dataesr/scientific-paragraphs-categorization huggingface dataset:
Biodiversity change Species richness was calculated within each 3° latitude by 6° longitude box and time for each pro le, considering data from plankton net, pump, CPR, and sediment trap samples in FORCIS (Fig. 1A ). The species richness in ForCenS was determined by calculating the number of species present in each sample and latitude, and compared to the ones obtained from FORCIS (Fig. 1B ). These analyses focused on 26 species that were found in both ForCenS and FORCIS, using the same taxonomic criteria. Species that were absent in ForCenS, such as B. variabilis, T. eisheri, and T. parkerae, were not considered as a comparison between the datasets is impossible. In a second step, the assessment aimed to determine any species loss or gain from the preindustrial to the postindustrial period.
For this analysis, the diversity in FORCIS and ForCenS was evaluated within each 4. 5° latitude by 9° longitude box and time, considering data from plankton net, pump, CPR, and sediment trap samples in FORCIS, as well as each sample in ForCenS. The species richness in FORCIS was subtracted from that in ForCenS within each grid to identify any changes (loss or gain) in species richness. This analysis focused on the major species (26 species) on a presence / absence basis (Extended Data Fig. 3 ).
Changes through latitude For the data presented in Figure Extended Data Fig. 2 , only studies that provide species counts in the North Atlantic, Antarctic, and/or Arctic Oceans, using data sourced from the FORCIS database were considered as they present the best temporal and spatial data coverage. The selected studies cover the period from 1980 to 2018 (Extended Data Fig. 2 ). The depth pro les of these data range from 0 to more than 100 meters. To examine the latitudinal abundance trend of PF species over time, the surface data (up to 100 meters) and deep-water samples (beyond 100 meters) from 1980 onwards against latitudes grouped in 10-degree intervals are plotted. This analysis speci cally focuses on the spring and summer seasons, which are best documented by data.
Spatial and vertical migration of planktonic Foraminifera The species' poleward migration was rst assessed within the FORCIS database. Thus, the loss and gain of species in the northernmost limit of the North Atlantic and Arctic Oceans is assessed on the PF living at depth ranges between 0 and 100 m during spring and summer before and after the cut-off year (1990). The maximum latitude of the northernmost 5% samples was calculated for all species before and after 1990e. The difference between the maximum latitude before and after 1990 was evaluated to assess the direction and magnitude of the latitudinal migration of the different species (Extended Data Fig. 7 ). The selection of various cutoffs for spatial migration is in uenced by the quantity of data available both before and after applying speci c lters that are sometimes very few between 1910 and 1970.
Acknowledgements The  FORCIS  project is supported by the  French Foundation for Biodiversity Research (FRB) [https://www. fondationbiodiversite. fr/] within the Centre for the Synthesis and Analysis of Biodiversity (CESAB) [https://www. fondationbiodiversite. fr/la-fondation/le-cesab/] and co-funded by  INSU LEFE program , and the  Max Planck Institute for Chemistry (MPIC) in Mainz, Germany.
Dumont et al. (2012)  assimilated remotely sensed albedo in the Crocus snowpack model  (Vionnet et al. , 2012)  to improve the modelling of the spatial distribution of the glacier mass balance. Navari et al. (2018)  further improved the Crocus model using satellitederived albedo to improve surface mass balance (SMB) along Greenland's Kangerlussuaq transect. Other datasets have also been assimilated to improve snow estimation, including snow cover fraction estimates from optical sensors (e. g. Toure et al. , 2018; Xue et al. , 2019)  and measured ice surface temperatures (e. g. Navari et al. , 2018). There have also been several studies assimilating joint datasets. For example, the MODISbased snow cover fraction and albedo have been assimilated in the Common Land Model LSM  (Xu and Shu, 2014)  and the Noah LSM  (Kumar et al.
While albedo parameters in ORCHIDEE have been optimised for vegetation and bare soil, this will be the first study optimising them for ice sheets. Our target area from this study is the Greenland ice sheet. This study is the first test of applying the ORCHIDEE data assimilation system over ice sheets to improve modelling albedo and, in turn, the surface mass balance of the ice sheet. Instead of using a single-site or multisite approach which samples the space, here, to exploit the full spatial coverage of the satellite retrievals, we optimise over the whole area of the GrIS to obtain one best set of model parameters applicable over the full ice sheet. Although this study is only over the GrIS, we can apply the method to other regions. We show how robust Bayesian parameter estimation is an important tool for model development.
We further highlight the different limitations and considerations needed to apply such an approach. The paper is organised as follows. Methods and data, including details about the ORCHIDEE LSM and its DA framework, driving and observational datasets, and performed experiments, can be found in Sect. 2. Section 3 lists the results, starting with an assessment of the prior. This is followed by the results of the main experiments and an evaluation over PROMICE (Programme for Monitoring of the Greenland Ice Sheet) in situ sites. In Sect. 3. 3, we look at the impact of the optimisation on the modelling of the SMB of the GrIS, as well as the different SMB components. In this section, we also perform a sensitivity analysis of the different parameters of the snow model for future work. Finally, the discussion and conclusions can be found in Sect.
(1) Here the B dec and τ dec parameters control the decay rate of snow albedo. f age =   τ snow (t) + 1 -τ snow τ max • dt • exp -P snow δ c -τ snow (t) 1 + g temp (T soil )   , g temp (T soil ) = max(T 0 -T soil , 0) ω β , (3) where P snow is snowfall, δ c is the snowfall depth required to reset the age of the snow, τ max is the maximum snow age, T 0 is the melting temperature (0 • C), T soil is soil temperature, and ω and β are tuning constants. Parameters A aged , B dec , τ dec , τ max , δ c , ω, and β from Eqs. (  1 ) and (3), along with the albedo of ice, α ICE , are the parameters we focused on in this study (listed in Table  1 ). 2. 2 Driving and observational datasets 2. 2. 1 Forcing provided by regional model (MAR) The ORCHIDEE model was forced using meteorological outputs from the regional climate model Modèle Atmosphérique Régional (MAR;  Gallée and Schayes, 1994; Kittel, 2021), version 3.
MODIS snow albedo In this study, we used satellite-derived snow albedo from the NASA (National Aeronautics and Space Administration) MODIS MOD10A1 product  (Hall et al. , 1995). This product uses data from the Terra satellite, which has a sunsynchronous, near-polar circular orbit crossing the Equator at approximately 10:30 local time  (Hall and Riggs, 2016)   on a given day, which is the case near the poles, the best value is kept. This best value is chosen based on solar elevation, distance from nadir, and cell coverage  (Hall and Riggs, 2016). In addition, pixels in MOD10A1 with solar zenith angles greater than 70 • are masked (night is defined as a solar zenith angle greater than 85 • ). Note that this dataset does not include data from the Aqua satellite. The version of MOD10A1 we used in this study was further processed by  Box et al.
(2017). Using data from collection 6 of MOD10A1  (Riggs et al. , 2015; Hall and Riggs, 2016) ,  Box et al. (2017)  de-noised, gap-filled, and calibrated the data into a daily 5 km grid covering Greenland for the years 2000-2017. This dataset was further validated against ground-based measurements from the PROMICE (Programme for Monitoring of the Greenland Ice Sheet) stations  (Fausto et al. , 2021) , and the residual bias in the dataset based on the solar zenith angle was corrected for using a linear regression according to time and latitude  (Box et al. , 2017). Finally, in this dataset, the April values are used for the winter months  (January, February, November, and December). This is because there is inadequate solar illumination to compute the albedo during these months. In this study, we used this dataset processed by  Box et al.
PROMICE in situ data Albedo observations from the PROMICE in situ network were used to evaluate the optimisation. The PROMICE programme was initiated in 2007  (Ahlstrøm et al. , 2008; van As et al. , 2011) , creating a network of on-ice automatic weather stations to provide in situ measurements of accumulation, ablation, and energy balance of the GrIS. Most sites come in pairs, with a lower station (L) placed near the ice sheet margin and an upper station (U) placed higher up in the ablation area  (Fausto et al. , 2021). As such, the majority of sites are found at the edges of the ice sheet. In some regions, there are also additional stations, for example, in the middle (M) of the lower and upper stations. The sites used in this study are listed in Table  2. We started the analysis with the year where all of March to November was available and ended the analysis with the year 2017 (or the last operational year) to be consistent with the rest of the work.
A Bayesian framework To perform the optimisations, we used ORCHIDAS, the OR-CHIDEE data assimilation system. ORCHIDAS is a variational DA system in which all observations within the assimilation time window are included in the optimisation. It uses a Bayesian statistical formalism  (Tarantola, 2005)  where errors associated with the parameters, the observations, and the model outputs are assumed to follow Gaussian distributions. The optimal parameter set corresponds to the minimum of a cost function, J (x): J (x) = 1 2 (y -M(x)) T R -1 (y -M(x)) + (x -x b ) T B -1 (x -x b ) , (4) where J (x) measures the mismatch between (i) the observations y and the corresponding model outputs M(x) (where M is the model operator) and (ii) the a priori (x b ) and optimised parameters (x). Each term is weighted by its error covariance matrices, R and B.
Furthermore, with this method, it is not possible to distinguish the nonlinear effect individual parameters have on the model output from the effect of their interactions with other parameters. It is also very dependent on the range of variations assigned to the parameters. Nevertheless, the Morris approach can still help in giving a broad overview of the most influential parameters and the model outputs they impact. Therefore, in addition to considering further structural changes, it will be necessary to further optimise the model's internal parameters against a range of datasets. With the evergrowing quantity of satellite datasets available, we could consider many different avenues. For example, we could use GRACE (Gravity Recovery and Climate Experiment) satellite mission data to constrain SMB  (Sasgen et al.
, 2020). To constrain ice velocity, we could use products based on Sentinel-1 retrievals  (Mouginot et al. , 2017; Andersen et al. , 2020) , and data from the ESA CCI land surface temperature project  (Karagali et al. , 2022)  could be used to constrain surface temperatures. Combining these datasets with MODIS albedo would result in a rich data source to optimise the model's internal parameters and learn about different processes governing the ice sheet.
Acknowledgements. Data from the  Programme for Monitoring of the Greenland Ice Sheet (PROMICE)  are provided by the  Geological Survey of Denmark and Greenland  (GEUS) at http://www. promice. dk(last access: 3 July 2023). They include sites financially supported by the  GlacioBasis programme as part of Greenland Ecosystem Monitoring  (https://g-e-m. dk/,last access: 3 July 2023), maintained by  GEUS  (ZAK, LYN) and by  Asiaq Greenland Survey (NUK_K). The WEG stations are paid for and maintained by the  University of Graz. We would like to thank  Xavier Fettweis  for providing us with the MAR data used to drive and evaluate the ORCHIDEE mode in this study. We would also like to thank the  ORCHIDEE  project team for developing and maintaining the OR-CHIDEE code. Financial support. This research has been supported by the  European Space Agency as part of a Climate Change Initiative (CCI)  fellowship (grant no.
Code availability. The source code for the ORCHIDEE version used in this model is freely available online via the following address: https://doi. org/10. 14768/e59644bf-2ab2-4826-8409-7ec83f9c56e3 (IPSL Data Catalogue, 2023), distributed under the CeCILL licence (http://www. cecill. info/index. en. html, last access: 3 July 2023, CeCILL, 2020). The ORCHIDEE model code is written in Fortran 90 and is maintained and developed under a Subversion (SVN) version control system at the Institute Pierre-Simon Laplace (IPSL) in France. The ORCHIDAS data assimilation scheme (in Python) is available through a dedicated website (https://orchidas. lsce. ipsl. fr, last access: 3 July 2023; ORCHIDAS, 2023). Data availability. The MAR v3. 11. 4 code and outputs used in this study are available at ftp://climato.
We therefore use iterative solvers. The main issue is how to efficient handle a large number or RHS. It will be shown in particular that block Krylov methods can efficiently fix this difficulty. We also propose some adaptations that significantly speedup the proposed reconstruction algorithm from section 3. Since this step is the most critical in our inversion algorithm and may apply to other large-scale inverse problems, more technical details will be provided on some practical implementations. with A ∈ M n,n (C), and both X and B ∈ M n,p (C). This is done using PETSc  [3, 4] , the linear algebra backend used in our numerical tests, which can convert the This manuscript is for review purposes only. coefficient matrix from (3. 4) stored using a MatNest, into the more general matrix format MatAIJ.
Such blocked operations, also used in block Krylov methods, have higher arithmetic intensities. In Figure  2  of  [23] , authors compare the cost of doing multiple sparse matrix-vector products versus a single sparse matrix-dense matrix product and show that it can be up to 400% more efficient with 64 columns. In Figure  6  of  [22] , authors compare the cost of doing multiple forward eliminations and backward substitutions with a single column vector versus a single forward elimination and backward substitution with a block of column vectors and show that it can be up to 250% more efficient with 128 columns. In KSPHPDDM, QR factorizations are computed using the CholeskyQR method which was thoroughly studied in  [38]. Users are free This manuscript is for review purposes only. to manipulate PETSc built-in types or provide their own preconditioned operator, but the data structure provided by PETSc and expected by KSPHPDDM assumes that blocks of vectors are stored in a standard contiguous column-major dense format distributed following a one-dimensional row partitioning among MPI processes.
For that reason, solving the full system (4. 1) with p = 779 right-hand sides is not tractable. Instead, the complete block of right-hand sides is decomposed into contiguous sub-blocks which are then solved in sequence. At the beginning of each new cycle, deflation is performed using a tolerance of 10 -10. That is, a rank-revealing QR factorization of the block of initial residuals is computed, and the Arnoldi process only iterates on blocks of size i ∈ 1; p such that R ii ≤ 10 -10 R 11. This is achieved in PETSc using the option -ksp matsolve batch size p ′ , which will then successively solve p This manuscript is for review purposes only. deflation tol 1e-10 -ksp matsolve batch size p ′ -ksp hpddm type bgmres. Four different values of p ′ are used: 390, 195, 98, and 49. This corresponds to respectively 2, 4, 8, and 16 successive subsystem solves.
However, when comparing the reconstruction results, it appears that the SMX probe provides more interesting information on the target deposit. Note that due to the fast resolution of the finite element problems, the remaining limiting operations are the level-set convection and the gradient computation. The first operation is currently done sequentially, but can be easily parallelized. For the second operation, the gradient is computed directly inside FreeFEM domain-specific language. It could be made more efficient by offloading this operation to a specific kernel written in a lower-level language, e. g. , C++, but this goes beyond the scope of this paper.
This could be a useful solution for many cities in low-income countries, for example, and could contribute to the WMO (2022) efforts to set up flood alerts worldwide. If acoustic sensors are to be used in future rainfall monitoring, further development of the acoustic sensors will be necessary, including minimization of recording uncertainties and the ability to transmit data in real time. Following our examination into using simple low-cost acoustic sensors, we can see the potential they hold. Data availability. The rainfall data collected by the acoustic sensors and by the meteoblue AG's rain gauges are publicly available via the following Zenodo repository: https://doi. org/10. 5281/zenodo. 7559671 (Peleg and Torelló-Sentelles, 2023). Supplement. The supplement related to this article is available online at: https://doi.
org/10. 5194/nhess-23-1233-2023-supplement. Author contributions. NP wrote the first draft of the manuscript and prepared the last figure. HTS deployed and maintained the sensor network, analyzed the data obtained from the sensors, and prepared Figs. 1  and 2. All authors equally contributed to revising and structuring the manuscript. Competing interests. At least one of the (co-)authors is a guest member of the editorial board of Natural Hazards and Earth System Sciences for the special issue "Hydro-meteorological extremes and hazards: vulnerability, risk, impacts, and mitigation". The peerreview process was guided by an independent editor, and the authors also have no other competing interests to declare. Disclaimer. Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements. The authors thank meteoblue AG (https:// www. meteoblue. com,last access:  26 March 2023 ) for providing the rainfall data for the city of  Zurich and Goodsell Systems Ltd. for their assistance and further developing the acoustic sensors used. We also thank  Marika Koukoula ,  Tabea Cache ,  Wenyue Zou , and  Zhaozhao Zeng  for their assistance deploying the sensors in Zurich and Milan. Financial support. Nadav Peleg  and  Herminia Torelló-Sentelles  were supported by the  Swiss National Science Foundation (SNSF) , grant no. 194649  (" Rainfall and floods in future cities "). Francesco Marra  was partially supported by the  Cariparo Foundation  through the  Excellence Grant   2021  to the "Resilience" project. Review statement. This paper was edited by  Paolo Tarolli  and reviewed by two anonymous referees.
Variations of the Decorrelation Length With the Measurement Resolution Decorrelation lengths used in GCMs are often derived from observational data from active remote sensing  (Jing et al. , 2016; Oreopoulos & Norris, 2011; Oreopoulos, Cho, & Lee, 2022). As shown in the previous section, the vertical resolution of the grid on which we generate the cloud scene can have a significant impact on the values of overlap parameters and decorrelation lengths. This may also be applied to the vertical resolution at which those instruments measure cloud fraction profiles, their overlap and hence decorrelation lengths. At the vertical resolution of those instruments, for example, 480 m for CloudSat, a layer is identified as entirely cloudy even if the cloud does not fully extend on the vertical of the layer.
Acknowledgments Our many thanks go to  Céline Cornet  and  Frédéric Szczap  for insightful discussions about this work. We thank the two anonymous reviewers for their comments and feedback, thanks to which the originally submitted manuscript was improved. We acknowledge support from the  Agence Nationale de la Recherche (ANR , grants  MCG-RAD ANR-18-CE46-0012 ) and the  Centre National d'Études Spatiales (CNES , project  EMC-Sat ).
Data Availability Statement A repository containing the scripts for the ERO algorithm presented in this paper is pulished on GitHub at https:// github. com/raphleb/ERO. git  (Lebrun, 2022). The software htrdr (version 0. 9. 1) used in this paper for the radiative computations is available at https://gitlab. com/meso-star/htrdr  (Forest et al. , 2023).
Discriminant Analysis A discriminant analysis (DA) was performed to check whether each measurement point could be identified as belonging to one of the five zones from the ECa measurements alone. DA consists of finding a discriminant function that projects the points onto a line passing through the centroids of the scatter plots corresponding to each zone in an optimal direction in order to best discriminate these scatter plots. However, this proven method has two drawbacks. The first is the linear nature of the approach, which does not necessarily match the nature of the boundaries between the different zones in the data hyperspace. The second is that the effectiveness of the discrimination is assessed on the same dataset that was used to find the discriminant function, and not on a dataset that is independent of the analysis result.
For the first two algorithms, the dataset was split into a training part and a test part. Fot this, the data were classified according to their electrical conductivity and every second sample (50%), every fourth sample (25%) and three out of four samples (75%) were chosen to form a training dataset, with the rest of the data used for cross-validation, i. e. , to check the performance of the method in classifying the measurement points according to their area of belonging. In this way, each subset of the data covers the entire ECa salinity range. The machine learning algorithms used do not have a linearity constraint, i. e. , they can accommodate non-linear (curvilinear) boundaries between different areas in the hyperspace of the data, and are therefore likely, if this is the case, to provide better results than discriminant analysis.
Concerning the flood zones, the points misclassified as belonging to the frequent flood zone were located on the former salt exploitation sector, or accompanied the drainage axes towards the halophyte zone. Again, a concentration of misclassified points accompanied the steep salinity gradient between the hills and the periodically flooded area. Similarly, the results from the machine learning analysis are presented in Table  5. The best results were obtained with the Bayesian naive classification and 5 nearest neighbours algorithms and considering 75% and 25% of the points for training and testing, respectively (Figure  7 ). On the maps in Figure  7 , the density of misclassified points was lower than in Figure  6  as the test sample was only 1042 points instead of the whole dataset for the other algorithms.
987). As a result, the information contained in the dataset is poor in terms of diversity, being limited to 1 or 2 parameters. These conditions are outside the usual framework of application of machine learning algorithms, which generally rely on a much larger number of parameters for discrimination  [35] [36] [37]. Salinity and the salt profile are major parameters in the differentiation of the five zones of the estuary. For the discriminant analysis, the best result is obtained from the raw data and the logarithmic transform of the salinity gradient information. The confusions concern areas with similar salinity ranges and a high degree of overlap (Table  2 ), with the two highsalinity inundation areas on the one hand, and the intermediate-salinity areas of bare soil or halophyte plants on the other.