicity, Fig. 4 (b) shows a univariate time series of subject 1 from a dataset (explained in Section VI-B1) and the selected closest subset according to the proposed heuristics. Using the proposed heuristics, the subjects that are closer in the training phase (coloured in red) show a similar trend in the forecasting phase.
B. Collective Temporal Realignment Typically, it is assumed that the time series in the training data are available from some fixed time t = t 0. However, in practical scenarios, the time series in the dataset may have different onsets and rates of progression. Dynamic time warping (DTW) accounts for the similarity in amplitude among time series by calculating the distance between them. It realigns the two time series non-linearly, onto a common set of instants such that the sum of the Euclidean distances between the corresponding points, is smallest. We propose a time series alignment based on the shape of the response variable. We try to find a time instant τ optimal with respect to the target response series such that when the response time series in the training dataset are lagged/led by τ optimal , their shape most resembles that of the target's response time-series.
After temporal realignment and dynamic subset selection based on the available target data (y) in the training and test dataset we apply Gaussian processes based prediction on { X , X + } as it is most resilient to the missing data in time series. We use the selected M << N time series that are in the closest subset of a given time series along with  (8). Mean Absolute Error (MAE) is used as the performance metric to evaluate the regression performance. MAE = 1 N N j=1 |y(t j m j ) -y pred (t j m j )|.