Currently, global directional wave spectra are routinely providing by synthetic aperture radar (SAR) on Sentinel-1 in Wave Mode and real aperture radar, i.e., SWIM onboard CFOSAT. However, SAR spectra suffer from azimuth cut-off effects, while SWIM spectra exhibit parasitic peaks and 180° ambiguity. Leveraging the complementary of these two satellite radars for directional spectra merging remains an open scientific challenge. In this letter, we propose a deeply-learned based 2D wave spectrum fusion model aiming to integrate CFOSAT SWIM and Sentinel-1A wave mode Level-2 products. After spatiotemporal collocating, and rejecting suspicious spectra, two-year period (June 2022 to June 2024) of 2D wave spectra triplets (S-1, SWIM, and ERA5) are used for the fusion model training. The deep learning merged spectra show good consistency with ERA5 benchmark regarding 2D spectra, the derived omni - directional energy distribution and the integrated wave parameters. Comparative analysis with ERA5 reanalysis demonstrates that our fused directional spectrum could effectively compensate for high-frequency information loss and spectral distortion in SAR products, meanwhile suppress SWIM's parasitic peaks and resolve directional ambiguity. Qualitatively, compared to ERA5, the Brüning’s correlation coefficient and square error of our fusion results reaches 0.95 and 0.17, significantly outperforming official SAR (0.79 and 0.58) and SWIM (0.83 and 0.52) products. The fusion mitigates SAR’s high-frequency losses and SWIM’s artifacts, enhancing ocean wave spectrum accuracy for improved geophysical applications.

Face recognition service providers protect face privacy by extracting compact and discriminative facial features (representations) from images, and storing the facial features for real-time recognition. However, such features can still be exploited to recover the appearance of the original face by building a reconstruction network. Although sev-eral privacy-preserving methods have been proposed, the enhancement offace privacy protection is at the expense of accuracy degradation. In this paper, we propose an adver-sarial features-based face privacy protection (AdvFace) approach to generate privacy-preserving adversarial features, which can disrupt the mapping from adversarial features to facial images to defend against reconstruction attacks. To this end, we design a shadow model which simulates the attackers' behavior to capture the mapping function from facial features to images and generate adversarial la-tent noise to disrupt the mapping. The adversarial features rather than the original features are stored in the server's database to prevent leaked features from exposing facial information. Moreover, the AdvFace requires no changes to the face recognition network and can be implemented as a privacy-enhancing plugin in deployed face recognition systems. Extensive experimental results demonstrate that Adv Face outperforms the state-of-the-art face privacy-preserving methods in defending against reconstruction at-tacks while maintaining face recognition accuracy.

Characterizing the uncertainties in buoy ocean wave records is critical not only for understanding the limitations ofin situwave measurements, but also for interpreting the implied accuracies of the remotely sensed products in which these buoy data are used as validation references. This letter preliminarily assesses the error of long-period swell heights (Hss) representing specific directional wave partition energy observed from deep-water buoys moored in the northeast Pacific. We propose a buoyHsserror estimation method by combining dual and triple collocation using data derived from buoys, two kinds of space-borne radars and numerical simulations. Compared to traditional methods, the proposed approach can reveal “absolute” errors (with respect to the underlying truth) from buoyHss, accepting and then confirming that swell heights from buoy, satellite and model are all uncertain. This study simultaneously employs ocean swell products derived from synthetic/real aperture radars (Sentinel-1A/B and CFOSAT/SWIM) and WaveWatch III® ocean wave model hindcasts to diagnose the accuracy of theHssvalues observed by buoys of National Data Buoy Center (NDBC) and Coastal Data Information Program (CDIP) during the period from July 2019 to October 2021. We quantify that the NDBC’s 3-m heave-pitch-roll buoy (CDIP’s Waverider buoy) recordedHsshave root-mean-square error of 0.17 m (0.12 m), or have about 10.65% (7.06%) uncertainty relative to the meanHssvalue (approximately 1.6 m). Our findings imply that the reference value uncertainties should be taken into account when understanding direct satelliteHssvalidation against buoyin situ.

Nowadays, Sentinel-1 (S-1) synthetic aperture radars (SARs) operating in wave mode and the real aperture radar (RAR) called Surface Waves Investigation and Monitoring (SWIM) onboard the China-France Oceanography SATellite (CFOSAT) are the only two kinds of spaceborne radars providing directional ocean wave information globally. To quantify the absolute uncertainties in the swell wave heights of a specific wave system (Hss) observed from these two spaceborne sensors, a triple colocation error model is exploited via WaveWatch III (WW3) wave model hindcasts for the first time. After implementing spatiotemporal collocation, cross-assigning swell partitions, and rejecting suspicious data, a database of the optimal-matched Hss triplets (S-1, SWIM, and WW3) is determined over a one-year period (June 2020 to June 2021). Qualitatively, traditional dual intercomparisons indicate the inconsistency between the Hss from both SAR and RAR radars in terms of systematic biases. Furthermore, the triple collocated error analysis quantitively reveals that, at a global scale, SWIM onboard CFOSAT has the least uncertainty in Hss (~0.2 m root-mean-square error (RMSE) and ~11% scatter index (SI)) compared with S-1 SAR (0.35-0.50 m RMSE and 17% - 26% SI depending on incidence modes) and WW3, under the assumption that the random errors of the three data sources are independent, indicating that the newly launched SWIM instrument is an invaluable resource of directional wave information for the scientific community. The results are discussed with respect to regional error characteristics along with a feasible explanation of error sources. The findings could be helpful for better understanding and synergistically exploiting the Hss datasets from these two spaceborne radars.

Wind-induced oriented textures (WIOTs) are commonly used to retrieve sea surface wind directions from synthetic aperture radar (SAR) images. In this study, we found that WIOTs are also related to sea surface wind speeds (SSWSs). The entropy values in the gray-level cooccurrence matrices (GLCMs) for SAR images containing WIOTs will become steady with increasing distance between pairs of pixels. Furthermore, these steady values of entropy (SVEs) show a clear linear relationship with SSWSs. As a result, an SSWS retrieval model was developed based on this relationship. We used 2222/2223 Sentinel-1 SAR images (wind speed ranges from 5 to 20 m/s) to fit/validate the algorithm. The retrieved SSWSs were compared with the European Centre for Medium-Range Weather Forecast (ECMWF) SSWSs, Cross-Calibrated Multi-Platform (CCMP) SSWSs, and Tropical Atmosphere/Ocean (TAO) buoy measurements, and the root-mean-square differences (RMSDs) were 1.78, 1.70, and 1.78 m/s, respectively. The new model was also tested for SAR images acquired under hurricane conditions. The wind comparisons against stepped-frequency microwave radiometer (SFMR) measurements show an RMSD of 1.28 m/s. Our model’s performance was also tested with the images at different spatial scales in the validation data set. Since the model is based on inherent image patterns, it still works well for SAR images without precise calibration.

Over the past five-year on-orbit running, the AMSR2 brightness temperature are systematically assessed and analyzed monthly. The histograms of cold measurements are used for tracking the drift of calibration. The monthly histogram is composed of TBprobabilities that fell within ± 10K difference between the AMSR2 observations and the first guess coldest simulations using radiative transfer model. The results of time series shows that average cold TBhas seasonal trend owing to cycled variations of sea surface temperature (SST) and water vapor (WV). There are total negative drifts of 0.8K and 2.4K at 18.7H and 23.8H channels. The standard deviations of time series at 23.8V and 36.5V are 4.7K and 3.4K greater than ones at other channels over five years. The main reason for this is that the cold measurements in -75° ~-45° region on the Southern Hemisphere play dominant role in monthly average.

This letter preliminarily assesses the accuracy of ocean wind products from the Ku-band scatterometer (HSCAT) onboard the recently launched Chinese satellite HY-2B. The wind vectors derived from HSCAT during the period from November 15, 2018 to April 30, 2019 are evaluated. The reference wind data include in situ measurements from the offshore meteorological buoys of the National Data Buoy Center, USA, and westerlies mooring of the National Ocean Technology Center, China, and scatterometer winds from the European Advanced Scatterometer (ASCAT) and Indian difference is limited to 25/V2 km, while the HSCAT winds are SCATSAT-1 Oceansat Scatterometer (OSCAT). The spatial temporally collocated with buoys and other scatterometers by less than 0.5 and 1.5 h, respectively. The comparison results show that the HSCAT data have a root-mean-square error (RMSE) of 0.95-1.20 m/s (14.7°-25.7°) regarding the wind speed and direction, respectively, indicating consistency between the HSCAT winds and the reference. Furthermore, better agreement is found for the HY-2B HSCAT winds processed using the Pencil-beam Wind Processor (PWP) algorithm, regarding wind speed (RMSE of 0.95-1.07 m/s) and particularly with respective to the wind direction (RMSE of 14.7°-19.6°), both satisfying the mission specification (<; 2 m/s and <; 20 for wind speed and direction, respectively). The encouraging validation results over the first 5 months demonstrate that the HY-2B HSCAT wind products will be useful for the scientific community.

In order to accomplish the Cal/Val of altimeters more conveniently and economically, we produced a method of sea surface height measurement using an M40 unmanned surface vehicle (USV) equipped with a GPS. The accuracy of the USV in measuring the SSH was evaluated by a campaign conducted in Zhiwan island, Guangdong province. The USV was placed together with the dedicated GPS buoy behind the rear of Runjiang 1 ship, at the same time and the same location. The SSH achieved from the two equipment was then compared with each other. The results showed that: 1) the SSH measured by the USV has an equivalent accuracy with the GPS buoy, and could be used in the Cal/Val of altimeters; 2) the USV and the GPS buoy can work properly in three class sea state situation according to the SWH derived from the GPS data; 3) the attitude of the GPS buoy was much smaller than the USV, but this did not affect the accuracy of the SSH measuring; 4) the USV still have to be improved to accomplish the Cal/Val of altimeters.

Synthetic aperture radar (SAR) imagery is routinely acquired at HH-polarization in high-latitude areas for measuring surface wind over the ocean. However, in the contrary of VV-polarization, there is no HH-polarization geophysical model function (GMF) exists to directly retrieve wind speed from SAR images. In general, HH-polarized normalized radar cross section (NRCS) is thus converted into VV-polarization and then conventional CMOD functions are used with auxiliary wind direction information for wind speed retrieval. In this letter, we propose a new GMF for SAR ocean surface wind speed retrieval, called CMODH, which relates the C-band NRCS acquired at HH-polarization over the ocean, to the 10-m height wind speed, incident angle, and relative wind direction. We first use more than 220 000 ENVISAT ASAR radar backscatter measurements collocated with ASCAT winds to derive the CMODH coefficients. Subsequently, 1459 RADARSAT-2 (RS-2) and 428 Sentinel-1A/B (Sl-1A/B) HH-polarized SAR acquisitions under different wind speeds are matched to in situ buoy observations to validate CMODH. The statistical comparisons between SAR-observed and simulated NRCS show a bias of -0.07 dB and a root-mean-square error of 1.62 dB for RS-2, and -0.01 dB and 2.48 dB for S1-1A/B. These results suggest that the proposed CMODH has the potential to directly retrieve ocean surface wind speeds using C-band SAR images acquired at HH-polarization, with no need for NRCS transformation by using various empirical and theoretical polarization ratio models.

Although basic understanding of the synthetic aperture radar (SAR) imaging mechanism of ocean waves has been achieved, challenges still remain. In this paper, a large number of quad-polarized SAR images are analyzed to help assess how the standard SAR imaging transformation applies to all polarization channels. Foremost, the azimuth cutoff, a parameter essentially governed by the detected wave motions, is today solely related to radar configuration and the ocean wave spectrum but not to the polarization configuration. As obtained, the analyses based on quad-polarized Radarsat-2 and Gaofen-3 products document the distinct dependence of azimuth cutoff on polarization and incidence angle. Especially for cross-polarized VH measurements, azimuth cutoff estimates are generally larger than copolarized HH ones, the latter already being larger than values estimated under VV configuration. This trend increases with the incidence angle. The systematic comparisons between SAR measurements and simulations further demonstrate that the present SAR nonlinear transformation may not properly take into account the differing coherence time associated with the multi-polarized observation of ocean scenes. In particular, to reproduce the large azimuth cutoff parameters of cross-polarized images, a reduced coherence time shall be expected. This measurable sensitivity shall enhance the capabilities of polarized SAR systems to precisely derive more ocean surface properties, especially the influence of wave breakers, by combining both the copolarization and cross-polarization measurements.

This paper assesses different retrieval schemes used for the Chinese Gaofen-3 Synthetic Aperture Radar (GF-3 SAR) co-polarized data. The data consist of 4186 GF-3 data points and collocated wind information from sources including the ASCAT scatterometer, HY2A-SCAT scatterometer, and National Data Buoy Center (NDBC) buoy wind data set. The VV-polarized geophysical model function (GMF) is a CMOD7 model while the HH-polarized GMF is a hybrid of the CMOD7 and PR model. Assessments involve comparisons between SAR-derived and collocated winds in terms of the root-mean-square difference (RMSD) and bias. First, a comparison between the two retrieval schemes for the VV-polarized data clearly shows that the optimal scheme performs better than the classical scheme for wind speed retrieval. Comparisons for HH-polarized data show similar results. These experiments indicate that the wind speed RMSDs for the GF-3 co-polarized data are within 2 m/s when using the optimal scheme. Moreover, the wind direction RMSDs from the two schemes have no significant difference, with values near 20°. Overall, these assessments indicate that the GF-3 co-polarized data are sufficient for operational wind speed retrieval using the optimal scheme. However, wind direction retrieval requires further improvement.

In wave mode, Sentinel-1A/B from ESA provide swell spectra dataset on a continuous and global basis since. In this paper, a method of a dynamical validation approach for SAR swell spectra is developed, in which the Sentinel-1A swell spectra are partitioned and propagated up to the vicinity of insitu reference along the great circle based upon the linear wave theory. Here, sentinel-1A wave mode data for the period of three months were dynamically validated against buoys from NDBC and CDIP networks. Comparison results show a good agreement with buoy measurements. Influent of buoy types on the validation results are also discussed.

Chinese first ocean dynamic environment satellite HY-2A was launched on August 2011, which has provided global significant wave height (SWH) for more than 5 years. In this study, the triple collocation error model has been introduced in the calibration and validation of HY-2A altimeter derived SWH. HY-2A wave height data are validated against in situ buoy data, and wave model hindcast from WaveWatch III, covering a period of four years. From the triple collocation validation analysis, HY-2A SWH data show an RMS (root mean square) of 0.2842 m and 0.2508 m for primary phase (Oct. 2011 to Apr. 2013) to the backup phase (Oct. 2013 to Apr. 2017).

Since July 4th 2016, the SARAL/Altika has been moved in a new orbit, and it has continuously provided wave height measurements for more than 1 year. Before using these data, the measurements need to be validated. Based on the in-situ buoys from the National Data Buoy Center (NDBC), the SARAL Ka-band significant wave height (SWH) and Sea Surface Wind (SSW) measurements were validated and have been corrected using a linear regression with in-situ measurements. Compared with NDBC data, the validation results of SARAL show a RMS (Root Mean Square) of 0.28 m for SARAL SWH measurements and RMS of 1.30m/s for SARAL SSW speed indicating capability of AltiKa providing SWH and wind speed products with reliable accuracy. Therefore the accuracy of SARAL SWH products is higher than that of Jason-1/2 SWH data, and does not require any correction.

The water vapor would lead to a variability of the speed of propagation in the atmosphere. This variability is able to result in 3~50cm uncertain error for sea surface height measurement with space-borne altimeter. Due to its large space-time variability, the wet tropospheric correction (WTC) is still considered as a significant error source in satellite altimetry. For the purpose of assessment of the WTC measured by SARAL MWR during the drifting phase, the inter-comparison has been performed between SARAL MWR and Jason-3 AMR. The bias and RMS of collocated WTC datasets in 2017 are -0.0075m and 0.053m respectively in contrast with bias of -0.0075m, and RMS of 0.053m. Analyzing the global latitudinal distribution of WTC data and anomalous value deeply, the WTC values in the both datasets are negatively correlated with latitude. Besides, there are more anomalous values at mid-high latitudinal sea area, especially the most at northern mid-high latitude. As a whole, SARAL MWR keeps stable and available during the drift phase.

Sentinel-1 ‘s SARs operate since April 2014 (S1-A) and April 2016 (S1-B) and routinely acquire images over coastal and open waters. Compared to its predecessor ENVISAT/ASAR, Sentinel-1 SAR offers several improvements such as a better Wave Mode imagette coverage, more systematic dual-polarizations, a new TOPSAR acquisition mode over coastal regions and improved Doppler estimator allowing higher resolution Doppler grid. Based on these additional capabilities, many algorithmic and use case scenario improvements have been tested and validated to provide a more complete ocean state view and first direct assessment of extreme events. Instrument level issues like the accuracy of the satellite restituted attitude could also be highlighted.

Significant wave height (Hs), is an important parameter, represented as the integration of directional wave spectra. Although many researchers have directly extractedHsfrom SAR images and got a great accuracy of retrieval, those approaches are not suitable for GF-3 SAR data. In this paper, we propose an empirical approach for SARHsretrieval, using λcestimated from the real part of image cross spectra obtain from VV-polarized Gaofen-3 (GF-3) wave mode data acquired in different radar beams (called wave-code). Results using GF-3 wave mode data from January to February 2017 indicate that the bias and RMSE errors are: 189 wave-code, -0.13 m and 0.57 m; 190 wave-code, -0.07 m and 0.34 m; 193 wave-code, -0.3 m and 0.59 m; 199 wave-code, 0.16 m and 0.68 m; 215 wave-code, 0.2 m and 0.87 m. they show a relative behavior between the retrievedHsand theHsextracted from WAVEWATCH-III (WW3). However, there is a significant error when WW3-extractedHsexceed 4 m. It seems that the model is not suitable forHsretrieval on high sea conditions.

The wet zenith delay(WZD) can be estimated by ground GPS stations as well as satellite altimeter. The Jason-2 altimeter has been an operational satellite, which provides the sea surface height with several centimeters, and have the high accuracy of measuring the WZD using a Microwave Radiometer (AMR). In this paper, we estimate the wet zenith delay (WZD) of 79 ground GPS stations using Jason-2 AMR from 2013 to 2016. The GPS stations are distributed in seven regions around the world. The distance between these GPS stations and the footprints of Jason-2 AMR was less than 150km. In the processing of GPS data, the GAMIT/GLOBK software with the VMF1 mapping function was used to achieve the GPS WZD. The results showed that the bias of the AMR and the GPS WZD was stable between the distance of 23km to 98km. The overall bias of GPS WZD was +5.68±21.96mm. Land still has a lot of influence to the AMR though new algorithm has reduced the variance within 25 km of coastline. Because of the variability of water vapor, the comparison between the GPS WZD and AMR was greatly high when the distance was more than 100km.

The Altimeters have been more and more used in ocean forecast. They have been used not only in ocean forecast validation but also be assimilated in ocean forecast model. Since August 2011, the HY-2 satellite has been launched successfully, and now it has been used in ocean wave model. This paper is armed to use the Jason-2 altimeter significant wave height (SWH) data to validate the accuracy of wave forecast, which has assimilated the HY-2 SWH. Compared with Jason-2 SWH, the validation results show that 24h RMS (Root Mean Square) and RE (Relative Error) were 0.49 m and 25.22%; 48h RMS and RE were 0.59 m and 29.19%; 72h RMS and RE were 0.88 m and 40.49%; The sea state of Northwest Pacific is mainly middle wave, mostly 54%, and the forecast RMS and RE are mostly 0.5m and 30% except the 72h forecast. And the accuracy of forecast SWH products are better in high ocean state than in low sea state.

Since August 2011, the HY-2 satellite has been launched successfully, and it has provided almost continuous wave height measurements for more than 4 years. Before using these data, the measurements need to be validated. Based on the in-situ buoys from the National Data Buoy Center (NDBC) and Jason-2 altimeter, the HY-2 Ku-band significant wave height (SWH) measurements were validated and have been corrected using a linear regression with in-situ measurements. Compared with NDBC SWH, the validation results of HY-2 SWH show a RMS (Root Mean Square) of 0.33 m, which is similar to Jason-1 and Jason-2 data with the RMS of 0.35 m and 0.37 m respectively; the RMS of corrected HY-2 SWH is 0.30 m, similar to 0.27 m and 0.23 m of corrected Jason-1 and Jason-2 data. Therefore the accuracy of HY-2 SWH products is close to that of Jason-1/2 SWH data, and the linear regression function derived can improve the accuracy of HY-2 SWH products.

At the horizon 2020, 2-D ocean wave measurements from 4 different satellites will be available. It will be a world first. Anticipating the large number of available data and the specificity of each sensor, we will have to define new methodologies to combine all different observations. This will offer new opportunities to describe ocean waves at global scale with improved time-space resolutions and will open new perspectives to study ocean waves. This paper deals with the perspectives for combining and exploiting ocean wave spectra measured from different space missions such as Sentinel-1, CFOSAT and HY-3. An example of application is shown on waves generated by hurricane Kilo.

Crossing swell, is a complicated sea state characterized by the co-existence of swell systems generating from different sources. Although many investigations have focused on the global swell climatology, our understanding of global statistical distribution for the crossing swell is still limited so far. In this paper, we present a global view of crossing swell using 10-years Synthetic Aperture Radar (SAR) derived directional swell spectra from Envisat ASAR in Wave Mode from 2003 to 2011. In contrast to analyze the directly but occasionally SAR captured sea state of crossing swell, we employ an approach of propagating observed swell taking advantage of the internal consistency of swells. Results indicate three dominated crossing swell areas termed “crossing swell pools”, in Pacific, Atlantic and Indian Oceans. The pool in Atlantic Ocean shows a relative stable behavior for all seasons, in contrast to the one in Indian Ocean with seasonal occurrence and the one in Pacific Ocean shrinking during boreal summer. Forming and seasonal variation of the crossing swells are interpreted using the swell origins derived from ASAR Wave Mode.

French-Indo joint mission SARAL/AltiKa is the first space-borne altimeter operating at Ka-band, which is expected to obtain finer resolution ocean surface wind speed and significant wave height (SWH) measurements particularly in coastal areas compared to the traditional Ku-band altimeters. In this paper, we present the preliminary validation results for the SARAL/AltiKa coastal SWH and wind speed against in situ measurements from four moored buoys in Taiwan Strait, China. The temporal and spatial differences between the SARAL/AltiKa and the in situ observations were limited to less than 30 min and 10 km, yielding 73 match-up pairs for the first 25 cycles of SARAL. Comparisons show Root Mean Square Error (RMSE) of 0.28m, bias of 0.11m for SARAL/AltiKa SWH, and RMSE of 1.76m, bias of -0.79m/s for SARAL/AltiKa wind speed indicating capability of AltiKa providing SWH and wind speed products with reliable accuracy in the coastal region of Taiwan Strait, even as close as 1.5 km to the shore.

In ESA's Envisat ASAR level 2 algorithm, it is assumed that the synthetic aperture radar (SAR) image cross spectra of mixed ocean waves were the summation of SAR image cross spectra of wind waves and that of swells. But our previous studies show that in addition to this, the cross spectra of mixed waves consist of an extra term (see the companion paper submited to this symposium). Just this term leads to an inherent error of this algorithm which has not been considered yet. This paper presents an error analysis of Envisat ASAR level 2 algorithm for ocean wave spectra retrieval in different significant wave height, wavelength, wave direction and wave component conditions based on simulation technique. It shows that the inherent errors (1) change with above parameters, and are always positive which mean the retrieved ocean wave height are overestimated; (2) increase for larger significant wave height; (3) increase for smaller wavelength; (4) increases for smaller propagation angle respect to azimuth direction. (5) increase for more wind wave component. Therefore, Envisat ASAR level 2 algorithm only works in small wave height, or large wavelength, or large propagation angle, or few wind wave component conditions.

A 6-parameter frequency spectrum with two peaks and a cos-2s type spreading function is used to simulate the mixed waves. The spaceborne and airborne synthetic aperture radar (SAR) image cross spectra of mixed waves in different significant wave height, wave length, wave direction and wave component are then calculated by using Engen's nonlinear transformation formula. Analysis based on above simulation indicate that (1) the cross spectra of mixed waves dilate in range direction and shrink in azimuth direction (the so-called azimuth cutoff effect); (2) the cutoff effect increases for waves with larger wave height, or for waves with shorter wave length, or for waves propagating closer the azimuth direction, or for waves containing more wind wave component, or for spaceborne SAR; (3) the cross spectra split into two parts for waves propagating along range direction (the so-called double-peak phenomenon); (4) the direction ambiguity of ocean waves can be removed by using the imaginary part of cross spectra; (5) in addition to the contribution of wind wave part and swell part of the mixed waves, the cross spectra of mixed waves consist of an extra term which leads to an inherent error when using ESA's Envisat ASAR level 2 algorithm to retrieve ocean waves (see the companion paper submited to this symposium).