The acoustic wind sensing trial was conducted in the Ligurian Sea, a sub-basin of the northwestern Mediterranean, in proximity to the DYFAMED (DYnamique des Flux Atmosphériques en MEDiterranée) oceanographic time series station (Fig. 1). This station is part of the national observation program MOOSE (Mediterranean Ocean Observing System for the Environment, https://www.moose-network.fr, last access: 28 May 2025), funded by CNRS–INSU, and has been integrated since 2016 into the national research infrastructure ILICO (Infrastructure de recherche littorale et côtière; Cocquempot et al., 2019).

Located at 43.42° N, 7.87° E, DYFAMED has served as a key reference site for air–sea exchange, upper ocean dynamics, and biogeochemical cycling since the early 1990s. The site is equipped with continuous meteorological and oceanographic monitoring, including high-quality wind speed and direction measurements from the Côte d'Azur meteorological buoy operated by Météo-France, located at the DYFAMED site. These data are reported at hourly resolution following WMO (World Meteorological Organization) standards and include wind parameters, air temperature, pressure, humidity, and sea state.

During the study period, wind speeds at DYFAMED ranged from 0.5 to 16.1 m s⁻¹, with a mean of 6.8 m s⁻¹ and a measurement precision of one decimal place.

The float used in this study was equipped with a passive acoustic module jointly developed by NKE and ABYSsens in collaboration with LOV. This module was specifically designed for integration into the PROVOR CTS5 BGC-Argo platform, with the aim of minimizing power consumption and data volume while remaining compatible with the operational constraints of the BGC-Argo program.

The module consists of two main parts enclosed in a dedicated external housing: (1) a low-noise HTI-96-Min hydrophone (sensitivity: -165 dB re 1 V µPa⁻¹; frequency range: 2 Hz–30 kHz), mounted externally to capture pressure fluctuations, and (2) an ABYSsens acquisition board, which conditions, digitizes, and processes the signal.

The acquisition system operates in a low-power pulsed mode (220 mW) with a sampling frequency up to 62.5 kHz and 24-bit resolution. To limit power usage and transmission needs, raw acoustic signals are not stored. Instead, the sensor performs direct onboard integration into 23 third-octave bands, spanning from 63 Hz to 25 kHz with a variable integration time (see Table 1). Higher-frequency bands (e.g., 3.15–25 kHz) used shorter integration times (50 ms), while low-frequency bands used longer windows (up to 500 ms).

The acoustic unit is mounted on the upper section of the float chassis and is configured to operate exclusively during the parking phase (500–1000 m depth; Fig. 3). During this phase, the float drifts with only routine background measurements (e.g., pressure, CTD), and acoustic acquisition is automatically suspended whenever noisy operations such as ballast pumping or CTD sampling occur, thereby avoiding contamination from self-noise.

The float system allows for flexible and modifiable configuration via satellite: the user can define the number of bands transmitted (23, 9, or a compact onboard estimate of wind/rain), the acquisition interval (typically 5–15 min), and the number of acoustic samples averaged per measurement. In this study, we used a 5 min interval with 10 averaged acquisitions per measurement (each acquisition is a spectral estimation using the integration times defined in Table 1).

The telemetry and energy impact of adding an acoustic sensor to a 6-variable biogeochemical float was evaluated by using the programming interface provided by NKE. The estimated reduction in the number of cycles varies from 18 % for acquisition every 5 min to 7 % for acquisition every 15 min during the whole parking drift of a 10 d Argo cycle and with 5 averaged acquisitions per acoustic measurement. The data volume increase depends on the transmission format: from ∼ 9 % for onboard wind–rain estimates (15 min period) to ∼ 85 % for a full 23-band spectrum (5 min period). A 9-band spectrum every 15 min – a likely recommended setup – adds ∼ 16 %. These overheads remain within the platform's capacity, confirming compatibility with concurrent BGC measurements.

Each sensor output transmitted by the float corresponds to the Third Octave Level (TOL), i.e., the sound pressure level integrated over a third-octave band, expressed in dB re 1 µPa. These TOLs represent the float's primary spectral product and are used as input to the wind speed retrieval models. The amplitude resolution of the transmitted data is 0.2 or 0.5 dB, with a dynamic range up to 127 dB. This discretisation arises because the data are transmitted as integers to save bandwidth, which requires selecting a resolution step.

To account for the attenuation of surface-generated noise with depth, a correction term β(h,f) was applied to all acoustic measurements (Fig. 2). Because β depends on the ambient temperature–salinity structure, we quantified hydrographic stability over the 60 d deployment using all profiles that reached at least 1000 dbar. Each profile was interpolated onto a 1 m grid and compared to the deployment-mean temperature/salinity profiles. Depth-averaged RMS deviations were 0.14 ± 0.04 °C for temperature and 0.06 ± 0.02 for salinity, and no profile exceeded |z=2 standardised deviation, confirming weak hydrographic variability. Because such differences are far below hydrophone measurement uncertainties, β(h,f) was computed once using the deployment-mean profile and applied uniformly to the full record. For longer or more dynamic missions, β(h,f) should be recomputed for each profile. Modern hardware makes this operation computationally inexpensive, but the negligible hydrographic variability in this deployment renders repeated recalculation unnecessary.

Following Cauchy et al. (2018), the correction takes the form: 1aTOL0(f)=TOL(h,f)+β(h,f),1bwhereβh,f=-10log⁡2∫0∞rsin⁡2θr,he-αflr,hlr,h2dr, with TOL(h,f) as the raw TOL measurement from the profiling float, h as the sensor depth, f the centre frequency of the band, r the horizontal distance from a surface noise source to the point vertically above the sensor, l the total pathlength between source and receiver (accounting for depth and refraction), including refraction effects, θ the angle between the emitted acoustic ray and the horizontal axis, and α the frequency-dependent attenuation coefficient for bubble-free water. The integral considers contributions from all surface-generated acoustic sources over the sea surface, assuming radial symmetry, and accounts for geometric spreading, frequency-dependent absorption, and angle-dependent energy emission along each path. This correction was originally derived for third-octave levels and is directly applicable here, as the float outputs TOLs at fixed centre frequencies. Then, depth-corrected third-octave levels TOL0(f) (dB re 1 µPa) were converted to spectral density levels SPL(f) (dB re 1 µPa Hz⁻¹) by normalising to the bandwidth of each band. In the following, SPL always refers to these depth-corrected, bandwidth-normalised values derived from TOL0(f). This step ensures consistency across frequencies and comparability with model spectra. In future deployments, this spectral correction will be applied directly onboard the float.

Two deployments of an acoustic-equipped float (PROVOR CTS5) were carried out near DYFAMED between February and April 2025 (Fig. 1). Deployment A lasted 30 d, from 10 February to 11 March, and Deployment B continued for 24 d starting on 12 March and remained active until 4 April. The float operated in park-and-profile mode at three parking depths (500, 700, and 1000 m; Fig. 2), collecting biogeochemical data during ascent and passive acoustic data exclusively during the parking phases to minimize self-generated noise.

While Riser et al. (2008) previously demonstrated the feasibility of acoustic wind sensing from Argo floats, their system transmitted only pre-processed wind estimates derived onboard using a simplified version of the algorithm by Nystuen et al. (2015), without retaining or transmitting spectral band data. This limited the possibility of reanalysis or applying alternative processing schemes. In contrast, the floats used in this study recorded and transmitted full third-octave band spectra, enabling detailed post-processing and algorithm refinement tailored to the float's specific acoustic characteristics.

Transient noise (i.e., episodic non-wind-related events) was mitigated by removing values exceeding the 99th percentile within a ±1.5 h window centred around each matched timestamp. This percentile corresponds to discarding roughly the top 1 % of samples over a 3 h window (≈2 min of data). No physically meaningful wind- or wave-driven variability relevant to this study evolves on such short timescales, making this filter effective at removing brief acoustic artefacts without suppressing real high-wind conditions. This approach is conceptually similar to the transient-noise mitigation used in glider-based PAM studies (e.g., Cauchy et al., 2018), which suppress short-lived spikes in the spectra to isolate wind-generated noise.

To further reduce short-term variability and emphasize quasi-stationary wind-driven acoustic patterns, we applied a 3 h rolling mean to each frequency band. This smoothing window is conceptually consistent with the profile-scale averaging used in glider-based acoustic wind studies (e.g., Cauchy et al., 2018), where acoustic measurements are aggregated over ∼ 2 h glider dives to suppress transient variability. While smoothing inevitably attenuates rapid fluctuations, the 3 h window stabilises the spectra without erasing multi-hour wind events relevant for air–sea flux applications. Alternative strategies, such as post-processing the wind speed estimates rather than the spectral bands, could be explored in future deployments if finer-scale variability is a priority.

Anthropogenic noise was mitigated using AIS vessel tracks. Because the float only provides GPS positions at the surface, we reconstructed a continuous trajectory by linearly interpolating its positions between successive surfacings at hourly resolution. Each 5 min acoustic record was then associated with the nearest interpolated position. An observation was flagged as potentially contaminated when an AIS-reported vessel was located within 20 km of this interpolated float position and within ±30 min of the acoustic timestamp. The 20 km radius corresponds to the distance over which ship-radiated noise commonly dominates the ambient sound field in the 1–10 kHz band under low-to-moderate sea states, while the ±30 min window accounts for the typically irregular AIS reporting interval offshore. As an additional safeguard, we excluded cases where the float-derived wind speed deviated from the DYFAMED buoy by more than the RMSE computed under uncontaminated conditions. This RMSE criterion is used only as a secondary check to capture possible contamination during periods of poor AIS coverage. Sensitivity tests indicate that moderate changes to these thresholds do not affect the main conclusions.

Empirical models have long been used to estimate surface wind speed from underwater ambient noise, exploiting the link between wind-driven bubble formation and acoustic energy in the 1–20 kHz band. These models typically relate surface wind speed U to the sound pressure level Lf measured in selected frequency bands. While many models use third-octave bands, others rely on custom-defined or narrowband frequencies, often with variable bandwidths (e.g., 16 % of the centre frequency in Vagle et al., 1990).

We applied four established wind retrieval models spanning a range of functional forms – cubic, two-regime linear–quadratic, composite, and two-regime log–linear. All wind models were applied using acoustic levels consistent with their original formulations (Table 2). This diversity allowed us to assess sensitivity to model structure and evaluate performance under float-specific conditions. Each model was first implemented using its published coefficients to generate wind speed estimates from float acoustic data, and the results were evaluated against collocated meteorological observations (Fig. 4). Subsequently, the parameters of each model were refitted using collocated float acoustic and wind data from the DYFAMED meteorological buoy (Figs. 4 and 5), which provides hourly 10 m wind speed. Model refitting was performed using nonlinear least-squares optimization (Table 3). Wind records from DYFAMED were matched to float measurements by nearest timestamp.

Following the spatial filtering approach of Cauchy et al. (2018), only float data within 40 km of DYFAMED were retained for refitting and validation (Fig. 1). This threshold corresponds to the estimated confidence radius around the DYFAMED meteorological buoy, within which wind speed measurements show high spatial coherence (R = 0.86, RMSE = 2.5 m s⁻¹) when compared to the AROME-WMED atmospheric model (Rainaud et al., 2014). Although originally derived from the spatial wind-field decorrelation scale reported by Cauchy et al. (2018), this 40 km radius reflects a regional mesoscale atmospheric property rather than a platform-specific constraint. Because our deployment occurred in the same NW Mediterranean basin, this decorrelation length remains appropriate for our case. We note, however, that this threshold is region-dependent and should be re-evaluated for future deployments elsewhere.

The updated coefficients were then used to generate wind estimates over the full float dataset. While this spatial proximity improves wind representativeness, it does not account for variations in wind fetch, a parameter known to influence ambient noise generation, particularly through wave and bubble field development (e.g., Prawirasasra et al., 2024).

These four models were selected to represent a range of analytical formulations commonly used in acoustic wind retrievals. They all use frequency bands where wind-driven bubble noise typically dominates the local ambient sound field, with reduced interference from low-frequency sources such as distant shipping. Our aim was not to exhaust all available models, but rather to evaluate a representative subset under consistent float-specific conditions, emphasizing the effect of model structure and local fitting.

The specifications and key features of each model are summarized in Table 2 for reference. For all models and validation steps throughout the rest of Methods section, wind speed refers to the standard 10 m wind speed, consistent with both the ERA5 reanalysis product and the DYFAMED buoy observations used for calibration and evaluation.

The first model, from Vagle et al. (1990), was derived from moored hydrophone data in the North Atlantic and relates wind speed to high-frequency noise at 8 kHz using a cubic formulation: 2UVagle1990=10-38.70+-38.702-4.7⋅38⋅(SPL8kHz-21.69)-7.38⋅2. Next, we applied the cubic model from Nystuen et al. (2015), developed using long-term acoustic records from fixed hydrophones in both the Pacific and Atlantic. This model targets wind-generated noise at 8 kHz and includes band-specific criteria to distinguish wind contributions from other sources such as rain and shipping (Table 2). 3UNystuen2015=0.0005⋅SPL8kHz3-0.0310⋅SPL8kHz2+0.4904⋅SPL8kHz+2.0871

We then tested the two-regime linear–quadratic model from Pensieri et al. (2015) at 8 kHz, developed using moored hydrophone data from the Ligurian Sea, near our study area. Calibrated for Mediterranean conditions, the model relates wind speed to ambient noise levels at the 8 kHz band, applying distinct linear and quadratic fits across low- and high-noise regimes. Notably, the transition between regimes is defined at 38 dB, corresponding to a wind speed of 2.39 m s⁻¹ in their framework. However, it is important to note that the threshold separating high and low regimes is not standardized across the literature and may vary between studies. 4UPensieri2015=0.044642⋅SPL8kHz2-3.2917⋅SPL8kHz+63.0160.1458⋅SPL8kHz-3.146,forSPL8kHz<38dB Finally, we included the two-regime log–linear model from Cauchy et al. (2018), developed using acoustic data from a glider operating in the western Mediterranean. Designed for mobile platforms, the model relates wind speed to third-octave noise levels centred at 3.15 kHz. The model uses distinct logarithmic and linear fits across two noise regimes.

This choice of 3.15 kHz, instead of the more commonly used 8 kHz, was based on empirical observations showing greater dynamic range and lower variance in this band, which may reflect sensor-specific factors or the sensor's mounting configuration on the glider (Cauchy et al., 2018). The relationship goes as: 5UCauchy2018=10.4×104⋅10SPL3.15kHz-Soff20+0.2×10411.6×104⋅10SPL3.15kHz-Soff20+12.5×104forU>10ms-1 The wind retrieval relationship is modelled using a two-regime log-linear function. The transition between regimes occurs at wind speeds of approximately 10–11 m s⁻¹, established empirically. To represent this switching behaviour, a relative threshold level is introduced, expressed as SPL – Soff, where Soff denotes the sea-state 0 noise reference. This formulation highlights when wind-driven noise becomes dominant relative to the reference background noise.

To assess the ability of float-derived acoustic measurements to estimate surface wind speed in regions lacking direct atmospheric observations, we developed a two-step framework based on (i) calibration to ERA5 reanalysis winds and (ii) residual correction using sparse in-situ measurements. The goal was to emulate realistic deployments of acoustic-equipped profiling floats in remote regions where only global reanalysis products and limited ship- or buoy-based wind measurements are available.

We applied four previously published wind retrieval models to float-measured sound pressure levels (SPLs) at 8 and 3.15 kHz. Using the original coefficients from these studies, wind speed estimates deviated significantly from collocated DYFAMED observations, particularly in their ability to reproduce the magnitude of wind events (Fig. 4a). This mismatch reflects the sensitivity of empirical acoustic models to deployment context, including platform geometry, acoustic propagation, and local noise environment.

When these same models were refitted using collocated float acoustics and DYFAMED wind observations within 40 km (Fig. 1), performance improved substantially (Fig. 4b; Fig. 7). Among the models, the cubic formulation by Nystuen et al. (2015) achieved the best fit (R2 = 0.88; Fig. 5b) and successfully captured the full observed wind range (0.5–16.1 m s⁻¹; Figs. 5 and 7). It was also the only model resolving wind speeds < 2 m s⁻¹, a regime often missed due to weak surface forcing and minimal bubble generation. This low-wind sensitivity strengthens its relevance for air–sea gas-exchange studies and suggests broad applicability in moderate wind regimes. High-quality wind estimates are particularly important for interpreting float-based biogeochemical measurements, as air–sea oxygen fluxes respond sensitively to short-timescale wind variability (Bushinsky et al., 2017).

However, even after successful fitting, the portability of acoustic–wind models remains uncertain. Factors such as noise contamination, ambient biological activity and regional propagation conditions can vary substantially between deployments, affecting both the shape and robustness of the acoustic–wind relationship (Gros-Martial et al., 2025b). Moreover, profiling floats introduce their own artifacts, which may arise from hydrodynamic turbulence, buoyancy engine activity, bubble release, or electronic interference, each of which can contaminate the acoustic signal independently of wind forcing. Even models developed in the same basin required refitting (i.e. Pensieri et al., 2015; Figs. 4, 5 and 7).

A promising direction would be to classify deployments into broader “acoustic environment types”, such as open-ocean gyres, coastal shelves, or high-latitude storm zones, within which shared model parameters could be defined and validated. This aligns with the priorities outlined in the Ocean Sound Essential Ocean Variable (EOV) Implementation Plan, which emphasizes the need for community-agreed metadata standards, calibration protocols, and classification schemes to support global comparability across acoustic deployments (Tyack et al., 2023). Evaluating these frameworks for profiling floats may help standardize acoustic wind retrieval and integrate it more effectively into global observing systems.

While site-specific fitting of acoustic wind models yields accurate float-derived wind estimates, such fittings are not feasible in most regions of the global ocean where in-situ wind observations are unavailable. To assess whether the acoustic–wind relationship can be generalized for remote deployments, we investigated the use of reanalysis wind products as a proxy reference for model fitting. Specifically, we used the ERA5 atmospheric reanalysis (Bell et al., 2021) to refit the Nystuen et al. (2015) model to float-measured acoustic data, simulating a scenario where no collocated buoy or shipboard wind measurements are available (Figs. 6 and 8).

Using time-matched float sound pressure level at 8 kHz and collocated ERA5 wind speed, we derived a new set of coefficients (Sect. 2.6), producing a general-purpose fit based solely on float data and reanalysis inputs. The goal was to test whether an existing model can be adapted for use in data-sparse regions, enabling scalable wind estimation from profiling floats.

As shown in Fig. 6a, the ERA5-calibrated Nystuen et al. (2015) model reproduced wind variability within the 2.5–10 m s⁻¹ range with moderate skill (R2=0.85), and performed best during Deployment A, when wind conditions remained relatively stable (Fig. 8). Performance deteriorated during stronger wind events, particularly in Deployment B, where the model systematically underestimated wind, with errors > 3 m s⁻¹ (Figs. 6a and 8).

Comparison with DYFAMED also revealed broader limitations of ERA5. Although ERA5 provides a globally consistent wind product, it diverged from buoy observations during several high-wind episodes (Figs. 6c, 8). This behaviour is consistent with earlier reports of reanalysis underestimating localised, orographically forced winds in semi-enclosed basins such as the Mediterranean (Bentamy et al., 2003; Bell et al., 2021). Such biases are critical in regions like the Southern Ocean, where frequent high-wind events dominate air–sea CO₂ fluxes and gas exchange scales nonlinearly with wind speed (Wanninkhof, 2014; Wanninkhof et al., 2025).

Thus, while float reanalysis-based calibration enables acoustic wind estimation in the absence of local observations, its accuracy depends strongly on the reliability of the reference product used for fitting.

While reanalysis-calibrated acoustic models offer a pathway for estimating surface wind speed in remote regions, the results in Sect. 3.2 show that this approach alone is insufficient during high-wind or rapidly evolving events. This limitation is especially critical in high-latitude regions such as the Southern Ocean, where extreme wind forcing drives critical fluxes of heat, momentum, and carbon (Gray et al., 2018; Dotto et al., 2019; Zhang et al., 2022; Gruber et al., 2023).