dataesr/scientific-paragraphs-categorization huggingface dataset:
In this section, we aim at pointing out the added value of the approach presented in Sect. 3 when dealing with models run at different spatial resolutions. We first present the distributions of the maxima of the three variables in order to analyse the differences and similarities between the reanalysis data sets. Then we compare single-variable and multivariable catalogues of both ERAI-2. 5 and NCEP2 to the XWS database. Finally, we analyse the catalogue of final events of each reanalysis data set in order to determine how many common events they share and conclude on the performance of the methodology.
Probability distribution functions The probability distribution functions (PDFs) obtained from the maxima time series of each variable are plotted in Fig. 6  for ERAI, ERAI-2. 5 and NCEP2. While the distributions of the MSLP anomaly and 10 m wind speed ratio are nearly identical from one data set to the other, the relative vorticity distributions differ. A first shift towards lower values is observed when downgrading the resolution from ERAI to ERAI-2. 5 and a second one when changing the model from ERAI-2. 5 to NCEP2 This stresses the added value of using intensity thresholds based on percentiles rather than absolute values in order to ensure the adaptability of the detection to different kinds of data sets.
Single-variable and multi-variable catalogues The results of the methodology are first shown in Fig. 4  with, for each reanalysis data set, the number of events generated with each of the variables, the number of common events to pair-wise variables and the number of events in the final set (i. e. events common to the three variables). The number of events common to the 3 variables is always reduced compared to the number of events within the catalogues of individual variables: 24 events with ERAI, 21 with ERAI-2. 5 and 33 with NCEP2. Table  3  summarises the number of insurance storms within each single-variable and multi-variable catalogues as well as the total number of detected events and the resulting ratio. In terms of selectivity, the intersection of the three variables still leads to a higher ratio than the singlevariable ratios.
With ERAI-2. 5, we get the same insurance storms and also miss  Herta (1990 ), Gero (2005)  and Emma (2008) for the same reasons as with ERAI. With NCEP2, the ratio is lower than the XWS ratio but remains higher than the single-variable ratios. This is explained by the fact that five insurance storms are not detected: Herta (1990),  Wiebke (1990 ), Lothar (1999 ), Gero (2005 ) and Emma (2008). These results highlight two issues that prevent the detection of all the insurance storms with our methodology. The first one is linked to the spatial resolution: a model run at a low resolution may not be able to reproduce small-scale systems such as  Wiebke (1990) and Lothar (1999). The underestimation of Lothar in NCEP2 was also mentioned in  Pinto et al. (2012). Thus there is little that can be done to allow the detection of these events in such a data set.
Comparison of the final events between reanalysis data sets Finally, we estimate the ability of the method to detect the same events from different data sets by computing the ratio of common events between two reanalysis data sets over the total number of events. The definition of a common event between two data sets is as follows: if two final events generated and selected in two different data sets share a common time step, we consider them to actually exhibit the signature of the same event in each data set respectively. Between ERAI and ERAI-2. 5, the ratio value is 0. 71: 15 common events divided by 21 events of ERAI-2. 5. Between ERAI-2. 5 and NCEP2, there are 16 common events within the 33 events of NCEP2; the resulting ratio is thus equal to 0. 48. This means that almost half of the final events of NCEP2 are the same ones as  those of ERAI-2.
5. Although the two reanalysis data sets do not provide the same information in terms of extremes (e. g. small-scale systems), we succeed in detecting almost 50 % of common extreme events. To compare,  Pinto et al. (2012)  selected the 10 top-ranked events detected with a wind-based loss index in 2 reanalysis data sets, ERA40 and NCEP. They found that only two events were present in both cases. They highlight the difficulty of comparing extreme events, in particular because because the location of high wind speeds may differ from one data set to the other. Finally, it would not be possible to get our result by considering the most intense events in one variable only. We show in Fig. 7  that the 10 reference storms are not the 10 most extreme events in any pair of reanalysis data sets and variables, which generalises the result obtained with ERAI only.
First, in terms of selectivity of events, we show that by taking the intersection of events selected with different variables separately, we not only reduce the total number of events but above all we retain most of the damaging ones. Second, when comparing the final events obtained with two different reanalysis data sets displaying important discrepancies in the reproduction of small-scale events, half of the final events are common to the two data sets, which suggests the robustness of the method. We still miss some of the insurance storms either for intensity reasons (one or three events according to the data set) or because of the offset effect (two events). However, the modification of the criteria in order to include those events leads to a depreciation of the overall results. The methodology has been developed for the ETCs associated with windstorms that could generate important damages in Europe.
Acknowledgements. Madeleine-Sophie Déroche  is grateful to the  AXA Research Fund  for the PhD grant that supports the research for this paper. The authors wish to express their gratitude to Gwendal Rivière as well as to the reviewers for their helpful comments. Edited by: B. D. Malamud Reviewed by:  U. Ulbrich  and one anonymous referee The publication of this article is financed by  CNRS-INSU.
Hayashi and Golder (1977)  and  Hayashi (1982)  discuss the ''space-time'' (wavenumberfrequency) spectra of realistic atmospheric models and datasets. We are not aware of any previous studies examining frequency-wavenumber domain spectral fluxes and transfers in idealized QG turbulence models, or in an oceanic context, as we do here. Note that our focus here is on isotropic wavenumber-frequency spectral diagnostics. In a companion paper, we analyze spectral diagnostics in the anisotropic wavenumber-frequency domain to better understand the role of nonlinearities in westward eddy propagation. We examine output from the same two-layer QG turbulence model utilized in ASFMRS. However, the realistic eddying ocean model utilized here is the Hybrid Coordinate Ocean Model (HYCOM;  Chassignet et al.
Spectral slopes in wavenumber and frequency space are not equal, as they would be if  Taylor (1938) 's hypothesis, which relates frequency to wavenumber spectra, held precisely. The limitation of the  Taylor (1938)  hypothesis in our results is consistent with discussions in  Hayashi and Golder (1977) , who found no simple relationship between the frequency and wavenumber spectra of kinetic energy in realistic atmospheric models and atmospheric datasets.
Acknowledgments. We thank three anonymous reviewers whose comments greatly improved the manuscript. Further helpful discussions with  Glenn Flierl ,  Steve Griffies ,  Joe Pedlosky , and  Carl Wunsch  are gratefully acknowledged. BKA and AJM acknowledge support from  Office of Naval Research (ONR)  Grant  N00014-11-0487 ,  National Science Foundation (NSF)  Grant  OCE-0960820 , and  University of Michigan  faculty startup funds. MM acknowledges support from a subcontract of the  ONR grant above  to the  University of Victoria. JFS and JGR acknowledge support from the projects '' Global and remote littoral forcing in global ocean models'' and ''Ageostrophic vorticity dynamics of the ocean ,'' respectively, both sponsored by  ONR  under Program Element  601153N. RBS acknowledges support from  Centre National de la Recherche Scientifique (CNRS) ,  NSF  Grants  OCE-0960834  and  OCE-0851457 , a contract with the  National Oceanography Centre, Southampton , and a  NASA  subcontract to  Boston University.
Introduction Significant wave height (SWH) of ocean surface wave is one of the most important parameters for offshore engineering application and ocean model forecast. Since decades ago, the spaceborne Synthetic Aperture Radar (SAR) has become a useful dataset for providing SWH, due to its high spatial resolution, wide spatial coverage and all-weather capability  [1, 2]. Especially, the SAR wave mode, which was employed by the European Remote Sensing Satellite-1/2 (ERS) SAR  [3] , Environmental Satellite (Envisat) Advanced Synthetic Aperture Radar (ASAR)  [4] [5] [6] , and is also adopted by the recently launched Sentinel-1A  [7, 8] , could provide global coverage of ocean wave information since 1991. Since then, the SAR wave mode SWH data have been used in the various applications from the ocean wave assimilation  [9]  to swell dissipation estimation  [10]  or swell source identification  [11].
However, the error analysis and quality assessment on these datasets are of vital importance to meet the requirement of these applications. Numerous studies have been carried out for the validation of SAR derived SWH data. Traditionally, the validations were performed against the buoy measurements (e. g. ,  [12] [13] [14] [15] [16] [17] ) or the ocean wave model outputs (e. g. ,  [18, 19] ). In such type of validation works, the quality of the SAR SWH products was simply assessed through the direct comparison using the standard statistical methods (e. g. , estimation of bias and/or Root Mean Square Error), assuming no error in the buoy observations or ocean wave model output results. However, this assumption does not hold strictly as both buoy and model data are subject to errors. On one hand, besides the instrument error of buoys, the sampling variability may not be negligible owing to the noticeable collocation distance of the observations from the buoy and the satellite  [20].
On the other hand, the quality of ocean wave model results is limited by the model configuration, parameterization and the input wind forcing. Thus, not only the error of SAR retrievals but also other factors may contribute to the validation statistics. Therefore, these methods only yield an inter-comparison, but not an "absolute" validation. In contrast to those direct inter-comparisons, the triple collocation error model, in which the errors in all the collocated triple datasets are taken into account, has been proposed  [21]. The novel and advanced error model requires three datasets, including in situ, remote sensed and model data, with an independent error structure. And this contributes to its major advantage of simultaneously providing the error statistics in each product and the relationships between different datasets.
In practice, this problem could be more severe for the case of SAR wave mode observations than altimeter data. Because SAR data density is smaller (an average of 100 km between data points for the Envisat ASAR wave mode), and the numbers of buoys with open access data are too limited, the SAR wave mode measurements and the buoys have very little opportunity to be collocated exactly in space. Therefore, the collocation distance between SAR and buoy is an important issue in the validation work, not only for the triple collocation, but also for the inter-comparison against buoy. In this paper, for the first time, the triple collocation error model is introduced in the validation of Envisat ASAR wave mode SWH data, in order to estimate the "absolute" error of ASAR derived SWH, and compare its quality to the datasets from buoys and wave model hindcast.
Envisat ASAR Wave Mode Data The SAR acquisition mode, so-called wave mode, is dedicated to detect the ocean wave information on global basis. In this wave mode, the Envisat ASAR has generated huge number of small SAR images (called imagettes) of 7 by 10 km every 100 km at the incidence angle of 23° and VV polarization, from its launch in March 2002 to the end of the mission in April 2012. The Envisat ASAR wave mode data used here were taken from 2003 to 2008, covering a period of six years. Examples of these Envisat ASAR imagette are shown in Figure  1. Under the quasi-linear assumption of SAR-Ocean imaging mechanism, European Space Agency (ESA) used a methodology to produce a level 2 wave mode product of ocean wave spectrum without a priori information  [30, 31]. The cross spectra technique  [32]  was also employed in the inversion scheme to remove the 180° ambiguity in wave propagation direction.
From the inverted ocean wave spectra the significant wave height Hs could be obtained by ( ) 4 , s H d dfF f = α α   (1) where F(f, α) represents the wave spectra in frequency (f) and direction (α) space. Although the level 2 ASAR products contain the ocean wave spectra, the objective of this paper is only limited to the quality assessment of the SWH product. The major reason for the limit is that the number of directional wave buoys deployed in the ocean is too small to achieve a triple collocated dataset of wave spectra as large as that of SWH. As discussed in the Section 4. 1, the triple collocation analysis requires a large dataset to produce the reliable results, and the SWH, but not wave spectra, could meet the requirement. The data used in the validation were selected by a quality control procedure.
Buoy Data Significant wave height data have been collected from 152 buoys, which are freely available from National Oceanic and Atmospheric Administration's (NOAA) National Data Buoy Centre (NDBC). The buoy data used here are obtained from three buoy networks: NDBC, the Coastal Data Information Program (CDIP), and the Environment Canada's Marine Environmental Data Service (MEDS). The locations of the buoys used for this study are depicted in Figure  2. Furthermore, the buoys deployed at deeper than 200 m water depth and greater than 50 km offshore distance, were selected, and with their locations shown in Figure  2.
Wavewatch III SWH Hindcast The third dataset used in this work are the significant wave height hindcast results from the database of IOWAGA (Integrated Ocean Waves for Geophysical and other Applications) project of IFREMER  [33]. The wave hindcasts were performed using the ocean wave model of WaveWatch III (hereafter ww3), forced by the Climate Forecast System Reanalysis winds, on 0. 5° × 0. 5° global grid. The model uses a parameterization called TEST451, with significant improvements for swell dissipation  [34, 35]. The hindcast database also provides SWH outputs at the location of NDBC buoys, which are used in this work. All the ww3 model SWH hindcast data from IOWAGA used here could be freely available from IFREMER. It should be noted here that, the IFREMER IOWAGA ww3 ocean wave hindcasts have not been assimilated with any observations (SAR or buoy) by now.
Based on the triple collocation error model above, the statistics of the Root Mean Square Error (RMSE) and Scatter Index (SI) can be obtained for every individual data. The definitions are as follows: 2 i i RMSE e = (4) 2 i i i e SI H = (5) where the i subscript represents for buoy, ASAR, and ww3, respectively. The scatter index is a statistical metric for ocean wave data inter-comparison. Essentially, it is a normalized measure of error that takes into account the average of the wave data. Lower values of the SI are an indication of a better data quality.
Collocation Criteria and Collocated Results For validation purpose, the data from Envisat ASAR wave mode, buoy, and ww3 wave model should be triple collocated in time and space. The temporal interval was limited to less than 30 min for the triple datasets. For spatial collocation, only the distances between SAR and buoy have to be taken into consideration, because the ww3 hindcast model used here outputs SWH at the exact location of buoys. Different distances between SAR imagettes and buoy observations have been chosen as maximum distance of collocation criteria, from 200 km to 10 km, stepped by 10 km. Figure  3  shows how this collocation procedure works as an example of 50 km. As shown in Figure  3 , the distance between imagette acquired at 19:16 UTC on 10 January 2008 and the buoy in the west of Moresby Island (with NDBC buoy ID 46208) is 31 km, less than the chosen maximum collocation distance of 50 km presented in red dashed circle.
The numbers of triple collocated data points through different distances are shown in Figure  4. One can see that, the collocated numbers drop significantly with the decreasing collocation distance, both for all buoys and deep open ocean buoys. Even for all the buoys, only less than 100 data points could be found with 10 km collocated distance for six years, although the number is above 17,000 with 200 km distance. Simulations indicated that more than 500 samples of collocated triplets are needed to achieve reliable results with small enough uncertainty  [37]. In this work, we used a stricter standard of 1500 samples, which yields an uncertainty within 6% according to the study in  [37]. Thus, the collocation datasets with collocation distance less than 50 km were excluded in the error analysis of following subsections.
Triple Collocation Comparison Results Using the triple collocation error model presented above, the significant wave height errors for each of the triple collocated datasets have been estimated. Figures  5  and 6  illustrate triple collocation comparison results of Envisat ASAR, NDBC buoy and ww3 wave model significant wave height data, with collocated distances of 50 km, 100 km, 150 km and 200 km, for collocations with all buoys and the deep and open ocean buoys, respectively. In order to look further into the trend of the comparison results, the estimates of calibrated coefficients, RMSE, and SI, for all collocated distances, are listed together in Tables  1  and 2. From Figures  5  and 6 , one may be curious about the "empty" bins in the scatter plots with regard to NDBC buoy. In fact, this is because that the buoy SWH measurements have a resolution of 0.
Error Analysis on Collocation Distance The estimation of the error for the Envisat ASAR derived SWH with the dependence of the collocation distance is shown in Figure  7. In the figure, the circles and lines refer the RMSE of Envisat ASAR SWH and the regression lines, respectively, while the blue and red symbols indicate the results from all buoys and those deployed in the deep and open ocean. It is shown that, the errors of Envisat ASAR are linear to the collocation distance, and decrease with the decreasing collocation distance. For RMSE of Envisat ASAR wave mode derived SWH estimated from datasets with all buoys and those in the deep and open ocean, linear regressions were performed with collocation distance. This provides RMSE as a linear function of collocation distance D, given by Equations (  6 ) and  (7) , for all buoys and the deep open ocean buoys collocations, respectively,  Using the linear function above, the error of Envisat ASAR for significant wave height with zero collocation distance can be obtained.
Discussion on Error of Envisat ASAR Wave Mode SWH in Coastal Waters As pointed out above, the triple collocated comparison indicates that the SWH errors of Envisat ASAR wave mode data are smaller in the deep and open ocean than the coastal regions. One of the major reasons is that the performance of the ocean wave retrieval algorithm of Envisat ASAR wave mode may be poor in the coastal waters, due to the modulation transfer function (MTF). The SAR MTF T adopted in the ASAR wave mode retrieval algorithm, consists of Real Aperture Radar (RAR) MTF T R and velocity bunching MTF  [1] : v R x T j kT T = -β + (8) ( ) / sin cos v y T k K j = -ω θ + θ (9) where β represents the range to velocity ratio of the SAR platform, θ the radar incidence angle, T v the orbital velocity transfer function and j 2 = -1.
Discussion on the Triple Collocation Results In this paper, we have applied the triple collocation technique to assess the quality of the ESA's Envisat ASAR wave mode SWH product. Therefore, it is interesting to discuss this first validation result from triple collocation technique with the previous studies, both the triple collocated comparison for the altimeter SWH, and the conventional comparison for the Envisat ASAR SWH. As shown in Section 4. 2, the triple collocation analysis produced the result that the Envisat ASAR has the largest error, followed by buoy errors, and the ww3 wave model has the smallest. The performance of buoy data may cause a little surprise, because the buoy SWH measurements are generally assumed to be of high quality and be used in numerous validation studies as the "truth" data.
In fact, this finding is consistent with the previous altimeter SWH triple collocated validation result. In the triple collocation analysis on SWH from ERS altimeter, ECMWF (European Centre for Medium-Range Weather Forecasts) wave model and buoys, the buoy errors were also found to be the largest  [26]. In their work, Janssen et al. attributed the largest error of buoy SWH data to the representativeness error, and the quality control issues  [26]. Although this could be a possible explanation of the larger buoy errors found here, it remains further studies. Li et al. presented a validation and inter-comparison of ESA's SWH derived from Envisat ASAR wave mode against buoy and wave model, and an RMSE of 0. 88 m and 0. 65 m were found in the comparison in respect to buoy and wave model, respectively  [19].
Both are larger than the triple collocation analysis result here (0. 55 m derived from dataset containing all buoys). The reason why the error from conventional comparison are larger may be that the triple collocation technique here could produce the "absolute" error, while conventional inter-comparison only yields the errors in respect to buoy or wave model and errors from the buoy and model data are not taken into consideration. From the scatter plots in Figures  5  and 6 , it is clear that the ASAR derived SWH has significant underestimation for high sea state, particularly when SWH is above 5 m, compared to the buoy or ww3 SWH. This saturation effect can be also found in previous validation studies  [15, 19] , and it is due to the stronger azimuth cut-off effect in high wave cases, affecting the quasi-linear assumption in the Envisat ASAR wave mode retrieval algorithm.
Conclusions The triple collocation error model technique is a promising method to estimate the error structures from remote sensing retrievals. In this paper, the triple collocation error model is applied to the error estimation and analysis on Envisat ASAR wave mode derived SWH data for the first time, using NDBC buoy and ww3 wave model data. Overall, SWH error of Envisat ASAR wave mode is in the order of 0. 5 m and 24% for RMSE and SI, which much larger than that of NDBC buoy and ww3 wave model. The analysis on the Envisat ASAR SWH error trend of the collocation distance shows a linear dependency of error on distance. Utilizing this linear relation, the absolute error of Envisat ASAR wave height was obtained with zero collocation distance. The RMSEs of 0. 56 m and 0. 49 m for the Envisat ASAR wave mode SWH are presented for the regions of all buoys and buoys in the deep and open ocean, respectively.
Acknowledgments The Envisat ASAR wave mode data has been provided from the Dragon-3 project ( ID 10412 ) and copyrighted to ESA. We are also grateful for the free access to buoy measurements provided by  NDBC. The work was partly supported by financial sponsorship of the  China Scholarship Council (CSC)  when  He Wang  was in  Laboratoire d'Océanographie Spatiale ,  IFREMER  as a visiting scholar. And the work was also supported by funding from the  Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration of China  (No. SOED1410 ).