M Meloni
email: marco.meloni@serco.com

J B Bouffard

Andrea M Doglioli

Anne Petrenko

G Valladeau

Petrenko A A C Valladeau

Toward science-oriented validations of coastal altimetry: Application to the Ligurian Sea

Keywords: Coastal altimetry, Mesoscale, Validation and verification, Northern current SB -UNMARKED

Introduction

Even if coastal zones cover only 8% of the entire ocean surface of the earth [START_REF] Stanev | Coastal-open ocean exchange. Black Sea examples from survey, satellite data and modelling[END_REF], they play a crucial role for global ocean circulation, as it provides dynamical boundary layers for physical, chemical and biological processes. Coastal regions are characterised by complex ocean dynamics; they are often dominated by small and rapidly evolving mesoscale/sub-mesoscale structures (hereafter "(sub-)mesoscale"), which play a major role in the transport of heat, salt and biogeochemical tracers [START_REF] Mcgillicuddy | Influence of mesoscale eddies on new production in the Sargasso Sea[END_REF][START_REF] Levy | The influence of mesoscale and submesoscale heterogeneity on ocean biogeochemical reactions[END_REF][START_REF] Mahadevan | The impact of submesoscale physics on primary productivity of plankton[END_REF] and significantly influence water-mass mixing and exchanges between the continental shelf and the open ocean [START_REF] Huthnance | Circulation, exchange and water masses at the ocean margin: The role of physical processes at the shelf edge[END_REF][START_REF] Muller-Karger | The importance of continental margins in the global carbon cycle[END_REF]. Despite their importance, the high spatial/temporal variability and complexity associated with (sub-)mesoscale dynamics make them difficult to study with sparse in situ observations [START_REF] Nencioli | In situ estimates of submesoscale horizontal eddy diffusivity across an ocean front[END_REF], requiring the development of modelling at kilometric [START_REF] Thomas | Submesoscale processes and dynamics[END_REF] and sub-kilometric horizontal space grids [START_REF] Gula | Submesoscale cold filaments in the Gulf Stream[END_REF][START_REF] Shcherbina | Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field[END_REF] as well as the use of high-resolution satellite observations [START_REF] Lehahn | Stirring of the Northeast Atlantic spring bloom: A Lagrangian analysis based on multi-satellite data[END_REF]Fu and Ferrarri, 2008;[START_REF] Bouffard | Lagangian analysis of satellite-derived currents: Application to the North Western Mediterranean coastal dynamics[END_REF][START_REF] Hu | Numerical study of eddy generation in the western part of the Gulf of Lion[END_REF]. The issue of characterising (sub-)mesoscale processes is particularly critical over the coastal domain, where the local Rossby radius is smaller than in the open-ocean [START_REF] Hallberg | Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects[END_REF].

Over the last three decades, progress in satellite altimetry has contributed to revolutionising physical oceanography, enabling the global characterization of openocean large scale and mesoscale processes [START_REF] Pascual | Combining new and conventional sensors to study the Balearic current[END_REF][START_REF] Pascual | Recent improvements in mesoscale characterization of the Western Mediterranean Sea: Synergy between satellite altimetry and other observational approaches[END_REF][START_REF] Fu | Large-scale ocean circulation[END_REF]. Satellite altimeters are particularly well adapted for observing open-ocean structures [START_REF] Fu | Eddy dynamics from satellite altimetry[END_REF] and represent an invaluable source of data, providing repetitive views of phenomena unachievable by other means [START_REF] Fu | Large-scale ocean circulation[END_REF].

One of the main challenges for the next decade is the characterisation of fine-scale processes in the coastal domain [START_REF] Cipollini | The role of altimetry in coastal observing systems[END_REF]. Achieving this goal requires not only the innovation of space-born instruments and processing techniques but also establishing ad-hoc validation approaches, allowing better assessment of potential improvements regarding the precision and accuracy of retrieved geophysical parameters. Increasingly more multi-disciplinary in situ data acquired by marine observatories and oceanographic campaigns are now being made available [START_REF] Palacz | Report of the workshop on the Implementation of Multi-disciplinary Sustained Ocean Observations (IMSOO)[END_REF] and can be used to derive quality indicators for coastal altimetry based on the assessment of along-track sea surface gradients complementary to the assessment of sea surface time series from tide gauges [START_REF] Bonnefond | Calibrating the SAR SSH of Sentinel-3A and CryoSat-2 over the Corsica Facilities[END_REF]. Here, we propose exploiting such in situ data resources to quantify the potential benefit of innovative coastal altimetry processing techniques for the characterization of smallscale ocean geostrophic currents.

Several previous studies have evaluated the capabilities of conventional pulse-limited Ku-Band altimetry to observe mesoscale dynamics in semi-enclosed seas, such as the Mediterranean Sea [START_REF] Vignudelli | Improved satellite altimetry in coastal systems: Case study of the Corsica Channel (Mediterranean Sea)[END_REF]Bouffard et al., 2008aBouffard et al., , 2008b[START_REF] Bouffard | Introduction and assessment of improved coastal altimetry strategies: case study over the North Western Mediterranean Sea[END_REF][START_REF] Birol | Using high sampling rate (10/20 Hz) altimeter data for the observation of coastal surface currents: A case study over the Northwestern Mediterranean Sea[END_REF][START_REF] Birol | Ku and Ka-Band Altimeter Data in the Northwestern Mediterranean Sea[END_REF][START_REF] Jebri | Interannual variations of surface currents and transports in the Sicily Channel derived from coastal altimetry[END_REF]. Despite significant advances, new coastal-oriented processing techniques require continuous optimisation and refinement by being systematically cross-compared with collocated multi-platform measurements. Over the last decade, several cruise campaigns using ship and glider measurements along with altimeter tracks have been carried out in the Western Mediterranean Sea [START_REF] Ruiz | New technologies for marine research: five years of glider activities at IMEDEA[END_REF]. For example, in [START_REF] Ruiz | Vertical motion in the upper ocean from glider and altimetry data[END_REF] study, glider-and ship-based measurements were performed under an ENVISAT track in order to provide a mesoscale description of the Balearic Front. Coastal and mesoscale dynamics analysis using conventional altimetry and gliders have also been described by [START_REF] Bouffard | Coastal and mesoscale dynamics characterization using altimetry and gliders: A case study in the Balearic Sea[END_REF][START_REF] Bouffard | Subsurface small-scale eddy dynamics from multi-sensor observations and modelling[END_REF] and [START_REF] Aulicino | Monitoring the Algerian Basin through glider observations, satellite altimetry and numerical simulations along a SARAL/AltiKa track[END_REF] over the Balearic Sea and the Algerian Basin respectively. More recently, significant improvements have been obtained as a result of the advent of new technologies, such as Ka-band measurements from SARAL [START_REF] Verron | The SARAL/AltiKa altimetry satellite mission[END_REF][START_REF] Troupin | Illustration of the emerging capabilities of SARAL/AltiKa in the coastal zone using a multi-platform approach[END_REF][START_REF] Pascual | Assessing SARAL data in the coastal zone: Comparisons with HF radar observations[END_REF] and SAR altimetry measurements from the CryoSat-2 and Sentinel-3 missions [START_REF] Bonnefond | Calibrating the SAR SSH of Sentinel-3A and CryoSat-2 over the Corsica Facilities[END_REF][START_REF] Pascual | A multiplatform experiment to unravel meso-and submesoscale processes in an intense front (AlborEx)[END_REF][START_REF] Morrow | Observability of fine-scale ocean dynamics in the Northwestern Mediterranean Sea[END_REF][START_REF] Dinardo | Coastal SAR and PLRM altimetry in German Bight and West Baltic Sea[END_REF][START_REF] Heslop | Sentinel-3A views ocean variability more accurately at finer resolution[END_REF][START_REF] Bouffard | CryoSat ocean product quality status and future evolution[END_REF][START_REF] Calafat | First evaluation of new CryoSat-2 products over the ocean[END_REF].

The goal of the present paper is to go one step further in the fine cross-analysis of coastal altimetry data and in situ measurements by determining the potential source of disagreements due to measurement errors and data processing limitations with respect to expected differences arising from physical content inhomogeneity and in situ reference level issues. Here, we utilise both Moving Vessel Profiler (MVP) and Acoustic Doppler Current Profiler (ADCP) acquired during the OSCAHR (Observing Submesoscale Coupling at High Resolution, [START_REF] Doglioli | Observing submesoscale coupling at high resolution[END_REF] Campaign along SARAL and Jason-2 altimetric tracks. We focus our analysis on the impact assessment of coastal-oriented altimetry processing strategies specifically developed and tested with experimental high frequency PEACHI products [START_REF] Valladeau | Using SARAL/AltiKa to improve Ka-band altimeter measurements for coastal zones, hydrology and ice: The PEACHI prototype[END_REF]. The obtained improvements are discussed with respect to regional 1Hz AVISO Sea Level Anomaly products (http://aviso.altimetry.fr/). Two kinds of Mean Dynamic Topographies (MTDs) have been also used and analysed in order to reconstruct Absolute Dynamic Topography (ADT).

After describing the study area and the characteristics of the in situ and space-based datasets used, the derived absolute geostrophic currents are compared to both ADCP and MVP measurements, which, in our knowledge, are used conjointly for the first time to evaluate coastal altimetry strategies. The paper then focuses on the quantitative and qualitative analysis of depicted ocean features, providing a critical discussion on the limitations and uncertainty associated with each observing system.

Study Areas

Although the issues addressed in this paper are of global relevance, its primary focus is on the North-Western Mediterranean (NWMed) Sea with particular emphasis on the Ligurian Sea area. Figure 1 shows the bathymetry of the selected area along with altimetry tracks (black lines), in situ measurements and the general circulation patterns.

The regional dynamics of the area is dominated by a cyclonic gyre circulation, the northern part of which is known as the "Liguro-Provençal Current" [START_REF] Millot | Mesoscale and seasonal variabilities of the circulation in the Western Mediterranean[END_REF][START_REF] Millot | Circulation in the Western Mediterranean Sea[END_REF] or the "Northern Current" (NC) (Millot and Taupier Letage, 2005). This slope current arises from the merging of the eastern and western Corsica currents in the Ligurian Basin. It then flows to the southwest along the continental slope until it reaches the Balearic Sea. The NC exhibits a permanent surface density front between the lighter coastal waters and the denser waters found offshore, generating a sea surface high gradient in the across-shore direction.

Several numerical studies [START_REF] Barrier | Strong intrusions of the Northern Mediterranean Current on the eastern Gulf of Lion: Insights from in-situ observations and high resolution numerical modelling[END_REF][START_REF] Zakardjan | Biological and chemical signs of upward motions in permanent geostrophic fronts of the Western Mediterranean[END_REF] and observations along the path of the NC, such as hydrographic measurements from R/V cruises and HF radar [START_REF] Forget | Observations of the sea surface by coherent L band radar at low grazing angles in a nearshore environment[END_REF][START_REF] Marmain | Assimilation of HF radar surface currents to optimize forcing in the Northwestern Mediterranean Sea[END_REF] describe this current as a complex dynamical feature marked by a large spectrum of spatial and temporal scales of variability. The NC is relatively narrow (~30-75 km) and its mean position lies within 60 km off the coast [START_REF] Petrenko | Variability of circulation features in the Gulf of Lions NW Mediterranean Sea: Importance of inertial current[END_REF]. The core of the NC is stronger and located about 10-40 km away from the coast in winter, while it is less defined and further offshore in late summer and early fall [START_REF] Birol | Aspects of the seasonal variability of the Northern Current (NW Mediterranean Sea) observed by altimetry[END_REF][START_REF] Piterbarg | Investigating frontal variability from repeated glider transects in the Ligurian Current (North West Mediterranean Sea)[END_REF][START_REF] Declerck | Assessment of the coastal dynamics in a nested zoom and feedback on the boundary current: The North-Western Mediterranean Sea case[END_REF].

Glider transects across the NC have been performed in the Ligurian Sea, such as in [START_REF] Cyr | A new glider-compatible optical sensor for dissolved organic matter measurements: Test case from the NW Mediterranean Sea[END_REF] and during the MOOSE project [START_REF] Quentin | HF radar in French Mediterranean Sea: An element of MOOSE Mediterranean Ocean Observing System on Environment[END_REF]. Two different parts constitute the main cyclonic circulation over this area: a small recirculation centred on the grey arrow in Figure 1 and a second one in the southwest separated by a local minimum in current intensity [START_REF] Marrec | Coupling physics and biogeochemistry thanks to high resolution observations of the phytoplankton community structure in the North-Western Mediterranean Sea[END_REF]. The ADT signature associated with this fine-scale circulation can be potentially observed using satellite altimetry measurements [START_REF] Bouffard | Coastal and mesoscale dynamics characterization using altimetry and gliders: A case study in the Balearic Sea[END_REF]. However, monitoring coastal dynamics from space is still challenging because of the numerous instrumental and geophysical limitations in addition to the fact that the altimeter footprints may encounter the coastline, corrupting the raw along-track remote-sensed signal [START_REF] Anzenhofer | Coastal altimetry and applications[END_REF][START_REF] Strub | High-resolution ocean topography science requirements for coastal studies[END_REF].

In situ observations

The in situ observations used in our study were acquired during the OSCAHR campaign [START_REF] Doglioli | Observing submesoscale coupling at high resolution[END_REF], whose scientific objectives included the characterisation of a sub-mesoscale dynamical structure and study of its influence on the distribution of biogenic elements and the structure and dynamics of the first trophic levels [START_REF] Marrec | Coupling physics and biogeochemistry thanks to high resolution observations of the phytoplankton community structure in the North-Western Mediterranean Sea[END_REF]. The cruise strategy utilises an adaptive approach based on the near real-time analysis of both satellite data and numerical modelling in order to identify the dynamical features of interest and track their evolution. Apart from its main scientific objectives regarding (sub-)mesoscale physical/biochemistry coupling the OSCAHR campaign also aims to validate new remote-sensing retrieval techniques (altimetry, ocean colour, planktonic assemblage reconstruction) and highresolution numerical modelling. In particular, we performed in situ measurements along three altimetric tracks shown in Figure 1 in the present study. The satellite and vessel passages are summarised in Table 1.

The R/V Téthys II is equipped with a hull-mounted ADCP RDI Ocean Sentinel 75 kHz; however, the methodology considered in this paper includes the usage of novel platforms of observation for sampling the ocean sub-surface layer at a high spatial and temporal frequency. In particular, we use a MVP200 equipped with a MSFFF I (Multi-Sensor Free Fall Fish type I). A total of 448 casts were performed along a 366km route (55 hours of effective work). During the free fall, for each cast, measurements of temperature, salinity and pressure were performed with a temporal resolution of 8-10 min, corresponding to a spatial horizontal resolution of ~ 1 km.

The CTD (Conductivity Temperature and Depth) sensor mounted in the MVP towed fish has the following precisions: ±0.005 [°C] for temperature and ±0.01 [mS cm-1] for conductivity. The density is estimated using the TEOS-10 (Thermodynamic Equation of Seawater) equation of state of seawater. Thereafter, temperature, salinity and density fields were used to estimate the Dynamic Height (DH) with respect to an arbitrary, no-motion reference level. This reference level is generally chosen to be at the maximum depth reached by the probe. Following [START_REF] Pond | Introductory Dynamical Oceanogrpahy[END_REF]:

DH = ∫ δ(T, S, p)dp (1)
where:

δ(T, S, p) = ρ(T, S, p) /0 -ρ(0,35, p) /0

(2) δ is the specific volume anomaly, i.e., the difference in volume between a unit mass of water at temperature T, salinity S and pressure p and a unit mass at the temperature T = 0°C, salinity S = 35.0 and pressure p.

In a local Cartesian coordinate with x axis pointing East, y axis pointing North, the geostrophic approximation is then applied to compute the MVP-derived current:

V = 6 7 • 9: 9;
(3) where f is the Coriolis parameter, g is gravity (9.8 m s -2 ) and h is the DH.

MVP-derived relative DH and geostrophic current (with respect to reference depth)

were compared with the geo-located SARAL and Jason-2 altimetry-derived absolute ADT and currents (with respect to the geoid). As compared to ocean gliders, using MVP has three main advantages: i) the probe performs free fall vertical profiles; ii) the sampling rate is higher and iii) the planned route (e.g., the altimetric track) is better followed, being the exact probe wed by the vessel. On the other hand, the main limit is a lower maximum operating depth. Subsequently, to understand the impacts of the reference depth and ageostrophic motions in the altimetry versus MVP comparisons, ADCP measurements were also considered in this study. The ADCP configuration used during the whole cruise included 60 cells, 8 m depth bins, an ensemble average of 1' and bottom tracking when possible (although most of the cruise took place out of reach of the bottom). The depth range extends from 18.5 m to 562.5 m with a vertically averaged error of 3.6 cm/s.

Coastal altimetry

In this paper, we used regional Mediterranean 1 Hz Jason-2 and SARAL Sea Level Anomaly (SLA), defined as the difference between the observed sea surface height and the mean sea level available and distributed by AVISO (User Handbook Ssalto/DUACS, 2016) as well as the experimental high frequency PEACHI (Prototype for Expertise on SARAL for Coastal, Hydrology and Ice) products [START_REF] Valladeau | Using SARAL/AltiKa to improve Ka-band altimeter measurements for coastal zones, hydrology and ice: The PEACHI prototype[END_REF]. Some specific retracking algorithms, corrections, editing procedures and MDT have been applied to these products and have been described below.

Retracking

One of the largest sources of errors in coastal altimetry is the inaccurate processing of the return waveforms. A significant number of ocean return waveforms near the coast indeed do not conform to the standard Brown model [START_REF] Brown | The average impulse response of a rough surface and its applications[END_REF]), as they are

SB -UNMARKED

affected by the noisier radar echoes from the land and/or calmer water contamination [START_REF] Vignudelli | Coastal[END_REF]. Several studies addressed this issue in the coastal domain.

For example, [START_REF] Brooks | Land effects on Topex radar altimeter measurements in pacific rim coastal zones[END_REF] analysed the TOPEX waveforms obtained when the altimeter transited from water to land and from land to water. They showed that waveform retracking can be used to extend the altimeter-derived sea surface topography several kilometres shoreward. [START_REF] Deng | Estimation of contamination of ERS-2 and POSEIDON satellite radar altimetry close to the coasts of Australia[END_REF] investigated the behaviour of ERS-2 and POSEIDON altimeter waveform data in the Australian coastal region and mapped a boundary, located approximately 22 km from the coast of Australia, within which the altimeter range may be poorly estimated. [START_REF] Deng | A coastal retracking system for satellite radar altimeter waveforms: Application to ERS-2 around Australia[END_REF] developed a retracking system that includes least-squares fitting of a five-parameter model and a threshold method applied to altimeter waveforms around Australia. In addition to the previously mentioned studies, Gomez-Enri et al.

( 2009) developed an experimental mixed Brown-specular retracker for the specular peak embedded within a Brown-type ocean waveform. More recently, new coastal retracking strategies have been developed and successfully applied, such as the ALES (Adaptive Leading Edge Subwaveform) [START_REF] Passaro | ALES: A multi-mission adaptive subwaveform retracker for coastal and open ocean altimetry[END_REF] and ALES+ [START_REF] Passaro | ALES+: Adapting a homogenous ocean retracker for satellite altimetry to sea ice leads, coastal and inland waters[END_REF], potentially applicable to all pulse-limited altimetry missions over both open and coastal ocean with the same accuracy.

In this study, three types of retracking algorithms have been applied to PEACHI products. Their main characteristics are described below: ii. MLE4 (Maximum Likelihood Estimator) [START_REF] Amarouche | Improving the Jason-1 ground tracking to better account for attitude effects[END_REF]): This algorithm is an evolution of the Red3 retracker but is optimised for coastal applications with the estimator that solves for 4 parameters, adding the slope of the waveform trailing edge with respect to the Red3.

iii. Adaptive [START_REF] Poisson | Development of an ENVISAT altimetry processor providing sea level continuity between open ocean and Arctic leads[END_REF]: This approach is based on a physical retracking model accounting for the mean square slope of the surface. It grants the model the capability to adapt from a diffuse waveform to a pure specular waveform. The model accounts for instrumental characteristics (point target response, Antenna Gain Pattern, etc.) and a numerical solution can be used. The fitting criterion used is a pure least square only if the waveform classification performed before the fitting identifies a peaky waveform.

For AVISO products, the performance of MLE3 retracking [START_REF] Amarouche | Improving the Jason-1 ground tracking to better account for attitude effects[END_REF] has been assessed. This retracking is similar to that for MLE4 but fits three unknown parameters (amplitude, arrival time and rise time) while the fourth, the trailing edge decay, is held fixed.

Geophysical Corrections

In addition to waveform retracking, other sources of uncertainties arise from the application of geophysical corrections to the altimetric sea surface height (SSH), defined as the height measured with respect to an arbitrary reference level, called the reference ellipsoid, which is not always optimised for the coastal domain. The main corrections used in this paper are listed in Table 2 and described in the following sections.

One of the most critical corrections is the wet tropospheric path delay, showing a standard error of +/-3 cm in the coastal domain [START_REF] Smith | First coastal altimetry workshop[END_REF]. Approaching the coast, wet tropospheric signals have a smaller space-temporal scale of variability, which are poorly resolved by numerical models or are less precisely estimated by onboard radiometer, the radiometric footprint being potentially corrupted by land contaminations. Until recently, most altimeter data in a 10-30 km coastal band of the NWMed were flagged as invalid and discarded from standard regional products (Bouffard, 2007;Bouffard et al., 2008aBouffard et al., , 2008b). The regional AVISO products used in this study contain an enhanced wet tropospheric correction near the coast (more details in [START_REF] Brown | A novel near-land radiometer wet path-delay retrieval algorithm: Application to the Jason-2/OSTM advanced microwave radiometer[END_REF]. The same approach has been applied to Jason-2 PEACHI products [START_REF] Valladeau | Using SARAL/AltiKa to improve Ka-band altimeter measurements for coastal zones, hydrology and ice: The PEACHI prototype[END_REF]. For SARAL PEACHI products, the method described in [START_REF] Valladeau | Using SARAL/AltiKa to improve Ka-band altimeter measurements for coastal zones, hydrology and ice: The PEACHI prototype[END_REF] has been applied, whereby the last valid brightness temperature (BT) is extrapolated and considered in place of the contaminated BT as input to the computation of the WTC -an approach that is less accurate than the Brown (2010) method but much simpler to configure and implement.

Although several algorithms for improving the wet path delay near the coast have been developed recently [START_REF] Cipollini | Satellite altimetry in coastal regions[END_REF][START_REF] Desportes | One-dimensional variational retrieval of the wet tropospheric correction for altimetry in coastal regions[END_REF][START_REF] Fernandes | Improved wet path delays for all ESA and reference altimetric missions[END_REF][START_REF] Fernandes | GPD+ wet tropospheric corrections for CryoSat-2 and GFO altimetry missions[END_REF], the detailed evaluation of related improvements do not lie within the scope of the present paper, which mainly focuses on the impact assessment of applying coastal-oriented retracking, editing and highresolution MDT.

Both AVISO and PEACHI products use the Dry Tropospheric correction computed from 6-hour span outputs from the ECMWF (European Centre for Medium-Range

Weather Forecasts) model. The dry tropospheric correction has a maximum standard error of +/-1-2 cm in the coastal domain [START_REF] Smith | First coastal altimetry workshop[END_REF].

For AVISO, the GOT4.8 [START_REF] Ray | Precise comparisons of bottom-pressure and altimetric ocean tides[END_REF] ocean tide solutions were applied, while the FES2012 was used for PEACHI [START_REF] Carrere | FES 2012: A new global tidal model taking advantage of nearly 20 years of altimetry[END_REF], despite the tide signals (and associated error) in the considered region being particularly low [START_REF] Alberola | Tidal currents in the Western Mediterranean Sea[END_REF].

With regard to the SSB, a 2D wind speed model as a function of backscatter and Significant Wave Height (SWH) was developed in the framework of the PEACHI project [START_REF] Valladeau | Using SARAL/AltiKa to improve Ka-band altimeter measurements for coastal zones, hydrology and ice: The PEACHI prototype[END_REF], while an empirical solution fitted on six months of SARAL GDR_C data (from NOAA Laboratory for Satellite Altimetry) was used in AVISO products (User Handbook Ssalto/DUACS, 2016). Alternative sea state bias (SSB) solutions are available in literature [START_REF] Tran | Sea state bias in altimeter sea level estimates determined by combining wave model and satellite data[END_REF][START_REF] Pires | A conceptually simple modeling approach for Jason-1 sea state bias correction based on 3 parameters exclusively derived from altimetric information[END_REF], aimed at developing a finer modelling of this effect, but have not been assessed in this study. The accuracy of SSB is about 2 cm [START_REF] Smith | First coastal altimetry workshop[END_REF].

In addition to the previously mentioned correction, the Global Ionospheric Map (GIM) from JPL (Jet Propulsion Laboratory) has been considered for the ionosphere correction for both AVISO and PEACHI products. Although the most accurate way to model the ionospheric effect is by using dual-frequency measurements (like in [START_REF] Imel | Evaluation of the TOPEX/POSEIDON dual-frequency ionosphere correction[END_REF], this approach is not applicable to SARAL, as it is a monoband radar altimeter. Thus, the JPL GIM model has been adopted in this study, as it is applicable to both Jason-2 and SARAL. The ionospheric correction has an error budget of +/-3 cm on derived SSH [START_REF] Callahan | Ionospheric variations affecting altimeter measurements: A brief synopsis[END_REF]. Both PEACHI and AVISO products are provided including a so-called Dynamic Atmospheric Correction (DAC) [START_REF] Carrère | Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing -comparisons with observations[END_REF].

Coastal Editing Strategy

As the PEACHI experimental products have a high rate sampling of 40Hz for SARAL and 20Hz for Jason-2, specific editing and filtering procedures have been developed, following methods described in [START_REF] Bouffard | Coastal and mesoscale dynamics characterization using altimetry and gliders: A case study in the Balearic Sea[END_REF]. Figure 2 depicts an example of this procedure applied on AltiKa track #429 in deriving the edited (red curve) and filtered (green curve) heights from the raw data (blue curve).

First, a ten-step recurrent 2*std editing algorithm was developed and applied to corrected high-rate along-track PEACHI SLA in order to remove residual spikes (see red curve on Figure 2). For each iteration, first, the difference between the altimetry raw and smoothed data was computed and then spikes higher than two standard deviations are flagged, removed and replaced by linearly interpolated values. The next iteration begins from this result by performing the spikes filtering and smoothing again. This recurrent procedure is repeated ten times in order to obtain the final edited and filtered SLA. At the end of these editing steps, 4% of spikes were eliminated from SARAL track #429 and 12% from SARAL track #674, while 7% spikes were filtered out from Jason-2 track #9. Thereafter, the edited high rate altimetric SLA was low-pass filtered (using a moving average filter) with a window of 2.5 km for SARAL (see green curve on Figure 2) and 8.5 km for Jason-2 in order to reduce residual noise, as in [START_REF] Bouffard | Coastal and mesoscale dynamics characterization using altimetry and gliders: A case study in the Balearic Sea[END_REF]. The MVP derived currents and ADCP currents were also smoothed from the raw signal with the same filter.

Mean Dynamic Topography (MDT)

The AVISO and PEACHI absolute geostrophic currents were then calculated from the ADT, using the [START_REF] Powell | An optimal filter for geostrophic mesoscale currents from along-track satellite altimetry[END_REF] filtering with a cut-off distance of 15 km, roughly corresponding to the local Rossby radius of deformation over the study area [START_REF] Grilli | The computation of Rossby radii between external forcing mechanisms and internal of deformation for the Mediterranean Sea[END_REF]. Two Mean Dynamic Topography (MDT) have been considered, spatially interpolated and added to the altimetric SLA in order to obtain the along-track ADT: the Rio "old" MDT (after RIO07), resolution 1/8º [START_REF] Rio | A mean dynamic topography of the Mediterranean Sea computed from altimetric data, in situ measurements and a general circulation model[END_REF]; see Figure 3a) and the Rio "new" MDT (RIO14) with resolution 1/16º [START_REF] Rio | Computation of a new mean dynamic topography for the Mediterranean Sea from model outputs, altimeter measurements and oceanographic in situ data[END_REF]; see Figure 3b).

A linear interpolation was applied to both RIO07 and RIO14 gridded MDTs to obtain an along-track MDT to be added to the altimetry SLA measurements.

The RIO14 benefits from the improvements enabled by the use of extended data sets and refined processing techniques. The updated data set spans the 1993-2012 period and consists of drifter velocities, altimetry data, hydrological profiles and model data.

The methodology is similar to the previous RIO07, which did not use any hydrological profiles. As compared to the RIO07, the RIO14 therefore features shorter-scale structures owing to the use of more in situ and satellite-based observations.

Impact of in situ MVP reference depth and sinopticity issue

As reported in section 3.1, temperature, salinity and density fields retrieved by MVP can be used to estimate DH with respect to an arbitrary reference depth, which is supposed to be a no-motion level. As the reference depth issue does not affect altimetry, a sensitivity study has been performed to highlight effects on the computation of MVP-derived surface geostrophic current when compared to altimetry (shown in Figure 4). shows the NC signature with a stronger temperature up to a depth of 90 m for latitudes higher than 43.35º (see Figure 10 and associated discussions).

The results obtained for the MVP transects out of the NC are different. For transect G -I, the mean reduction of altimetry and MVP current difference is observed up to a 140-m depth, whereas the differences go up for a higher depth (as for surface layers).

This pattern could be potentially linked to the sub-surface currents associated with a strong and rapidly evolving mesoscale feature intercepted by this transect but not seen by transect H -G. Transects G -I and H -G are almost collocated but have a time separation of about one day (see Table 2) during which dynamical conditions may have changed with fine-scale surface features having moved in between the two MVP passes. This is confirmed by examining the vertical temperature profiles on which changes are clearly observed along the water column (see Figure 10 and associated discussions). These high-frequency variations cannot be observed by instantaneous altimetry measurements, while they affect the MVP measurements all along the data sampling, emphasising potential impacts of synoptic issues in altimetric versus in situ comparisons.

According to the above results (also confirmed by using Red3 or Adaptive retrackers in the sensitivity study) and despite the spotted sinopticity issue, the agreement between altimetry and MVP is generally satisfying when considering the deepest reference level (different for each of the four considered transect) as well as 20-30 km offshore (the grey square on Figure 4). On one hand, the deepest reference level has been kept for the remaining analyses and is the one adopted in the results presented in section 4.3 On the other hand, two alternative retrackers (Red3, Adaptive) have been used and evaluated to highlight the potential improvement in the 20-30 coastal bands.

Impact of physical content and reference depth

In order to assess the potential impact of the reference depth on the MVP retrieved current, geographical plots of the differences of the surface across-track current ADCP-MVP (coloured dots) have been computed (Figure 6), superposed to the crosstrack component of the deep ADCP current, measured at 270 m depth. Comparison between surface across track MVP and ADCP derived currents are shown in Figure 7 for each of the cruise transects. The principal differences between the two in situ observing systems highlighted in Figure 7 should be mainly related to the fact that ADCP measures the total absolute current and contains both geostrophic and ageostrophic motion, while the MVP measurements are referenced to an unknown no-motion level and -as altimetrycapture the single geostrophic component.

Figure 6 shows that if a strong deep current is present at 270 m, the no-motion hypothesis is not verified, which consequently creates inconsistencies when comparing DH-derived MVP currents with the ones from ADCP (and hence with altimetry). This is evident from transect F -G, E -F and F -E, where the differences between the two observing systems are particularly high (> 0.16 ms -1 ). This is also valid when examining transect A -B, where a strong deep current is visible in Figure 6, generating a difference of 0.10 ms -1 between surface MVP and ADCP currents. On the other hand, transects G -H and H -G show small differences and high correlation (> 0.95), although the ADCP measurements show finer-scale dynamics, perhaps due to ageostrophic variations that occurred during the time of route H -G and not during the same geographical transect G -H. During the period from October 30 to November 2, 2015, a strong north-easterly wind event with velocity up to 70 km h -1 was recorded over the whole area [START_REF] Marrec | Coupling physics and biogeochemistry thanks to high resolution observations of the phytoplankton community structure in the North-Western Mediterranean Sea[END_REF], reinforcing highfrequency and small-scale features

In addition, looking at in situ comparison statistics (Table 3), anticorrelated value was found for transect F -G as well as significant differences for transects E -F, F -E and F -G. Moreover, ADCP observations on Figure 7 show small-scale dynamics, not depicted by altimetry and MVP (for example along the transect D -A), but attesting the presence of high-frequency ageostrophic likely variations.

471

After geostrophy, one of the major contributions to the ocean surface currents is the 472 Ekman response of the ocean to high-frequency wind stress. Various studies have 473 focused on understanding and modelling these currents in a more effective and 474 comprehensive manner [START_REF] Ralph | Wind-driven currents in the tropical Pacific[END_REF][START_REF] Lagerloef | Tropical Pacific near-surface currents estimated from altimeter, wind, and drifter data[END_REF]Elipot and 475 Gille, 2009;[START_REF] Rio | High-frequency response of wind-driven currents measured by drifting buoys and altimetry over the world ocean[END_REF][START_REF] Rio | New CNES-CLS09 global mean dynamic topography computed from the combination of GRACE data, altimetry, and in situ measurements[END_REF][START_REF] Rio | Use of altimeter and wind data to detect the anomalous loss of SVP-type drifter's drogue[END_REF]. The potential impacts of ageostrophy 476 signatures from Ekman have been tentatively assessed in this study using 477 GlobCurrent version 2 Ekman current at 0.25° resolution, 3-hourly, available from 478 2002 to 2014 (accessed from http://www.globcurrent.org/). However, due to the 479 coarse resolution of the GlobCurrent products and a lack of coverage over the coastal 480 domain, it was not possible to assess precise Ekman impacts on the study area. A 481 product with finer resolution should be processed in future GlobCurrent versions but 482 was not available at the time of this study. 483

The following section reports the comparison between satellite altimetry and MVP 484 with particular emphasis on the impacts of altimetry processing. 485 486 487

4.3

Impact of altimetry processing SARAL tracks #429 and #674 together with Jason-2 track #9 SLA, ADT and derived currents were compared to MVP geo-located measurements (Figure 8). Tables 4 and5 report the mean statistical scores per mission. In total, combinations of 12 comparisons per track have been performed between satellite altimetry measurements (considering different products, MDT and corrections) and in situ MVP/ADCP transects. The analysis has been performed up to 14.5 km from the coast for SARAL track #429, 37 km for SARAL track #674 and up to 13 km for Jason-2 track #9.

Examining the comparison plots between Jason-2 track #9 and MVP transect A-D (Figure 8a), it can be seen that the two bumps visible in currents at Latitude 43.2°and

43.4° are related to the interception of the NC, which intersects the altimetric track twice due to its orientation with respect to the main flow. The NC signature is also evident when looking at SARAL track #429 from which the main current peak of 0.55 m/s at Latitude 43.25° is captured by MVP and ADCP measurements (Figure 8b). Along the SARAL track #674 and in situ transects G -I and H -G, a dipole-like mesoscale structure is observed in each altimetric dataset (see section 4.4; Figures 8c and8d).

Despite good general agreement between altimetry and MVP, some important discrepancies were also observed. For track #429, the mean difference with respect to the MVP and ADCP current are 0.08 m/s and 0.20 m/s, respectively. These significant differences might potentially be due to land contamination affecting altimetry measurements approaching the coast and not processed with optimal retracking and/or local corrections. MVP and ADCP show some disagreements along the transect A -D, whereas ADCP -not affected by reference level issue -and altimetry (track #9) show quite a similar pattern with an increasing velocity when approaching the coastline.

When compared to ADCP and MVP-derived current, the benefit of adding MDT to the altimetric SLA is obviously confirmed for all considered tracks and missions; this is particularly evident for SARAL tracks, for which an improvement of 30% in correlation was observed. When compared to the RIO07 MDT, the use of the RIO14 further improves the comparison scores in terms of correlation between altimetry data and MVP, with a mean increase of 10% for both AVISO and PEACHI products (Tables 4 and5).

Using the PEACHI products, the mean and standard deviation differences between MVP and altimetry are still reduced: the overall mean difference goes from 0.04 m/s to 0.02 m/s for SARAL and from 0.35 m/s to 0.26 m/s for Jason-2 for 1 Hz AVISO and PEACHI products respectively. Comparison statistics (Table 4) show that for PEACHI products, the adaptive retracker provides better performances in coastal regions (correlation > 0.9) for both 40 Hz SARAL and 20 Hz Jason-2 sensors when compared to standard 1 Hz regional AVISO.

With regard to previous studies [START_REF] Birol | Ku and Ka-Band Altimeter Data in the Northwestern Mediterranean Sea[END_REF][START_REF] Verron | The SARAL/AltiKa altimetry satellite mission[END_REF][START_REF] Troupin | Illustration of the emerging capabilities of SARAL/AltiKa in the coastal zone using a multi-platform approach[END_REF], considering AltiKa sensor on-board, SARAL provides better statistical agreement with in situ than the Ku-band mission, such as Jason-2 and, particularly in this study, using the combination with RIO14 and adaptive retracking, confirming that the Ka band is more reliable in resolving fine-scale coastal dynamics. From a general point of view, the comparison between altimetry and MVP over the study area is improved when considering experimental PEACHI high-rate altimetry data rather than the Mediterranean regional AVISO products. The NC signatures and small-scale oceanic features are, however, well captured by both datasets. Despite this encouraging result and as testified by cross-comparisons with collocated ADCP transects, the MVP measurements cannot be considered as a perfect reference dataset for validating coastal altimetry. This is due to its sensitivity to the reference level with regard to determining the DH along with the highlighted sinopticity issues induced by high frequency and partially ageostrophic small-scale dynamics occurring during data acquisition.

Observed circulation patterns

As shown on Figure 9, the combined use of surface altimetry and sub-surface in situ measurements (MVP and ADCP) allows the observation of small scale and coastal hydrodynamic features that are consistent with frontal structures depicted by PODAAC Sea Surface Temperature data (SST, L4 data, JPL OurOcean Project, 2010).

In Figure 9, looking at transect A -B, the NC main path, with high current velocity (> 0.3 ms -1 ) is intercepted by altimetry around Latitude 43.25º and 6.8º Longitude.

The associated surface frontal structure is also clearly captured by ADCP and MVPderived current as well as from remote-sensing SST image. There, the vertical structure is characterised by the temperature profile of MVP, with higher temperature > 18 ℃ (Figure 10) caused by the NC main flow and depicted up to its maximum depth (80 m).

More East and offshore, an eddy-like structure is instead depicted at the surface by altimetry, ADCP and MVP-derived currents along the transect G -I. Along the same transect, satellite SST also shows a zone of low temperature with values below 17 ℃.

This zone is surrounded by warmer boundary waters characterised by SST higher than 17 ℃, suggesting ascendant vertical pumping of cold water in the central part of this small-scale dynamical feature.

Both in situ and satellite-derived surface current directions indicate that this mesoscale feature is linked to a cyclonic recirculation of the NC in the Ligurian subbasin. [START_REF] Marrec | Coupling physics and biogeochemistry thanks to high resolution observations of the phytoplankton community structure in the North-Western Mediterranean Sea[END_REF] reported on this event, also attributing the important role of Ekman pumping, induced by a strong wind event just before the OSCAHR cruise, which has an impact on ocean biogeochemistry. Besides the strong wind event occurring during the first day of the cruise, the region has experienced several wind events two weeks before the cruise [START_REF] Marrec | Coupling physics and biogeochemistry thanks to high resolution observations of the phytoplankton community structure in the North-Western Mediterranean Sea[END_REF], inducing a strong decline in SST. The low temperature patch described by satellite SST and MVP profile supports the Ekman pumping hypothesis. This process was also important in fertilizing the upper layer with nutrient-rich upwelled waters. The monitoring of small-scale processes in the coastal domain using satellite-based observations represents a key challenge in oceanography. In this paper, we discussed the issue of validating and optimising coastal altimetry data in areas characterised by fine-scale dynamics.

It has been discussed that regional 1 Hz altimetric data from AVISO are not always reliable close to the coast, and new experimental post processed and edited high rate PEACHI altimetric data have been considered to better resolve regional fine-scale features. Comparison statistics show that experimental high-rate PEACHI products using the adaptive retracker provide better performances in coastal regions for both 40 Hz SARAL and 20 Hz Jason-2 missions. Moreover, the use of the new RIO14

MDT instead of the RIO07 one increases the correlation scores with respect to in situ measurements.

The use of MVP platform has been assessed, as it was never used for validating coastal altimetry, highlighting the main challenges, advantages and limitations with respect to gliders. Further, regarding the MVP dataset, the importance of the reference level and sinopticity issues were discussed, and a sensitivity study was performed to highlight the effect on the derived geostrophic currents. It has been shown that, as for glider, measurements from the MVP are very promising for validating coastal altimetry techniques but cannot be considered as a perfect reference dataset by themselves. In this respect, the combined use of collocated MVP, altimetry and ADCP appears to be relevant, not only for validation purpose but also to better characterise the surface and sub-surface regional dynamics of the study area, including the North Current flow and the induced cyclonic recirculation in the eastern side of the Ligurian Sea. New benchmarking will also be performed, where the most recent developments in geophysical corrections and new retracking methods in coastal domains will be taken into consideration.

From a more general point of view, this study illustrated the complexity of setting up adequate in situ validation networks for coastal altimetry in areas dominated by geostrophic and ageostrophic fine-scale oceanographic processes. It confirmed the key importance of developing ad-hoc validation approaches using multiple types of collocated instruments, which allow diagnosing and understanding the physical content and mechanisms of the observed oceanic features. Recent (Sentinel-3) and future high-resolution topographic missions, such as Jason-CS, Sentinel-6 and SWOT, will continue to provide improved ocean parameters that can significantly help in understanding climate changes, coastal and (sub-)mesoscale dynamics. Their full exploitation and integration into re-analysis and forecasting system will however depend on our capability to continuously develop science-oriented diagnostics and uncertainty estimation. This objective can only be achieved through the deployment and maintenance of long-term, independent, fully characterised and traceable multisensor in situ observations (so-called "Fiducial Reference Measurements", FRM), collocated along altimetry tracks. Figure 15 PEACHI Altimetry (grey for SLA+RIO07 and red for adaptive retracking, cyan for Red3 retracking and green for MLE4 retracking for SLA+RIO14) vs AVISO altimetry (light grey for SLA+RIO07 and grey for SLA+RIO14) vs in situ (magenta for MVP, blue for ADCP). Different markers for both AVISO and PEACHI altimetry are related to elevations and currents computed with a different MDT (crosses for RIO07 and diamonds for RIO14). First column reports track geolocation, second column reports ADT (m) vs Latitude and third column reports satellite across track current (ms-1) derived from ADT computed adding RIO14 to SLA vs Latitude together with in situ derived current vs Latitude. The distance to the coast is also reported in Kilometres.

List of Figure Captions

Figure 16 Surface circulation pattern derived from in situ (magenta for MVP and blue for ADCP) and PEACHI altimetry data (black). SST data is also shown with a Spatial Resolution of 0.062º (Latitude) x 0.062º (Longitude) and temporal resolution of 1 day. The SST maps is an average over the OSCAHR cruise time period (29 th October 2015 to 6 th November 2015). White arrows depict the surface oceanographic features reported also in Figure 10 vertical profiles. Figure 17 MVP Salinity and temperature vertical profiles. The oceanographic features are reported with white arrows.

Figure 1

 1 Figure 1 OSCAHR cruise transects (in letters) showing MVP vertical salinity profiles (coloured rectangles), geo-located with altimetric tracks #9 from Jason-2 and tracks #429 and #674 from SARAL. The main flow of the NC is shown with black arrows, the recirculation with a grey arrow and the Ligurian Sea area is highlighted by the red box.

  Innovant de Système de Traitement pour les Applications Côtières et l'Hydrologie) (Coastal and Hydrology Altimetry product handbook, 2010): This algorithm selects an analysis window centred on the main leading edge of the waveform and retracking parameters in this reduced window [-10; +20 samples] with a Maximum Likelihood Estimator solving for 3 parameters (range, amplitude and Sigma composite).

  Figure 2 also shows (in black) the 1 Hz AVISO product, highlighting the differences with respect to high-rate PEACHI products in terms of SLA-observed features.

Figure 2

 2 Figure 2 PEACHI high rate altimetry SLA editing and filtering for SARAL track #429. The black line corresponds to the AVISO 1 Hz track.

Figure 3

 3 Figure 3 RIO07 (a) and RIO14 (b) MDT overlapped by the derived mean current.

  The latter shows the different MVP-derived geostrophic currents computed by varying the reference depth, compared with PEACHI geostrophic currents using the MLE4 retracker. Each of the four transects has a different maximum depth for which valid measurements are available: 293 m for transect A -B, 330 m for transect D -A, 321 m for transect G -I and 278 m for transect H -G. Figure 5 reports the mean and standard deviation of the differences between PEACHI and MVP at different reference depths.Examining the comparison statistics reported in Figure5, it can be seen that the differences are reduced between altimetry and MVP datasets for transect D -A and H -G when considering a deeper reference level. For transect H -G, the difference between the two sensors is reduced from 0.052 m/s for a reference depth of 90 m to 0.028 m/s for a reference depth of 278 m. The same conclusion is obtained for transect D -A and transect A -B with a mean reduction from 0.092 m/s to 0.041 m/s and from 0.210 m/s to 0.178 m/s, respectively. This is potentially caused by the deep flow of the NC along the Ligurian continental slope. The vertical temperature profile

Figure 4 Figure 5

 45 Figure 4 Reference depth sensitivity study for transects A -B, D -A, G -I and H -G. Different colours are associated with different reference depths (in meters) considered in the vertical integration of MVP data while the PEACHI altimetry data (MLE4 retracker) are shown in black. The magenta line represents the MVP derived currents at the maximum operating depth. The shaded grey areas in transects A -B and D -A correspond to 20 km from the coast.

Figure 6

 6 Figure 6 Geographical plot of the differences (coloured dots) of the surface across track current ADCP-MVP. The vectors are related to the cross-track component of the ADCP current at 270 m depth.

Figure 7

 7 Figure 7 Comparison between MVP (magenta) and ADCP currents (m/s) vs. Latitude (raw data in thin blue, filtered and smoothed data in dashed thick blue) for each transect.

Figure 8

 8 Figure 8 PEACHI Altimetry (grey for SLA+RIO07 and red for adaptive retracking, cyan for Red3 retracking and green for MLE4 retracking for SLA+RIO14) vs AVISO altimetry (light grey for SLA+RIO07 and grey for SLA+RIO14) vs in situ (magenta for MVP, blue for ADCP). The different markers used for both AVISO and PEACHI altimetry are related to elevations and currents computed with a different MDT (crosses for RIO07

Figure 10

 10 Figure 10 depicts the salinity and temperature vertical sections of MVP transects A -

Figure 9

 9 Figure 9 Surface circulation pattern derived from in situ (magenta for MVP and blue for ADCP) and PEACHI altimetry data (black). SST data is also shown with a Spatial Resolution of 0.062º (Latitude) x 0.062º (Longitude) and temporal resolution of 1 day. The SST maps is an average over the OSCAHR cruise time period October 29, 2015 to November 06, 2015). White arrows depict the surface oceanographic features reported also in Figure 10 vertical profiles.

Figure 10 MVP

 10 Figure 10 MVP Salinity and temperature vertical profiles. The oceanographic features have been depicted with white arrows.

Figure 11

 11 Figure11OSCAHR cruise transects (in letters) showing MVP vertical salinity profiles (coloured rectangles), geo-located with altimetric tracks #9 from Jason-2 and tracks #429 and #674 from SARAL. The main flow of the NC is shown with black arrows, the recirculation with the grey arrow and the Ligurian Sea area is highlighted by the red box.

Figure 12

 12 Figure 12 PEACHI high rate altimetry SLA editing and filtering for SARAL track #429. The black line corresponds to the AVISO 1 Hz track.

Figure 13

 13 Figure 13 RIO07 (a) and RIO14 (b) MDT overlapped by the derived mean current.

Figure 14

 14 Figure14Reference depth sensitivity study for transects A -B, D -A, G -I and H -G. Different colours are associated with a different reference depths (in meters) considered in the vertical integration of MVP data, while PEACHI altimetry data are shown in black. The magenta line represents the MVP derived currents at the maximum operating depth. The shaded grey areas in transects A -B and D -A correspond to 20 km from the coast. Figure5Mean (blue) and standard deviation (yellow) of the current differences between PEACHI and MVP.

Figure 6

 6 Figure 6 Geographical plot of the differences (coloured dots) of the surface across track current ADCP-MVP. The vectors are related to the cross-track component of the ADCP current at 270 m depth.

Figure 7

 7 Figure7Comparison between MVP (magenta) and ADCP currents (raw data in thin blue, filtered and smoothed data in dashed thick blue) for each transect.

Table 1 Satellite in situ (MVP + ADCP) synchronization Trace Satellite Passage Beginning waypoint MVP Start Ending Waypoint MVP end Time Diff.

 1

		31/10/15	30/10/15	30/10/15	-21 h
	Jason-2 #9	D	A
		16:56	15:30	23:30
	SARAL	30/10/15	31/10/15	01/11/15	+35 h
		A	B
	#429	05:02	01:30	06:30
	SARAL	07/11/15	03/11/15	04/11/15	-89 h
		G	I
	#674	18:02	23:00	03:00
	SARAL	07/11/15	04/11/15	05/11/15	-63 h
		H	G
	#674	18:02	23:30	06:00

Table 2 Altimetry data characteristics

 2

						Spatial
	SLA	MDT	Retracker	Sampling SLA Coastal Editing	Filtering Corrections
							Wet tropo (Brown, 2010)
	AVISO	RIO14					Dry tropo (ECMWF Model)
	Jason-2	RIO07					Ionospheric (GIM from JPL)
			MLE3	1 Hz	No	No	Tides (GOT4.8 (Ray, 2013)
							SSB (User Handbook
	AVISO	RIO14					Ssalto/DUACS, 2016)
	SARAL	RIO07
							DAC (Carrère and Lyard,
							2003)
							Wet tropo (Brown, 2010
					10-step recurrent		for Jason-2 and Valladeau
	PEACHI Jason-2	RIO14 RIO07		20 Hz	algorithm (Bouffard et al.,	8.5 Km	et al., 2015 for SARAL)
					2010)		Dry tropo (ECMWF Model)
							Ionospheric (GIM from JPL)
			Red3
			MLE4				Tides (FES2012 (Carrere et
			Adaptive		10-step recurrent		al., 2012))
	PEACHI SARAL	RIO14 RIO07		40 Hz	algorithm (Bouffard et al.,	2.5 Km	SSB (Valladeau et al.,
					2010)		2015)
							DAC (Carrère and Lyard,
							2003)
	4	Results and discussions

Table 4 PEACHI ADT and V vs MVP average comparison statistics (correlation) per retracking method (the level of significance is 95%)

 4

							Total Average
	Satellite	MDT	Parameter Adaptive MLE4 RED3	per MDT
		RIO14	ADT V	0.93 0.75	0.90 0.67	0.78 0.79	0.87 0.74
	SARAL	RIO07	ADT V	0.58 0.76	0.55 0.51	0.30 0.71	0.48 0.66
		Total Average	ADT	0.75	0.72	0.54	0.67
		per Retracking	V	0.76	0.59	0.75	0.70
		RIO14	ADT V	0.92 0.71	0.91 0.74	0.77 0.73	0.87 0.73
	Jason-2	RIO07	ADT V	0.83 0.70	0.81 0.74	0.71 0.72	0.79 0.72
		Total Average	ADT	0.88	0.86	0.74	0.83
		per Retracking	V	0.71	0.74	0.73	0.72

Table 5 AVISO ADT and V vs MVP average comparison statistics (correlation) per retracking method (the level of significance is 95%)

 5

	Satellite	MDT	Parameter	MLE3
		RIO14	ADT V	0.86 0.82
	SARAL	RIO07	ADT V	0.60 0.76
		Total Average	ADT	0.73
		per Retracking	V	0.79
		RIO14	ADT V	0.87 0.71
	Jason-2	RIO07	ADT V	0.70 0.68
		Total Average	ADT	0.79
		per Retracking	V	0.70

Acknowledgments

We would like to thank the DT-INSU people from la Seyne sur Mer and, in particular, Malika Oudia for her help in the administration work and Céline Heyndrickx and Frédéric Le Moal for their technical support. We would specially like to mention Genavir and Julien Fenouil for assisting us with the MVP.

MVP and the associated captors were brought by IFREMER and LOPB with cofunding by the Centre Européen de Technologies Sous-Marine (CETSM -Contrat de

Projet Etat Région 2007-2013 en PACA) and the French ANR FOCEA (project ANR-09-CEXC-006-01 to M. Zhou and F. Carlotti). We would also like to extend our thanks to J. Thomas Farrar (MIT) for his suggestions on the cruise strategy. The


Fast audio-haptic prototyping with mass-interaction physics

J L * J V † U . G A , CNRS, G INP * , GIPSA-LAB, 8 G , F , * I E U . G A
This paper presents ongoing work on the topic of physical modelling and force-feedback interaction. Specifically, it proposes a framework for rapidly prototyping virtual objects and scenes by means of mass-interaction models, and coupling the user and these objects via an affordable multi-DoF haptic device. The modelled objects can be computed at the rate of the haptic loop, but can also operate at a higher audio-rate, producing sound. The open-source design and overall simplicity of the proposed system makes it an interesting solution for introducing both physical simulations and force-feedback interaction, and also for applications in artistic creation. This first implementation prefigures current work conducted on the development of modular open-source mass-interaction physics tools for the design of haptic and multisensory applications.

I

In recent years, the access to digital fabrication technologies coupled with the surge of do-it-yourself electronics and a drive from the Virtual Reality industry have given rise to a new interest in haptics: once considered only as costly lab equipment reserved to specific academic fields, a new generation of force-feedback and vibrotactile devices now offer affordable open designs, that can be built, customised or tampered with, and used by individuals for a vast range of purposes including musical & artistic creation [ , ].

Prototyping haptic interactions generally involves creating and computing a physical scene that the user will interact with through the device. However, tools for designing the virtual scenes (such as CHAI D ) are often difficult to apprehend. We argue that following the increased accessibility of haptic solutions, equally accessible tools should allow for simple and fast prototyping of modular virtual scenes, applicable to any number of purposes, including haptic-audio multi-modal VR.

This paper proposes such a framework using a new open-source massinteraction physical modelling engine and an existing open-source / open-hardware haptic device. First, we briefly introduce the context of force-feedback interaction technologies and physical modelling concepts for designing multisensory virtual scenes. Our prototyping framework is then presented and illustrated through a series of examples. Finally, we will offer perspectives for future work.

N I D R

Throughout the history of information technologies, advances in computation methods and process have always evolved in tight relationship with technologies allowing humans to interact with the machine. In recent years, global trends in HCI have shifted from input peripherals (such as the keyboard and mouse), towards natural interaction through speech recognition, motion capture and gesture recognition, and virtual reality technologies.

Blending digital realities with the real physical world is now commonplace, and to this end technologies have evolved significantly both in performances and affordability, driven essentially by the video-game and entertainment industry. However, focus has primarily been on visual aspects (CGI animation, etc.), sometimes sound (through immersive D audio techniques), but rarely on the sense of touch or physical presence inside a virtual scene, using haptic (or force-feedback) technologies. Indeed, the sense of touch relies on a coupled action-perception loop [ ], distributed across the entire human body. Hence, when developing or using haptic systems capable of "rendering" this interaction with a virtual entity, one is faced with two main technological challenges:

• Simulating the immediacy of the action-perception loop: in a forcefeedback chain the computer receives position data from a sensor, computes interaction forces based on a virtual scene, and sends these forces data back to mechanical transducers . All of these operations take time, and hardware/software architectures must allow a sufficiently fast loop to convey the impression of immediate action-reaction, and also for stability reasons [ , ].

• Sufficient degrees of freedom: very few human gestures can be reduced to a small number of degrees of freedom, and applied in only one or a few points. However, designing haptic systems with a large number of DoF and/or contact points poses many mechanical challenges. Various systems have been proposed, from penlike interfaces [ ], to exoskeletons [ ] or haptic gloves [ ], but in each case they are generally specifically tailored to a specific type of interaction.

Developments and applications of haptic devices for artistic creation can be traced back to the late s [8]. Since then, a steadily growing scientific community has formed around the use of force-feedback and vibrotactile technologies applied to the fields of music and digital arts [ ].

O -

Due to their mechanical complexity and often dedicated hardware/software, haptic systems are generally considered costly. Among others, we can cite the Phantom system [ ], or the TGR from ACROE [ ]. The gaming industry has led to some cheaper alternatives, such as the Novint Falcon [ ], at the cost of reduced performance. What's more, the rapid evolution of computer systems and peripherals has rendered the software and hardware compatibility of proprietary/commercial solutions increasingly problematic as drivers are not always maintained for recent operating systems.

In the case of impedance-based haptic devices.

Copyright is held by authors These systems are cheaper to build and repair, use simple communication protocols, and minimise or entirely circumvent the use of any proprietary software. We decided to use the Haply system for our work. Similarly to the Fire-Fader, it relies on an Arduino-based board (the Haply M ) to process sensor data and drive motors, and communicates over USB (through a virtual serial port) with a simulation context running on a host machine. However, the FireFader offers one or several DoF sliders that are connected to one-dimensional sound synthesis simulations, whereas the Haply is a DoF (cf. Figure ) system that can be extended to , allowing exploration of more complex interaction modalities with multidimensional virtual environments. The open-source hAPI programming interface allows to easily configure the haptic device and interact with a virtual scene.

Figure : The -DoF Haply force-feedback device

D

A question of equal importance to the force-feedback peripheral itself concerns how a multimodal (visual, audio and haptic) virtual scene can be designed, computed and "rendered" for the user to see, hear and feel. We categorise two main approaches, shown in Figure :   Distributed Approach Complex virtual scenes are often distributed into separate computational processes for each modality [ ]. Visual rendering is handled at a relatively low rate ( -Hz, latency of up to ms tolerated), audio is processed at a high-rate ( . kHz, with latency under ms), and physics are generally computed around kHz, with critical latency conditions for the haptic loop ( ms or less). This scheme is especially adapted in cases where audio or visual processes may rely on abstract (non-physical) algorithms. However, it does pose the problem of defining mapping and control relationships between the processes. If the correlation between different modalities is not sufficiently explicit, the sensation of believability and presence of the virtual objects may suffer.

Single Model Approach An alternative way of designing multimodal virtual scenes is to model them with a single formalism (cf. Figure b). Physical modelling allows creating scenes of deformable objects that exhibit visual, mechanical and acoustic behaviour. The object that we touch is the one we see, and that we hear. This approach is sometimes http://www.haply.co referred to as multisensory, and guarantees coherence between the different modalities. Works such as [ 6, ] use this approach with massinteraction physical modelling, a formalism presented below.

M -I P M

Representing mechanical systems by means of punctual masses linked together by elements such as springs or dampers, and submitted to various constraints, is one of the most common ways to describe and calculate their behaviour. From Newton's laws we know the equation of movement of a mass in a given referential; the action of springs, dampers and other elements can be mathematically described or approximated by well known formulas. By resolving the equation system composed of the equations of each element in a mechanical construction, we obtain the global behaviour.

Mass-interaction physical modelling and simulation [ ] relies on exactly this principle: the inertial behaviours of material elements and interactions (springs, dampers, etc.) are described by simple discrete-time difference equations, following a given discretisation scheme (see [ , ] for algorithms and implementation details). Positions and forces can be expressed as scalar values (for D systems) or as D or D vectors according to the spatial attributes of the scene. Mechanical constructions are then built by assembling masses and interactions together in a network, setting physical parameters and initial conditions, and then computing the behaviour over time. Figure shows a topological representation of a mass-interaction model. Owing to their inherent simplicity and efficient computation, lumped methods such as mass-interaction physics have been widely used and studied in the field of haptics, for the design of virtual deformable matter and haptic interaction models [6, 8, ], including for direct forcefeedback interaction with virtual musical instruments [ , ]. However, we notice a relative lack of open and accessible frameworks or tools allowing for modular and unified design of multisensory virtual objects and scenes, that can be considered for their visual, acoustical, haptic behaviour, or indeed any combination of the three.

In the following section, we present our contribution to such a framework in the form a mass-interaction physics engine that can be coupled with an open-hardware force-feedback device (in our case, the Haply) in order to create any kind of haptic or audio-haptic virtual scene.

A P -H P F

Our prototyping framework is based on P , an open-source Java based programming environment tailored for sketching D and D animated scenes. It is currently one of the most popular tools used to introduce and teach interactive and visual programming, while remaining capable of complex rendering, communication with hardware, and even physical modelling . What's more, hAPI, the Haply programming interface, is written in Java and is directly fitted for running within Psketches. Although, it is not an audio programming environment as such, external libraries can be used to add real-time sound synthesis functionality.

A -J

P

is a new open-source modular mass-interaction physics engine prototype, recently developed by the authors. As opposed to existing physical modelling libraries within P , P allows designing D physical objects through modular networks of masses and interactions, easily integrating any type of user interaction (for manipulation, parameter modification, dynamic topology changes, etc.), and building any type of visualisation process on top of the created model. As in any mass-interaction system, the main types of physical elements proposed by P are:

• Mass-type modules: Three-dimensional masses, oscillators and fixed-Points, as well as D masses (constrained on the z plane) or D masses (that only vibrate along the z plane).

• Interaction-type modules: Three-dimensional interactions such as springs, dampers, contacts, enclosing bubbles, etc. For specific use cases, D springs have also been implemented.

One of the main design goals for P is simplicity of use and direct access to each element of a physical model, including during run-time. Each mass or interaction is labelled with a specific name or identifier that can be used to connect the element to others, to read its state or change its physical parameters during the simulation. Metacategories of physical elements can be created to allow for grouped parameter modifications. In addition to specific physical parameters, global "air friction" and gravity direction/force of the entire virtual scene can be configured and modified. Figure shows the general code structure when creating a physical model.

I H D

From the point of view of the physical simulation, the haptic device is represented by an avatar: a mass-type module, called HapticInput D.

Instead of calculating a new position based on its previous states and the forces applied to it (as a regular mass would), this module sends its force signal out to the real haptic device's transducers and sets its position from the haptic device's sensor data. We use the existing hAPI functions to transform the encoder values of the two motors into a D position by calculating the kinematics of the linkage arms, and reciprocally to translate forces applied in a D space to torque values applied to the motors. Therefore, the end-user has only to consider the device's end-effector in a D plane and connect it directly to the simulation. The 8-bit resolution of the encoders can result in strong quantisation of the position data and fairly "jumpy" physical behaviour. We chose to feed the raw position value into an Exponential Weighted Moving Average filter with a high weighting decrease. As such the filter adds latency, theoretically impacting haptic stability. However, given the low resolution position data, the trade-off of smoother data versus the small increase in latency leads to no observable increase of instability. Time has not yet allowed for complete real/virtual calibration of the haptic device. For now, the real → virtual position gain alpha and the virtual → real force gain beta (cf. Figure ) are empirically defined by the user depending on the mechanical impedance of the virtual scene/objects.

E U E : P

Haptic Simulation Framework In the case of non-audio haptic simulations, the P sketch is organised as shown in Figure : the haptic input/output communication with the Haply Board, the kinematics and the physical computation all run in a dedicated thread running at a fixed-rate, generally kHz. The draw() method renders the model by observing its state at a lower display rate. The rendering process can be generic (visualise all mass-type and interaction-type elements according to pre-defined drawing routines) or custom-coded by the user. Portability and ease of use is an important consideration. The sketches run on Mac, Linux and Windows, the only noticeable difference measured being the scheduling performance of the haptic thread: early tests show a higher dropout rate (missed steps in the haptic-loop) on a Windows system, correlated with system load; however, on a standard Linux OS the scheduling is more robust, and very few steps are missed. Performance in these conditions is satisfactory, meaning there is no need for a dedicated Real-Time OS, sometimes used in high-performance synchronous systems [ ].

Real-time Audio-Haptic Simulation Framework

Handling real-time audio streams in Processing can be done using the MINIM library 6 , which implements the common Unit Generator paradigm, found in environments such as Super Collider [ ]. A P UG class has been created, extending the MINIM UG template. It contains the mass interaction model (built and initialized in the class constructor), and computes steps whenever needed (by overriding the uGenerate() method). The system is slightly more complex here:

• The haptic thread runs at kHz, getting the haptic I/O and performing the kinematic transformations. At each step, it sets a new position value from incoming sensor data, and discharges the force from the model to the haptic device (sending it to the motors).

• The sound synthesis UG runs at the audio rate ( . kHz), providing new audio data by computing steps of the physical model whenever needed through a callback API. The haptic avatar module upsamples and smoothes raw position data from the haptic device, using by the EWMA filter. Symmetrically, force applied by the model to the avatar is accumulated into a buffer until it is consumed by the haptic thread (see [ ] for details regarding multirate audio mass-interaction systems with haptics).

• The visualisation thread (draw() method) observes the model positions and creates the visual representation.

A lock synchronisation system ensures mutual exclusion in the critical sections of the haptic, sound synthesis and rendering threads, thus avoiding temporary glitches & errors that can be induced by concurrent memory access (e.g. reading the model state in the display thread while it is being updated by the physics thread).

6 http://code.compartmental.net/tools/minim/

R & E

A number of Haply-specific examples can be found the in the example section of the P github repository , as well as ready-to-use templates in which the user has only to add his/her physical model code and visualisation specificities. Below, we present four simple cases:

H E : H
This simple example attaches a chain of D masses to the haptic device (which moves on the x-y plane). The springs are fairly loose, but the combined weight of the virtual masses is enough to add significant inertial behaviour to the system: when dragging the chain, one can feel the effort needed to set them in motion, and must work with/against their momentum when stopping or changing direction.

H E : E M

In this model, two-hundred D masses are enclosed within a sphere (using bubble interactions) and above a flat surface (using planeContact modules). Each mass has contact interactions set up with all other masses, as well as with the haptic input module. Gravity and air friction are configured so that the masses fall down onto the plane, and eventually stop moving. By "rummaging" around with the haptic device, the user interacts simultaneously with many masses, sending them bouncing up against the edges, giving a global "stirring" motion, and so forth.

Dropping the haptic thread rate to Hz allows to increase the number of masses to 6 , at the cost of reduced bandwidth (less sharp dynamics) in the physics computation.

Figure :

The "Enclosed Marbles" example sketch.

A -H E : P S

Using the real-time audio architecture described in the previous section, this model illustrates the simple case of a plucked string. The string itself is composed of masses constrained to move along the x-y plane (keeping a constant z value), connected by damped D springs, and ended with two fixed points. Contact interactions link the haptic device to each mass of the string, with a given sphere of action (analogous to the "width" of the plectrum), so that the user can pluck the string in any part (in the middle, near the bridge, etc.) and also excite and rapidly dampen the string in specific areas to obtain palm-mute or natural harmonic effects. A similar example combines multiple strings placed below each other, so that they can be played one at a time or strummed together. It can be noted that in the case of D strings, the resting length of the springs relative to the elongation imposed by the extremities is a key factor in the physical behaviour, in particular regarding non-linear tension effects [ ] such as the "twang" or pitch glide at high excitation levels. This will be illustrated in the last example.

A -H E : T R S

This model explores the non-linearities of D strings by pushing the situation to the extreme: the string is still attached to a fixed point at one end but the other end is a very heavy mass set with an initial velocity. This mass slowly stretches the string until it recoils, then loosening up until it is completely limp, before stretching again. What's more, by plucking or exerting pressure on the string, the user can influence the course of the heavy mass, resulting in bizarre "worm-like" behaviour, the string sometimes wrapping almost entirely around the haptic device (as seen in Figure .

These four examples serve as a small introduction to what is possible with the platform. The modular design of the physics and the haptic interaction allow creating all kinds of virtual objects and interaction scenarios, the only real limit being the computational complexity that can fit

P & F W

This work offers several possible axes for improvement:

. Performance, stability and robustness of the haptic device: the Haply's D printed plastic parts lack rigidity and present some play between mechanical elements (especially concerning the linkage arm pivots). This could be addressed by making sturdier aluminium parts based on the provided mechanical schematics. The motor performance also presents some limits for small amounts of force feedback (it takes a certain threshold of command torque for the motor to actually move). For these reasons, implementing stiff spring interactions directly between the device and a virtual point is problematic, as unstable oscillations tend to occur.

. Calibration of the real/virtual chain: through mechanical characterisation of the device and dedicated calibration models, it should be possible to set exactly how a mass of gram in the virtual model is projected into the real world, and reciprocally, helping to standardise the parametrisation of virtual models and make them easier to port to & from other haptic devices.

. Optimisation of the simulation engine: this work is a prototype developed entirely in Java and has prioritised object-oriented concepts and global intelligibility over lean, speed-oriented processing. Switching the core engine to a more powerful language such as C++ while keeping user-friendly model building functions is an interesting perspective for future work.

The authors feel that the presented system constitutes an interesting base for teaching students about modular physical modelling and forcefeedback interaction : the overall framework is very straightforward and concise, placing emphasis on the concepts of mass-interaction physical modelling, the specific time constraints of haptic feedback loops and real-time audio computation. The entire system is open-source, multiplatform and very affordable. As with any newly released open-source tool, the next step is to measure its ease-of-use and robustness in a variety of applications and contexts, hopefully developing a community of users and contributors over time.

C

In The simplicity and affordability of the proposed system makes it an ideal candidate for teaching students about force-feedback interaction and mass-interaction physical modelling. More generally, is serves as a general framework for modular, open haptic interaction design. We aim to host a series of introductory workshops in the coming months. [ ] S. Sinclair and M. M. Wanderley. A run-time programmable simulator to enable multi-modal interaction with rigid-body systems.

Interacting with Computers, ( -): -6 , 8.

[ ] W. Verplank. Haptic music exercises. In Proceedings of the conference on New interfaces for musical expression, pages 6-. National University of Singapore, .

[ ] W. Verplank, M. Gurevich, and M. Mathews. The plank: designing a simple haptic controller. In Proceedings of the conference on New interfaces for musical expression, pages -. National University of Singapore, .

  Partially in response to these issues, several open-hardware systems have been proposed, such as the simple low-tech haptic systems designed by Bill Verplank [ , ]. More recently, the rise of digital fabrication technologies and open-electronics have given rise to new, affordable and open-source & hardware haptic devices, such as Edgar Berdahl & A. Kontogeorgokapopoulos' FireFader [ ], or the Haply system [ ].

Figure

  Figure : a) Distributed approach to multi-modal virtual scenes (left), b) single model approach (right).

Figure :

 : Figure : Representation of a mass-interaction model, composed of different types of mass and interaction elements.

  Figure : Creating a mass-interaction physical model with P .

Figure :

 : Figure : Full user-model interaction chain for non-audio haptic simulations. The kinematic calculations, physical computation and position/force I/O are all performed in a haptic thread, running at kHz. The model is rendered at a lower rate in the draw() method.

Figure 6 :

 6 Figure 6: Chain of masses (green) attached to the Haply system (red) by springs.

Figure 8 :

 8 Figure 8: D Plucked String Example. The haptic mass (red) is pressed against the string.

Figure :

 : Figure : Various screen shots of the "recoil" string. The green point is fixed, whereas the yellow one is a very heavy mobile mass, causing the string to tighten/loosen, wrap around the Haply device, etc.

  this paper, we have presented a new open-source & openhardware framework for prototyping audio-haptic interaction with massinteraction models. Based on the Haply device, a new physics engine prototype, and the P sketching environment, users can easily create scenes composed of virtual objects and interact with them. Two scenarios allow the physical computation to either be calculated in sync with the haptic data acquisition & computation loop, or in a higher rate thread in the form of a physics-based Unit Generator for real time audio. A first batch of examples shows promising results. The D haptic device offers new interactions with virtual acoustical objects; augmenting the current Haply device to or DoF should open further perspectives.

  ] M. Giordano and M. M. Wanderley. Perceptual and technological issues in the design of vibrotactile-augmented interfaces for music technology and media. In International Workshop on Haptic and Audio Interaction Design, pages 8 -8. Springer, . [ ] A. Gupta and M. K. O'Malley. Design of a haptic arm exoskeleton for training and rehabilitation. IEEE/ASME Transactions on mechatronics, ( ): 8 -8 , 6. [ ] V. Hayward, O. R. Astley, M. Cruz-Hernandez, D. Grant, and G. Robles-De-La-Torre. Haptic interfaces and devices. Sensor Review, ( ): 6-, .[ ] A. Kontogeorgakopoulos and C. Cadoz. Cordis anima physical modeling and simulation system analysis. In th Sound and Mu-] J. Leonard, N. Castagné, C. Cadoz, and A. Luciani. The msci platform: A framework for the design and simulation of multisensory virtual musical instruments. In Musical Haptics, pages -6 . Marlière, F. Marchi, J.-L. Florens, A. Luciani, and J. Chevrier. An augmented reality nanomanipulator for learning nanophysics: The.

						[ ] R. B. Gillespie and S. O'Modhrain. Embodied cognition as a motivat-
						ing perspective for haptic interaction design: A position paper. In
						World Haptics Conference (WHC),	IEEE, pages 8 -86. IEEE,
						.
						sic Computing Conference	, pages	-8 . National and
	R					Kapodistrian University of Athens,	.
						[ 6] J. Leonard and C. Cadoz. Physical modelling concepts for a collec-
	[ ] E. Berdahl and A. Kontogeorgakopoulos. The firefader: Simple,	tion of multisensory virtual musical instruments. In New Interfaces
	open-source, and reconfigurable haptic force feedback for musi-	for Musical Expression	, pages	-,	.
	cians. Computer Music Journal, ( ): -,	.
						Springer,	8.
	Signals, pages	-68. MIT Press,	.	[ 8] S. In International Conference on Cyberworlds	8, pages -.
	[ ] C. Cadoz, A. Luciani, and J. L. Florens. Cordis-anima: a modeling	IEEE,	8.
	and simulation system for sound and image synthesis: the general	[ ] S. Martin and N. Hillier. Characterisation of the novint falcon hap-
	formalism. Computer music journal, ( ): -,	.	tic device for application as a robot manipulator. In Australasian
	[ ] N. Castagné and C. Cadoz. Physical modeling synthesis: balance between realism and computing speed. In Proceedings of the COST	Conference on Robotics and Automation (ACRA), pages Citeseer, .	-.
	G-6 conference on the digital audio effects (DAFX-), page 6,	.	[ ] T. H. Massie, J. K. Salisbury, et al. The phantom haptic interface:
	[6] M. C. Cavusoglu and F. Tendick. Multirate simulation for high fi-delity haptic interaction with deformable objects in virtual environ-ments. In Robotics and Automation, . Proceedings. ICRA' . IEEE International Conference on, volume , pages 8-6 .	A device for probing virtual objects. In Proceedings of the ASME winter annual meeting, symposium on haptic interfaces for virtual environment and teleoperator systems, volume , pages -. Citeseer, .
	IEEE,	.				[ ] J. McCartney. Rethinking the computer music language: Supercol-
	[ ] S. Ding and C. Gallacher. The haply development platform: A mod-	lider. Computer Music Journal, 6( ):6 -68,	.
	ular and open-sourced entry level haptic toolset. In Extended Ab-	[ ] S. Papetti and C. Saitis. Musical haptics: Introduction. In Musical
	stracts of the	8 CHI Conference on Human Factors in Computing	Haptics, pages -. Springer,	8.
	Systems, page D	. ACM,	8.
	[8] J.-L. Florens. Coupleur Gestuel Retroactif pour la Commande et le
	Controle de Sons Synthetises en Temps-Reel. PhD thesis, Institut
	National Polytechnique de Grenoble,	8.
	[ ] J.-L. Florens, A. Luciani, C. Cadoz, and N. Castagné. Ergos: Multi-
	degrees of freedom and versatile force-feedback panoply. In Euro-
	Haptics	,	.
	[ ] J.-L. Florens, A. Voda, and D. Urma. Dynamical issues in interac-
	tive representation of physical objects. In EuroHaptics	6 con-
	ference, pages	-,	6.

[ ] J. Blake and H. B. Gurocak. Haptic glove with mr brakes for virtual reality. IEEE/ASME Transactions On Mechatronics, ( ):6 6-6 , . [ ] C. Cadoz and J.-L. Florens. The physical model : Modeling and simulating the instrumental universe. In Representations of Musical [ [

https://processing.org/ https://github.com/diwi/PixelFlow

https://github.com/mi-creative/miPhysics_Processing