In Situ Validation of Altimetry and CFOSAT SWIM Measurements in a High Wave Environment
1. Introduction
Satellite altimetry has been central to developing our understanding of ocean circulation and dynamics (e.g., Fu and Le Traon 2006; Storer et al. 2022). Observations of wave metrics from the Surface Waves Investigation and Monitoring (SWIM) instrument on board the Chinese–French Ocean Satellite (CFOSAT), launched in 2018, are also providing valuable contributions to oceanographic research (Hermozo et al. 2022). To ensure the quality of these observations, ongoing validation of the data is required. In situ observations form an important part of mission validation plans, providing an independent check on satellite data. Given in situ studies are local rather than global by nature, a diverse range of sites are required to appropriately characterize altimetry performance (Bonnefond et al. 2019). For wave metric validation, in situ data from wave buoys are often used (e.g. Dobson et al. 1987; Jiang et al. 2022), along with comparisons with wave model simulations, and in situ data from Voluntary Observing Ships (e.g., Hauser et al. 2021; Grigorieva et al. 2022). For sea surface height validation, in situ approaches at specific locations complement relative approaches using, for example, altimetry crossovers (Gaspar et al. 1994) and tandem phase measurements (Ablain et al. 2010)—both of which have the advantage of having large sample sizes over the global ocean but lack the full independence of in situ methods.
While there is a recognized need for geographically diverse in situ validation data, challenges associated with deployments of instrumentation in remote open ocean environments are significant. The majority of in situ wave data from moored buoys and platforms are within 50 km of the coast (Dodet et al. 2020). While coastal areas are of great interest (e.g., Passaro et al. 2021), this leaves large areas of open ocean undersampled from an in situ wave perspective. The four primary in situ altimetry validation sites for absolute sea surface height (SSH) validation are also all located close to coastlines and are in regions of relatively calm sea states (Bonnefond et al. 2011). The sparsity of in situ data in high wave regions, particularly in the Southern Ocean (Babanin et al. 2019), contributes to deficiencies in the validation of altimetry significant wave height (SWH) products (Schlembach et al. 2020). Indirectly, this also affects SSH estimates given the need for accurate sea state bias corrections (Born et al. 1982). With the recent launch of the pathfinder Surface Water and Ocean Topography (SWOT) mission there is a greater need for collocated sea state and SSH validation measurements due to the additional complexities presented by waves in wide swath interferometric altimetry (e.g., Peral et al. 2015).
The Southern Ocean Flux Station (SOFS) mooring is located 47°S (Fig. 1) and provides a unique opportunity to capture in situ wave and SSH data in a high wave energy environment. To achieve this, a dual-frequency geodetic quality Global Navigation Satellite System (GNSS) receiver was added to SOFS in 2019. As a satellite validation site, SOFS has the advantage of hosting many oceanographic and atmospheric instruments in addition to GNSS (Schulz et al. 2012), which provide information on a range of variables influencing wave conditions and SSH. While GNSS measurements have been used for altimetry validation for some time (e.g., Born et al. 1994; Watson 2005; Yang et al. 2017; Chupin et al. 2020), questions remain regarding the performance of geodetic GNSS and influence of mooring platform dynamics in a region where SWH in excess of 9 m is not uncommon.
Location of the SOFS8 and SOFS9 deployments in relation to the altimetry missions considered in this study. The average significant wave height in the region has been calculated over the year 2019 from the Copernicus gridded SWH product WAVE_GLO_PHY_SWH_L3_NRT_014_001 available online (https://doi.org/10.48670/moi-00179). Fronts of the Antarctic Circumpolar Current are shown per Orsi et al. (1995), available online (https://cmr.earthdata.nasa.gov/search/concepts/C1613496025-AU_AADC).
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
Using GNSS buoys for wave monitoring and satellite validation is a growing practice, with GNSS buoys showing the ability to provide reliable directional spectra estimates (e.g., Raghukumar et al. 2019; Beckman and Long 2022). GNSS can be used in a variety of ways for wave measurements, including differential kinematic processing that requires a base station nearby (e.g., Bender et al. 2010), making use of GNSS Doppler observations as is done with the Datawell DWR-G buoy (de Vries et al. 2003), or using real-time GNSS position observations with high-pass filtering to significantly reduce the measurement noise as is done with the Spotter buoy (Raghukumar et al. 2019) and other open ocean GPS moorings (e.g., Waseda et al. 2014). For this study we postprocess the 2-Hz GNSS measurements using precise point positioning (PPP) techniques, referred to hereon as “geodetic GNSS.” This method does not require a base station, has a greater data processing requirement than the off-the-shelf products such as Datawell DWR-G and Spotter, but has the benefit of simultaneously providing accurate positions in an absolute reference frame as well as estimates of tropospheric water content.
To assess the benefit of adding geodetic GNSS to the SOFS mooring, we focus on the validation of SWH and sea level anomaly (SLA) from nadir altimetry, and directional spectra and wave metrics from the SWIM instrument on board CFOSAT. The observation strategy from SWIM results in directional spectra estimates over large swaths of approximately 90 km either side of nadir (Hauser et al. 2017), ruling out coastal sites for validation purposes. In situ measurements of directional spectra in the open ocean are currently sparse, so additional observations of this sort are valuable for both validating satellite measurements, and to improve wave modeling (Rapizo et al. 2018; Babanin et al. 2019).
In this paper, we present the first GNSS-based altimetry and SWIM validation results from the SOFS mooring. We demonstrate the robust ability of GNSS to observe the instantaneous sea surface at 2 Hz using PPP processing in a high wave energy environment. From this, we derive SWH, directional wave spectra, and initial SLA estimates. We compare these with products from Jason-3, Sentinel-3A, Sentinel-3B, and CFOSAT (SWIM) missions over specific windows between March 2019 and April 2021. We present the comparison results, and finally discuss the advantages and limitations of using geodetic GNSS measurements for validation of satellite products in the open ocean.
2. Study site
SOFS is located in the subantarctic zone, ∼500 km southwest of the island of Tasmania (Australia). This deep sea mooring extends through approximately 4 km of water and is subject to the consistent westerly winds and large swell systems typical of the Southern Ocean (Young et al. 2020). The Southern Ocean also sees intense eddy generation associated with the Antarctic Circumpolar Current (ACC; Meredith 2016). The SOFS mooring is well north of the polar front where these dynamics are strongest (Fig. 1). The SLA at this site has a standard deviation of 0.08 m, with infrequent events exceeding ±0.15 m (7% of the record over the satellite era).
The SOFS mooring was first deployed in 2010 for the main purpose of measuring air–sea fluxes in the Southern Ocean (Schulz et al. 2012). The mooring is redeployed yearly at a slightly different location (within 10–100 km). Despite the challenges of establishing a mooring in such an extreme environment, SOFS has a strong track record for delivering observations in these conditions (see, e.g., Rapizo et al. 2015; Bharti et al. 2019). This study will focus on two deployments: SOFS8 and SOFS9, as shown in Fig. 1 and described in Table 1.
SOFS8 and SOFS9 deployment details.
3. Datasets
a. SOFS mooring
The primary data used in this study are GNSS observations from the new receiver installed on SOFS8 and SOFS9. The GNSS equipment for both deployments consisted of a Resolute-Polar receiver with Septentrio AsteRx-m2 board and a Javad TriAnt antenna. Data were observed at 2 Hz. Because of battery limitations, the receivers could not collect data for the full duration of each deployment. Instead, data were observed continuously for one month before entering an episodic mode to prioritize data capture during altimetry passes (see Fig. S1 in the online supplemental material).
Multi-GNSS data were observed, with both SOFS8 and SOFS9 recording global positioning system (GPS) and Globalnaya Naavigazionnaya Sputnikovaya Sistema (GLONASS) data. The antenna height above water level for each of the surface platforms is approximately 3.4 m. Given uncertainties associated with the weight of the complete mooring surface platform and suspended infrastructure, we have not attempted to quantify antenna height more precisely—we are not attempting to derive absolute SSH in this analysis.
Each SOFS deployment is equipped with a Microstrain 3DM-GX1 motion reference unit (MRU). The MRU samples acceleration driven by platform motion at 5 Hz for 10 min every hour. In addition to the MRU, every second SOFS deployment includes a Triaxys 3D accelerometer. This uses a slightly different sampling strategy, with observations for 20 min every 2 h at a rate of 1.28 Hz (Rapizo et al. 2015). For this study, the wave observations from the MRU on both deployments and the observations from the Triaxys on SOFS9 were all used in comparison with GNSS and SWIM products. SOFS also records climate-quality atmospheric observations through an Air–Sea Interaction Meteorology (ASIMET) system (Schulz et al. 2012). The system includes two barometers observing atmospheric pressure with observations at 60-s intervals. Wind speed and direction are also measured at 60-s intervals from two sensors.
Many other atmospheric and oceanographic sensors on SOFS were not used in this study. Full details can be found in the Southern Ocean Time Series reports (e.g., Wynn-Edwards et al. 2020, 2022). The SOFS data can be accessed through the Australian Ocean Data Network portal (https://portal.aodn.org.au/).
b. Satellite products
For SWH and SLA comparisons, level-2 along-track data at 1 Hz from Jason-3, Sentinel-3A, and Sentinel-3B were extracted using the Radar Altimetry Database System (RADS) (Scharroo 2022). GDR-F data for Jason-3 were used. For Sentinel-3A and Sentinel-3B, processing baseline PB04 was used. These provide SWH and SLA at 1 Hz (approximately 7-km intervals along track). Along-track SWH data from CFOSAT’s nadir altimeter were also used (processing level L2P, version OP05). To investigate further wave parameters, the CFOSAT SWIM data from the level-2 “wave box” product were used (product L2PBOX, version OP05). These products provide estimates of directional spectra, dominant wavelength, and dominant direction over 90 km × 70 km off-nadir boxes on either side of the nadir track (Guillot et al. 2022).
In addition to the along-track and SWIM data, gridded SWH and SLA products were assessed. For SWH, the level-4 gridded product from the Copernicus Marine Environmental Monitoring Service (CMEMS) was used, which provides a daily estimate of instantaneous SWH at 1200 UTC (noon) on a 2° grid (product identifier: WAVE_GLO_PHY_SWH_L4_MY_014_007). For SLA, the Integrated Marine Observing System (IMOS) Australian region product was used, which provides daily SLA values on a 0.2° grid (http://oceancurrent.imos.org.au/). The level-4 gridded SLA product from the CMEMS was used for comparison, which provided daily values on a slightly lower-resolution 0.25° grid (processing level L4, version vDec2021). The amount of data incorporated into the gridded SLA estimates is dependent on the spatial and temporal correlation scales of the SLA signal, with approximately 300 km and 60 days of data contributing to estimates at the SOFS latitude (Pujol et al. 2016).
4. Methods
a. GNSS processing
The GNSS processing method was designed following lessons learned through processing GPS equipped buoys at the Bass Strait altimeter validation facility [see early work by Watson et al. (2003) and most recently Zhou et al. (2020) and Legresy et al. (2022)]. In comparison with Bass Strait, the SOFS site is highly dynamic, the much larger SOFS mooring covers an ∼8-km-diameter watch circle (cf. ∼200 m at Bass Strait), and the large distance to land of ∼500 km prevents the use of differential positioning using a nearby base station. For this study, the raw GNSS data were processed using NASA/JPL’s GipsyX software (v2.0) as described by (Bertiger et al. 2020). The kinematic PPP (Zumberge et al. 1997) approach applied through GipsyX allows high-rate, multiconstellation, precise positions to be estimated with respect to the International Terrestrial Reference Frame (ITRF).
The raw observations were exported to RINEX V3.04 (RINEX Working Group 2018) with dual-frequency observations of 1C, 1W, 2W for GPS and 1C, 2P for GLONASS used in this analysis. To generate 2-Hz SSH estimates, each day of GNSS data was divided into three overlapping sessions of 9-h length. Each session was preprocessed with the GipsyX “Ace” data editor, then processed in GipsyX at a low data rate of 5 min using Centre National d’Etudes Spatiales (CNES) multi-GNSS clock and orbit products (Loyer et al. 2012, accessed from https://cddis.gsfc.nasa.gov/archive/gnss/products/). CNES products were used as these are multi-GNSS products, unlike the default Jet Propulsion Laboratory (JPL) products that do not include GLONASS information at the time of writing. Products from other analysis centers were not tested for this study. This low-rate solution was used to determine an initial trajectory of SOFS that could then be used to extract nominal tropospheric delays calculated through the Vienna Mapping Function 1 and associated meteorological reanalysis products (VMF1; Boehm et al. 2006). Because of the large watch circle and dynamic nature of the surface platform, these low-rate nominal positions and tropospheric delays were essential in producing the subsequent high-rate solutions.
The high-rate solutions were then computed in a two-step process. First, a 1-Hz solution was generated using a relatively loose process noise for position (2 m s−1/2, allowing for motion of the surface platform) and tropospheric wet delay [0.09 mm s−1/2, following Selle and Desai (2016)]. The 1-Hz positions are then provided as nominals for the final 2-Hz processing, with the 1-Hz tropospheric wet and dry delays held fixed. Using the 1-Hz positions as nominals was found to significantly improve the final solution, as determined by the reduction in number of observations removed in the postfit editing stage of the analysis (expressing as fewer points with large formal uncertainties in the final output). Ambiguities were not resolved to integer values due to wide lane bias products from CNES being inconsistent with GipsyX products.
For all solutions, ocean tide loading effects were removed using the FES2014b model (http://holt.oso.chalmers.se/loading/; Bos and Scherneck 2013) in the CM frame (Fu et al. 2012). All other settings including treatment of the solid Earth tide and solid Earth component of the pole tide were chosen to be consistent with the altimetry data processing and are detailed in section 2 of the online supplemental material.
Sensitivity tests were carried out to assess the impact of using GPS only instead of GPS + GLONASS, various wet troposphere constraint values, and various satellite elevation cutoff angle values. These tests showed marginal improvement when using GPS + GLONASS instead of GPS only. The results showed little sensitivity to the other parameters tested, with SWH root-mean-square difference (RMSD) values generally at the millimeter level, and SSH RMSD values at the centimeter level, when compared with the standard processing approach used in this study (see section 3 in the online supplemental material).
Geocentric positions at 2 Hz relative to the IGb14 realization of ITRF14 (Altamimi et al. 2016) were converted to geodetic coordinates on the TOPEX ellipsoid, correcting for the nominal antenna height of 3.4 m to derive SSH (again, we note the antenna height is approximate and we are not seeking absolute validation here). Topocentric east and north coordinate components (relative to a nominal median location for each deployment) were computed for later use in computing directional wave spectra.
Outliers in the 2-Hz SSH record were identified as points with a formal error in position of greater than 40 mm, being around double the median formal error for the record of 21 mm. Such increases in formal errors are commonly associated with brief periods of reduced tracking thus potentially biased coordinate estimates. Adopting this arbitrary threshold removed 2.1% of points from the combined SOFS8 and SOF9 record. The cleaned 2-Hz record was checked for further outliers using the first difference of the SSH values, but no further outliers were identified. The completeness of the cleaned SSH record varies over the deployments with, for example, a 7-day period in which no points were removed as outliers, and one anomalous period causing a large data gap of ∼27 h. There were no apparent observation or processing failures due to rough conditions, despite individual wave heights (from peak to trough) of over 20 m being recorded (Fig. 2c). The majority of postfit data edits within GipsyX (that then contribute to the small number of SSH outliers) were likely caused by receiver firmware limitations, which have since been resolved.
Example GNSS processing outputs from SOFS over different time periods during a period of high wave activity: (a) 24 h of 2-Hz SSH (light blue) together with smoothed SSH (dark blue) and SWH (gray), and (b) 48 h of smoothed SSH (dark blue) to illustrate semidiurnal tidal signal. Note that SWH (right axis; gray) in (a) and (b) reaches 12.7 m. (c) Four minutes of 2-Hz SSH (light blue) during a time with an individual wave exceeding 20 m (from crest to trough). Formal errors in position are also shown (right axis; red), including two epochs (after 1913:00 UTC) with errors greater than 50 mm, where the positions have been removed as outliers.
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
Following outlier detection, the 2-Hz SSH values were smoothed with a 25-min moving average smoother to remove high-frequency signals, following Zhou et al. (2020), and output at a 120-s rate. Sensitivity of the smoother window length on the altimetry comparison results was tested, with lengths of 12, 25, 50, and 100 min being assessed (see Table S7 in the online supplemental material). An example period of 2-Hz SSH results is shown in Fig. 2.
b. Derived wave parameters
The GNSS wave parameters derived in this study were SWH, directional spectra, dominant direction, and dominant wavelength. Sensitivity tests were conducted to determine the optimal GNSS time window used to calculate the wave parameters, with lengths of 30, 60, and 120 min being tested. Summary results for all three window sizes are shown in the online supplemental material (Table S6 in the online supplemental material). Hereon we use the longer window length of 120 min as this showed the greatest agreement with satellite products across the majority of wave parameters.
1) Significant wave height
The GNSS SWH was calculated as 4 times the standard deviation of clean 2-Hz SSH estimates over a rolling 120 min window. Windows containing less than 50% (i.e., 60 min) of 2-Hz data were skipped (<1% of the clean SSH record). The record was checked for outliers by visually assessing the first differences of SWH, resulting in 120 min of data from SOFS9 being removed.
2) Directional spectra
Directional spectra were computed for 120 min bins of 2-Hz displacement data in east, north, and up directions, centered on the CFOSAT overflight times. Bins were checked for completeness, with all having greater than 92% of available data. Gaps were filled via linear interpolation (with the largest gap in the data used being 32 samples). A linear model was removed from each coordinate component before padding gaps with zeros. The DIWASP MATLAB toolbox (V1.4; Johnson 2012) was used to calculate the directional spectra from the three displacement components (i.e., time series in north, east, and up), using the direct Fourier transfer estimation method (Barber 1961). Directional spectra were generated with a directional resolution of 3°, and a frequency resolution of 0.002 Hz between 0.053 and 0.161 Hz to cover the frequency range of interest for SWIM comparisons. Using 3D displacements allows the 180° ambiguity in wave direction to be resolved, noting we reintroduce this ambiguity for comparisons between the GNSS and SWIM spectra (see Fig. 3).
An example directional spectrum calculated from 120 min of GNSS data: (a) the frequency spectrum, (b) the spectrum after the dispersion relation has been applied to convert period to wavelength and the spectrum has been resampled to match the SWIM spectral resolution, and (c) the spectrum after introducing the 180° ambiguity for consistency with the SWIM products.
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
The power spectral density estimates for each coordinate component showed significant energy around ∼0.4 Hz in the horizontal components. While this is outside the range of interest for SWIM, the impact of filtering the signal was investigated and a small number of directional spectra estimates were found to be sensitive to this high-frequency variability. A simple moving average was therefore used to smooth all of the 2-Hz data in east, north, and up coordinate components to attenuate the high-frequency signal. A nine-point moving average filter was used noting this attenuates waves shorter than half of the shortest wavelength (70 m) observable by SWIM. For subsequent analysis of wave spectra, we make no additional consideration of the dynamics of surface platform and mooring cable tension effects—we return to this point in the discussion.
For comparisons with the SWIM products, the GNSS directional spectra were converted from frequency to wavelength using the deep-water dispersion relation {wavelength = [9.81/(2π)] × period2; Talley et al. 2011} and then resampled to the SWIM spectral resolution of 15° in direction, and between 8 and 50 m resolution in wavelength. As the SWIM spectra has a 180° ambiguity (Tison and Hauser 2018), the GNSS spectra were folded at 180° for consistency by adding the values in each bin from 0° to 180° to the corresponding bins from 180° to 360° (Fig. 3). Wavelength values outside the SWIM specification range of 70–500 m were excluded.
3) Dominant wavelength and direction
The dominant wave direction and wavelength were determined from the GNSS directional spectra after resampling to the SWIM resolution. To do this, we used the weighted mean of all data from the region surrounding the spectral peak extending down to ⅔ of the maximum energy value. This method was chosen to be consistent with the calculation of dominant direction and wavelength from the SWIM spectra (Tison and Hauser 2018). As the spectra was mirrored and therefore contained two peaks, the dominant direction between 0° and 180° was used.
c. Derived sea level anomaly
Sea level anomalies were derived from the smoothed SSH data by removing a tidal signal and mean sea surface (MSS) height correction from the smoothed locations, applying an inverse barometer (IB) correction, and finally applying a tilt correction (Fig. 4). For the results presented here we assume the buoyancy position is not changing with time (i.e., the height of the antenna above the water is not being affected by mooring platform hydrodynamic effects). As the changing buoyancy position has not been considered, and the accuracy of the tilt bias correction has not been assessed, we expect errors in the GNSS SLA estimates to be correlated with sea state to some extent. These SLA estimates are therefore presented as an initial investigation into the feasibility of extracting such information from the SOFS GNSS.
The processing steps to derive sea level anomaly from the smoothed GNSS sea surface height results: (a) the tidal signal (range of ∼1 m), (b) the effect of atmospheric pressure (range of ∼0.6 m), (c) the tilt correction (range of ∼4 cm) (and wind speed to show the clear relationship), and (d) the resultant sea level anomaly. Note the different axis scales for (a)–(d).
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
The ocean tide and MSS at each epoch in the smoothed SSH record was calculated at the smoothed position using the FES2014b and CLS15 models, respectively (Lyard et al. 2021; Pujol et al. 2018). Atmospheric pressure was derived from the two barometric sensors on SOFS to calculate an IB correction. Data from both sensors were cleaned based on quality flags and then linearly interpolated to the smoothed GNSS time series. The IB correction was calculated from each sensor as IB (mm) = −9.948 × p′ (Wunsch and Stammer 1997; Wang et al. 2022) with p′ being the observed atmospheric pressure anomaly from a reference of 1013 hPa. The IB correction from the sensor with the most complete data record prior to interpolation was applied, and intercomparisons between the two sensors were used to confirm the sensor stability and check for anomalous values. Comparisons between sensors showed only small differences, with mean and standard deviation of corrections of −10 and 4 mm, respectively, for SOFS8 and −0.2 and 2 mm, respectively, for SOFS9. We note the local IB correction applied to the SOFS SLA estimates differs from the IB correction applied to the altimetry measurements. As any difference in the IB corrections will contribute to the SLA comparison differences, comparisons with no IB corrections to either in situ or along-track altimetry SLA estimates were computed alongside the SLA comparisons to indicate the magnitude of this contribution.
To account for the bias in SSH caused by the tilt in the large surface platform, the MRU quaternion data were used and applied to the nominal 3.4-m GNSS antenna height above water level. Given the MRU logging strategy of 5-Hz data for 10 min every 1 h, computation of a continuous tilt bias reflecting high-frequency motion of the platform was not possible. Instead, the mean tilt bias was computed for each available 10-min period yielding an hourly tilt bias time series that was subsequently applied following linear interpolation. The resultant correction was highly autocorrelated, and strongly correlated with the square of wind speed (see Fig. 4c, along with section 5 in the online supplemental material). This low-frequency correction accounts for the reduction in antenna height above water due to the changing average deflection of the antenna from the vertical. Note for SOFS9 the MRU data do not extend to the final 36 days of GNSS data. The median tilt bias calculated from the remainder of the SOFS9 record was used for these 36 days. Antenna height changes due to higher-frequency motion of the mooring platform are assumed to have no impact on the SLA, SWH, or directional spectra estimates.
d. Satellite product comparisons
Using the sea level and wave products derived from the SOFS GNSS data, comparisons were made to both along-track altimetry missions, and the SWIM products from CFOSAT. While the primary focus here is on the SWH and SWIM wave parameter comparisons in a high wave environment, the initial SLA estimates have also been investigated. In addition, gridded altimetry products providing daily estimates of SLA and SWH have been used.
1) SWH comparisons
The GNSS SWH values were compared with the along-track altimetry SWH estimates, with SOFS8 compared with Jason-3, Sentinel-3A, and CFOSAT (nadir altimeter), and SOFS9 compared with Sentinel-3B and CFOSAT (nadir altimeter). As the altimetry SWH values are relatively noisy (e.g., see Dodet et al. 2020), altimetry estimates of SWH were averaged over multiple 1-Hz points along track to improve precision. We found the along-track SWH noise dominated the signal at around 21 km for 1-Hz altimetry estimates (with nominal ∼7-km spacing). A three-point moving average was therefore used to smooth the altimetry SWH values (see full analysis in section 6 of the online supplemental material). These SWH estimates were then compared with the GNSS derived SWH calculated from the 120 min of 2-Hz data centered on the time of overflight (Fig. 6). The GNSS derived SWH was compared with the MRU SWH estimate for every hour.
For comparisons with the CMEMS gridded SWH product, the daily instantaneous SWH was interpolated in space to the relevant SOFS location at midday each day, and then compared with the GNSS SWH estimate at this time. In addition, the SOFS MRU SWH estimates were assessed against the gridded product for comparison at the same time step.
2) SWIM wave parameter comparisons
Comparisons of GNSS derived wave parameters were made to SWIM wave box products with extents covering the SOFS mooring location. Observations from the Triaxys sensor on the SOFS9 deployment were compared with the wave box products for the 15 overflights during the GNSS recording period for this deployment. The Triaxys comparisons were then used to provide an in situ reference to help assess the GNSS results. Due to issues with the directional observations from the Triaxys sensor for SOFS9, only the wavelength comparisons have been considered (see full Triaxys comparison results in section 7 of the online supplemental material).
The agreement between SOFS and SWIM directional spectra were assessed using the two-dimensional pattern correlation index, following Hauser et al. (2021), and using the method described in Hasselmann et al. (1996). An example of the SOFS and SWIM directional spectra is shown in Fig. 5. Comparisons of dominant directions and dominant wavelength were also assessed (Fig. 7). Note we have not attempted to validate the various wave partitions in the SWIM product.
Example directional spectra from (a) SOFS GNSS and (b) SWIM wave box product on 24 Jun 2019. Spectra were compared using the two-dimensional pattern correlation index (Hasselmann et al. 1996).
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
3) SLA comparisons
The GNSS SLA time series was compared with the along-track SLA values for each of the relevant missions, and to the gridded altimetry SLA products from IMOS and CMEMS. We have not attempted to calculate absolute bias values in this work, so all SLA comparisons have had the median offset removed, effectively removing any residual antenna height offset and any bias in the altimetry from the results. For the altimetry along-track comparison, the SLA value at the point of closest measurement (PCM) for each pass was used. This was compared with the GNSS SLA value nearest in time to the altimetry overpass. If there were no GNSS values within 20 min of the altimetry, no comparison was made. For the gridded product comparisons, the gridded values were interpolated in space to derive the altimetry SLA estimates at the SOFS locations. These interpolated values were compared with daily GNSS SLA estimates, calculated using a 24-h moving average of the 120 s rate GNSS SLA data described above.
5. Results
a. Altimetry SWH comparisons
There is good agreement between the GNSS derived SWH and each of the nadir altimetry missions. The combined root-mean-square error (RMSE) for all SWH comparison points is 0.16 m, with a mean bias of 0.04 m (n = 60) and a standard error about the mean of 0.02 m (±0.04 m at the 95% confidence level). The RMSE and mean bias for each individual mission is shown in Fig. 6.
Significant wave height comparisons between along-track altimetry and GNSS derived values for SOFS8 and SOFS9 deployments, with the root-mean-square error (m), mean bias (m), number of samples, and standard error (m) shown for each: (a) comparisons with Jason-3, Sentinel-3A, and Sentinel-3B mission, and (b) CFOSAT L2 nadir product SWH comparisons, with the points in red showing the SWH after calibration relative to wave buoys, and the points in gray showing values with the bias correction removed.
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
Unlike the Jason-3 and Sentinel-3 data, the CFOSAT L2 SWH data have already been calibrated relative to wave buoys following Sepulveda et al. (2015). Comparisons against GNSS SWH were made with and without the calibration bias applied. Without calibration, RMSE and mean bias were 0.29 and 0.20 m, respectively. With the supplied calibration, these reduce to 0.16 and 0.02 m, respectively (n = 28).
The comparisons between the MRU and GNSS estimates of SWH show larger differences. The hourly MRU minus GNSS SWH residuals for the combined deployments have an RMSE of 0.30 m, and a mean bias of 0.12 m (n = 4496). We note that comparisons with the gridded altimetry SWH product also show a positive bias 0.24 m when compared with the MRU data, while the GNSS is in closer agreement to the gridded product with a mean bias of 0.05 m.
b. SWIM wave parameter comparisons
The wavelength comparisons between the Triaxys on SOFS9 and the SWIM products were assessed prior to the GNSS comparisons. The SWIM minus Triaxys wavelength residuals have an RMSE of 32.4 m and a mean bias of 9.8 m for the 15 comparisons (Fig. 7d). The SWIM minus GNSS wavelength comparisons over the same period show similar agreement, with an RMSE of 28.6 m and a mean bias of −16.4 m, suggesting the GNSS system is performing well.
Comparison results between the SWIM wave box products and the SOFS mooring measurements: (a) the correlation index (Hasselmann et al. 1996) between the directional spectra from SWIM and from SOFS GNSS, the (b) dominant direction and (c) dominant wavelength comparisons between SWIM and SOFS GNSS, including one outlier shown in gray, and (d) dominant wavelength comparisons between SWIM and the Triaxys instrument from the SOFS9. Note that (a)–(c) cover both deployments whereas (d) only shows comparisons from SOFS9 because there was no Triaxys instrument on SOFS8.
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
As the GNSS was recording for both SOFS8 and SOFS9 deployments, comparisons with the SWIM wave box products over the whole recording period were assessed, providing 23 individual comparisons. Excluding one outlier, there is good agreement between the GNSS and SWIM dominant directions (SWIM minus GNSS RMSE = 9.1°, mean bias = −2.4°), with 20 out of 23 points falling inside the SWIM specifications that state an accuracy of 15° (Hauser et al. 2021). The directional spectra also show good agreement, with all comparisons having a correlation greater than 0.57, and the median correlation for all comparisons being 0.67 (Fig. 7).
c. Altimetry SLA comparisons
The sea level anomaly calculated from the GNSS record at SOFS shows reasonable agreement with the altimetry (Fig. 8). The along-track altimetry SLA minus GNSS SLA residuals have RMSE values of 49, 39, and 40 mm for Jason-3, Sentinel-3A, and Sentinel-3B, respectively, from 11 comparisons with Jason-3 and Sentinel-3B, and 6 comparisons with Sentinel-3A. If the IB corrections are removed from both in situ and altimetry estimates, the RMSE values change only marginally to 48, 33, and 42 mm for the three missions. Sensitivity tests on the smoothing window length also show only small differences, with RMSE values changing by up to ±8 mm for window lengths from 12 to 100 min (see Table S7 in the online supplemental material). The comparisons with the gridded SLA products have slightly smaller RMSE values than the along-track comparisons, with the daily residuals from the IMOS grid having an RMSE of 32 mm, and from CMEMS having an RMSE of 37 mm (from 205 daily comparisons in each case).
Sea level anomaly comparisons with altimetry data and products for (left) SOFS8 and (right) SOFS9. Along-track altimetry SLA estimates (colored points) are shown at the point of closest measurement. Note that the offset between the altimetry products and the GNSS record has been subtracted to remove any absolute bias. The bottom plots show SWH for comparative purposes.
Citation: Journal of Atmospheric and Oceanic Technology 40, 10; 10.1175/JTECH-D-23-0031.1
6. Discussion
a. SWH
The GNSS SWH estimates showed little sensitivity to the GNSS processing approach and showed good agreement with the four along-track altimetry missions considered (Fig. 6). The combined RMSE and bias in SWH of 0.16 and 0.04 m, respectively, are each of a similar magnitude to the values reported in global validation studies using offshore buoys. In the SWH validation work for the Sea State CCI dataset, Dodet et al. (2020) reported RMSE and bias values of 0.23 and 0.04 m (noting that they use a different set of altimeters from this study). Quartly and Kurekin (2020) investigated the sensitivity to buoy data selection and reported RMSE values of generally less than 0.2 m for Jason-3, and around 0.21 m for Sentinal-3A for the “best open ocean” set of buoys. The SOFS GNSS therefore appears to be performing at least as well as the existing wave monitoring systems for measuring SWH.
Larger sample sizes are needed to assess individual mission biases at this site robustly, with Jason-3, Sentinal-3A, and CFOSAT (corrected) biases not being statistically different to zero at the 95% confidence level. The positive biases for Sentinel-3A and Sentinel-3B are consistent with other validation studies using larger significant wave heights (e.g., Yang and Zhang 2019). The Sentinel-3 products used here are synthetic aperture radar (SAR) mode altimetry products, which have challenges associated with wave parameterization at long wavelengths. Under these conditions, higher uncertainties and biases can be expected (Moreau et al. 2018). This differs from the traditional pulse limited low-resolution mode (LRM) products from both CFOSAT and Jason-3.
It is interesting to note that Dodet et al. (2020) found a larger RMSE and negative bias of 0.47 and −0.17 m, respectively, for comparisons between altimetry and modeled values in the Southern Ocean. While the sample size from SOFS is small (n = 60) and captures none of the spatial variability in SWH, our in situ results show excellent altimetry SWH performance in the Southern Ocean for the altimetry products considered here. This supports the suggestion that the high RMSE and negative bias from Dodet et al. (2020) is a reflection on poorer quality modeled values for this region, rather than altimetry errors Given the challenges associated with modeling wind-wave growth in the Southern Ocean, this is unsurprising. We note that assimilating directional wave observations from CFOSAT has been shown to significantly reduce this SWH bias in models (Aouf et al. 2021).
Sensitivity tests showed that agreement to all altimetry missions worsened when using a shorter GNSS time window (60 or 30 min as compared with 120 min), with the combined RMSE increasing from 0.16 to 0.22 m, and the combined mean bias increasing from 0.04 to 0.07 m (see Table S6 in the online supplemental material). Further work to determine the optimal averaging approach (in time for the GNSS, and in distance for the along-track altimetry) may further improve the consistency between the in situ and altimetry estimates.
Given the sampling of available data and the use of an objective mapping process, the gridded products offer a greater number of comparisons than individual along-track missions. For SWH, the objective mapping process used to generate the daily instantaneous estimates takes data from up to 36 h around 1200 UTC each day and uses a weighted mean of all data within the 2° grid cell (Charles 2021). Our comparisons with the gridded SWH product were only used to investigate the mean bias in SWH, which we did not expect to be greatly impacted by the interpolation induced errors in the gridded product. The mean bias of 0.05 m is in keeping with the small biases seen in the along-track assessments from each mission and supports the finding that the GNSS at SOFS is performing well for SWH validation purposes.
Comparisons between the MRU and GNSS SWH estimates show a larger than expected bias of 0.12 m. Findings from a previous accuracy assessment of the SOFS MRU document a bias of 0.06 m for Triaxys–MRU comparisons on SOFS2 and SOFS4 (Rapizo et al. 2015). Results from a similar MRU on the “Pulse” mooring show a bias of 0.05 m for MesoWAM model − MRU estimates (Schulz et al. 2011). As we find a large bias between the MRU and altimetry gridded product of 0.24 m, we suggest the larger than expected difference between the MRU and GNSS is likely due to larger errors in the MRU, rather than indicating poor GNSS estimates. We have not investigated why the MRU SWH estimates appear to not be performing as well as on previous SOFS deployments.
b. SWIM wave parameters
The open-ocean environment of the SOFS mooring allows us to provide an in situ point validation of the SWIM products from CFOSAT. The GNSS is capturing the wave frequency spectra well, as evidenced by the consistency between the Triaxys and GNSS dominant wavelength comparisons with SWIM estimates (RMSE values of 29 and 32 m, respectively). The GNSS results are also consistent with the wavelength validation results presented by Hauser et al. (2021), who showed RMSE values generally between 30 and 40 m when comparing the 10° beam to modeled wave parameters.
For wavelengths below 400 m, the GNSS comparisons show less variability than the Triaxys comparisons. For longer wavelengths there are no Triaxys comparisons, and there is an apparent negative bias in the SWIM estimates relative to the GNSS (Fig. 7). As only four long wavelength comparison points have been observed, more data would be needed to investigate this. There is no known reason to expect the GNSS to be biased at longer periods, or for SWIM to be biased at long wavelengths. One possible explanation is that the dispersion relation used here does not account for factors such as currents, and the impact of spectral shape on the relationship between periods and wavelengths, both of which are expected to bias the wavelengths derived from observations of wave period (Andreas 2009; Plant 2009). We do, however, note that a bias of the opposite sign is expected from these effects (i.e., GNSS derived wavelengths are expected to be shorter than physical wavelengths). Other discrepancies in the comparisons are likely to arise from fundamental differences in observation type and processing between 2D slope spectra from SWIM and the 3D displacement spectra from GNSS.
Despite not having the Triaxys directional information for comparison, the excellent agreement between the dominant direction and the directional spectra indicates both the GNSS and SWIM are performing well in this environment. For dominant directions, the RMSE of 9.1° is lower than presented in other validation results, with Hauser et al. (2021) reporting an RMSE of 19.2° (for the 10° beam) from a global comparison with modeled spectra. In other in situ comparisons, Jiang et al. (2022) reported an RMSE of 21.3° (for the L2PBOX product) from 391 comparisons with wave buoys, and Liang et al. (2021) reported an RMSE of 41.8° (for the 10° beam) from 1152 comparisons with buoy data. It is important to note our small sample size (n = 22) in comparisons presented here. The one outlier in the comparison results (Fig. 7) appears to be caused by an anomalous value in the SWIM wave box product. We note the correlation index between the GNSS and SWIM directional spectra for this comparison is still reasonably high (0.68), indicating the recorded wave state from both the in situ and satellite are still well matched. This anomalous value is not seen in the 6°, 8°, 10°, or “combined” beam products from the SWIM L2 data. If the L2 product is used rather than the wave box product for this comparison point, differences in wavelength (to the GNSS estimate) reduce from 223 to 70 m, and differences in direction reduce from 74° to 2.1°, in keeping with the rest of the comparison points.
A small number of the GNSS directional spectra estimates were found to be sensitive to high-frequency variability, particularly in the vertical. The dominant direction and wavelength estimates for four candidate overflight times changed significantly if the high-frequency component (>0.22 Hz) was smoothed in the coordinate time series. Spectra from smoothed data were in much closer agreement with the SWIM estimates, with the smoothing of the height component having the greatest effect. Comparison metrics were further improved if the GNSS directional spectra were calculated using the power spectral density of the horizontal coordinates only, with median correlation index increasing to 0.77, dominant direction RMSE and bias reducing to 6.8° and −0.7°, respectively, and dominant wavelength RMSE and bias reducing to 32.7 and −20 m, respectively. This suggests some sensitivity within the direct Fourier transfer estimation approach used (Barber 1961). Scope exists to refine this approach to take into account platform motion and potentially GNSS-specific noise characteristics.
There are several reasons to expect good performance of the SWIM instrument specifically at the SOFS location. The SOFS mooring has the advantage of being far from any coastlines, which can have an impact on the satellite observations and create more complex wave dynamics (e.g., Oruba et al. 2022; Li et al. 2022). The assumption that the wave conditions are homogenous throughout the 90 km × 70 km wave box is more likely to be valid at the SOFS location than at other in situ sites due to the relatively consistent forcings, deep water and lack of nearby land. The typically unimodal, swell dominated conditions (Rapizo et al. 2015) are well suited to the SWIM measurements (Hauser et al. 2021) and also reduce the potential for comparison errors due to the mismatching of wave partitions. SOFS is therefore highly desirable as an in situ validation site to assess SWIM performance in favorable conditions.
c. SLA
Comparisons with three altimetry missions indicate that GNSS mounted on SOFS can be used to produce high quality SLA estimates in a high wave environment, with RMSE values of between 40 and 50 mm (Fig. 8). While our SLA comparisons yield larger metrics of variability that those reported from the three primary in situ validation sites (standard deviation values between 16 and 32 mm; Bonnefond et al. 2022), we note these sites experience much calmer sea states. Considering the inherently challenging conditions of the open-ocean, high wave environment at SOFS, and noting that increasing SWH contributes to higher SLA errors in altimetry estimates, the results from SOFS are better than first expected. This is particularly encouraging given the buoyancy position and high-frequency tilt bias of the mooring has not yet been considered.
As with SWH, comparisons with the gridded SLA product will contain interpolation (objective mapping) artifacts. For example, the CMEMS SLA gridded product interpolation spans a large spatial and temporal window of approximately 300 km and 60 days at the SOFS latitude (Pujol et al. 2016), and relating this temporal and spatial interpolation to an equivalent sampling of our GNSS SLA time series is not simple. Given this challenge, the RMSE values of between 30 and 40 mm for the IMOS and CMEMS products, respectively, demonstrate the ability of GNSS at SOFS to successfully observe SLA.
d. Limitations
The GNSS receiver and processing for the SOFS8 and SOFS9 deployments were in part limited by receiver firmware limitations, which have since been patched. For both deployments the receiver was initialized ∼500 km from the study site, and issues were seen in the clock behavior until an in situ power cycle of both receivers. The change in clock behavior during deployments may have affected processing within GipsyX, as seen in the varying percentages of points with high formal errors throughout the deployments. To achieve optimal results, various processing and preprocessing (editing) techniques often need to be tailored to the receiver’s behavior. In addition, we assume the outlier detection based on formal errors provided by GipsyX is effectively removing coordinates that have been biased due to brief periods of lower numbers of GNSS signals being tracked. Assessing the validity of this assumption and its original driver is challenging, and further data-driven approaches to outlier detection could be explored in future.
The SLA estimates are likely affected by sea state to some extent. It is well known that platform dynamics (especially in a tethered configuration) as a function of variable sea conditions can bias GNSS SSH estimates (e.g., Zhou et al. 2020). The large physical size of the SOFS surface platform (∼3.4 m from antenna to sea surface) increases the potential influence of both tilt and buoyancy position bias relative to smaller buoys. Although the dynamic effects of smaller platforms (with respect to the instantaneous sea surface) can be considered negligible as they are of higher frequency than the ocean waves being observed (Raghukumar et al. 2019), this will likely not be the case for as large a platform as SOFS. While the low-frequency tilt bias was estimated using the MRU rotations, the accuracy of the correction is challenging to assess without the significant costs of deploying additional instruments on board the SOFS platform. The low-frequency tilt bias is a small correction with a range of 0.08 m over the deployment period (as compared with an SLA range of 0.58 m), and the striking correlation between tilt correction and wind speed (Fig. 4c) provides some confidence in this correction. However, further investigations are needed to determine how the long period swell and changing sea state impact the platform dynamics.
No attempt was made to estimate buoyancy position changes; however, the correlations shown in the online supplemental material (Fig. S6 in the online supplemental material) suggest that the surface platform is being pushed higher out of the water in rougher conditions (approximately 13 mm per 1 m increase in SWH). This bias will likely be a function of many variables including sea state, distance of the surface platform to its anchor point, current velocity, and variable cable friction (with biofouling) affecting cable drag. The SLA estimates could be improved by determining the buoyancy position of SOFS using the various sensors that the mooring is equipped with. The combination of current measurements, high-frequency inertial measurements, load cell measurements, and GNSS positions to determine the distance to anchor have not yet been exploited to estimate buoyancy changes. Data from these sensors offer an opportunity to derive an empirical model for buoyancy corrections at this mooring. This will allow investigations into the effect of wavelength and wave height on SLA estimates, with the potential to reduce the sea state induced errors in SLA. However, assessing the validity of such a model without the use of altimetry SLA estimates (which will also be affected, to some extent, by sea state) is particularly difficult at SOFS due to the fundamentally challenging nature of the study site. In addition to this, as there are correlations between wind, sea state, air pressure, platform motion, and the sea surface nontidal residual (Bonaduce et al. 2020), obtaining accurate absolute measurements of SSH from a platform such as this across diverse wave conditions remains a significant challenge.
With the limitations of this study in mind, it is also worth highlighting the advantages of geodetic GNSS for altimetry and SWIM validation. For observing waves, the GNSS sensor costs significantly less than directional wave measuring systems such as the Triaxys. GNSS systems are also small and lightweight, both of which allow them to be relatively easy to install on mooring platforms. The ability to change the sampling window length during postprocessing is one of the advantages of the GNSS PPP approach over many commercially available wave buoys with fixed sampling regimes. The other unique advantage of the high rate geodetic GNSS technique used here is that it provides both directional wave measurements and SSH observations. Providing collocated SSH and sea state information in the open ocean could prove particularly valuable for new missions such as SWOT, where complex interactions between sea conditions and SSH estimates are expected (Dubois and Chapron 2018).
7. Conclusions
We instrumented the SOFS mooring in an energetic region of the Southern Ocean with GNSS hardware to assess its application to altimetry and SWIM validation. Limited by available power for these trial deployments, we successfully obtained 188 days of 2-Hz data and processed using a PPP approach. The GNSS data provided robust results in all wave conditions, including extreme events with individual wave heights greater than 20 m, and a median SWH of 3.8 m across all data. The initial comparisons of GNSS-based SWH to altimetry show good agreement (RMSE = 0.16 m), consistent with other in situ studies despite the average SWH at this site being much higher than at most wave buoy locations. Directional spectra comparisons show excellent agreement with the SWIM wave box product, with dominant direction differences having an RMSE of 9.1°, and 20 out of the 23 comparisons being within the 15° accuracy specification for the SWIM instrument. This good performance is also reflected in the directional spectra comparisons that show a median correlation of 0.67.
We demonstrate the ability to observe SLA, with a standard deviation of 0.03 m when compared with a daily gridded sea level anomaly product (n = 205). This will be of particular interest during the fast sampling phase of the Surface Water and Ocean Topography (SWOT) mission, as collocated sea surface height and wave observations in a high wave energy environment may prove important in decomposing the effect of various errors. For all missions, the SOFS location represents an important validation location in this under sampled region and wave environment.
Acknowledgments.
This study was supported by Australia’s Integrated Marine Observing System (IMOS) Satellite Altimetry Calibration and Validation Sub-Facility—IMOS is enabled by the National Collaborative Research Infrastructure Strategy (NCRIS). It is operated by a consortium of institutions as an incorporated joint venture, with the University of Tasmania as lead agent. The Southern Ocean Time Series (SOTS), supported by IMOS and Australian Antarctic Program Partnership (AAPP), has been instrumental in making this study happen as a result of the addition of the GNSS system to the SOFS surface platform. The SOTS Team, Elizabeth Shadwick, and Eric Schulz and the technical staff were very supportive in making this happen and providing mooring data (https://imos.org.au/facilities/deepwatermoorings/sots). Thanks are given to Peter Jansen for his assistance and making some engineering data available. The wave analysis and CFOSAT comparison contribute to the CFOSAT validation team “Australian Applications for CFOSAT: Wind and Wave Climate of the Southern Ocean” project. Author Benoit Legresy’s contribution is also supported by the Australian National Environment Science Program (NESP) Climate Science Hub Project CS-2.10 and the AAPP Oceanography project. We thank NASA Jet Propulsion Laboratory for the GipsyX software, products, and support. This research was supported by the Australian Research Council Special Research Initiative, Australian Centre for Excellence in Antarctic Science (Project Number SR200100008). Author Andrea Hay is supported by a Research Training Program scholarship from the Australian government and a Postgraduate Studentship from CSIRO. We also thank two anonymous reviewers whose comments helped to improve this paper.
Data availability statement.
The CNES GNSS clock and orbit products are openly available through the online archives of the Crustal Dynamics Data Information System (CDDIS) of the NASA Goddard Space Flight Center (https://cddis.nasa.gov/archive/gps/products/). The CFOSAT wave box products were provided by AVISO (ftp://ftp-access.aviso.altimetry.fr). The altimetry data are openly available and were sourced through the Radar Altimetry Database System (Scharroo 2022) and from the Copernicus Marine Environmental Monitoring Service (https://marine.copernicus.eu/access-data/). The SOFS data are openly available through the Australian Ocean Data Network (https://portal.aodn.org.au/).
REFERENCES
Ablain, M., S. Philipps, N. Picot, and E. Bronner, 2010: Jason-2 global statistical assessment and cross-calibration with Jason-1. Mar. Geod., 33, 162–185, https://doi.org/10.1080/01490419.2010.487805.
Altamimi, Z., P. Rebischung, L. Métivier, and X. Collilieux, 2016: ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth, 121, 6109–6131, https://doi.org/10.1002/2016JB013098.
Andreas, E. L., 2009: Relating the drag coefficient and the roughness length over the sea to the wavelength of the peak waves. J. Phys. Oceanogr., 39, 3011–3020, https://doi.org/10.1175/2009JPO4189.1.
Aouf, L., D. Hauser, B. Chapron, A. Toffoli, C. Tourain, and C. Peureux, 2021: New directional wave satellite observations: Towards improved wave forecasts and climate description in Southern Ocean. Geophys. Res. Lett., 48, e2020GL091187, https://doi.org/10.1029/2020GL091187.
Babanin, A. V., and Coauthors, 2019: Waves and swells in high wind and extreme fetches, measurements in the Southern Ocean. Front. Mar. Sci., 6, 361, https://doi.org/10.3389/fmars.2019.00361.
Barber, N. F., 1961: The directional resolving power of an array of wave detectors. Ocean Wave Spectra, Prentice Hall, 137–150.
Beckman, J. N., and J. W. Long, 2022: Quantifying errors in wind and wave measurements from a compact, low-cost wave buoy. Front. Mar. Sci., 9, 966855, https://doi.org/10.3389/fmars.2022.966855.
Bender, L. C., N. L. Guinasso, J. N. Walpert, and S. D. Howden, 2010: A comparison of methods for determining significant wave heights—Applied to a 3-m discus buoy during Hurricane Katrina. J. Atmos. Oceanic Technol., 27, 1012–1028, https://doi.org/10.1175/2010JTECHO724.1.
Bertiger, W., and Coauthors, 2020: GipsyX/RTGx, a new tool set for space geodetic operations and research. Adv. Space Res., 66, 469–489, https://doi.org/10.1016/j.asr.2020.04.015.
Bharti, V., E. Schulz, C. W. Fairall, B. W. Blomquist, Y. Huang, A. Protat, S. T. Siems, and M. J. Manton, 2019: Assessing surface heat flux products with in situ observations over the Australian sector of the Southern Ocean. J. Atmos. Oceanic Technol., 36, 1849–1861, https://doi.org/10.1175/JTECH-D-19-0009.1.
Boehm, J., B. Werl, and H. Schuh, 2006: Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data. J. Geophys. Res., 111, B02406, https://doi.org/10.1029/2005JB003629.
Bonaduce, A., J. Staneva, S. Grayek, J.-R. Bidlot, and Ø. Breivik, 2020: Sea-state contributions to sea-level variability in the European seas. Ocean Dyn., 70, 1547–1569, https://doi.org/10.1007/s10236-020-01404-1.
Bonnefond, P., B. J. Haines, and C. Watson, 2011: In situ absolute calibration and validation: A link from coastal to open-ocean altimetry. Coastal Altimetry, S. Vignudelli et al., Eds., Springer, 259–296.
Bonnefond, P., P. Exertier, O. Laurain, T. Guinle, and P. Féménias, 2019: Corsica: A 20-yr multi-mission absolute altimeter calibration site. Adv. Space Res., 68, 1171–1186, https://doi.org/10.1016/j.asr.2019.09.049.
Bonnefond, P., B. Haines, B. Legresy, and C. Watson, 2022: Absolute calibration results from Bass Strait, Corsica, and Harvest facilities. OSTST Meeting, Venice, Italy, EUMETSAT and CNES, https://doi.org/10.24400/527896/A03-2022.3623.
Born, G. H., M. A. Richards, and G. W. Rosborough, 1982: An empirical determination of the effects of sea state bias on Seasat altimetry. J. Geophys. Res., 87, 3221–3226, https://doi.org/10.1029/JC087iC05p03221.
Born, G. H., M. E. Parke, P. Axelrad, K. L. Gold, J. Johnson, K. W. Key, D. G. Kubitschek, and E. J. Christensen, 1994: Calibration of the TOPEX altimeter using a GPS buoy. J. Geophys. Res., 99, 24517, https://doi.org/10.1029/94JC00920.
Bos, M. S., and H.-G. Scherneck, 2013: Computation of Green’s functions for ocean tide loading. Sciences of Geodesy—II, G. Xu, Ed., Springer, 1–52.
Charles, E., 2021: QUID for WAVE TAC product, WAVE_GLO_PHY_SWH_L4_MY_014_007. Copernicus Marine Environmental Monitoring Service Doc. CMEMS-WAVE-QUID-014-007, 31 pp., https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-WAV-QUID-014-007.pdf.
Chupin, C., and Coauthors, 2020: Mapping sea surface height using new concepts of kinematic GNSS instruments. Remote Sens., 12, 2656, https://doi.org/10.3390/rs12162656.
de Vries, J. J., J. Waldron, and V. Cunningham, 2003: Field tests of the new Datawell DWR-G GPS wave buoy. Sea Technol., 44, 50–55.
Dobson, E., F. Monaldo, J. Goldhirsh, and J. Wilkerson, 1987: Validation of Geosat altimeter-derived wind speeds and significant wave heights using buoy data. J. Geophys. Res., 92, 10 719–10 731, https://doi.org/10.1029/JC092iC10p10719.
Dodet, G., and Coauthors, 2020: The Sea State CCI dataset v1: Towards a sea state climate data record based on satellite observations. Earth Syst. Sci. Data, 12, 1929–1951, https://doi.org/10.5194/essd-12-1929-2020.
Dubois, P., and B. Chapron, 2018: Characterization of the ocean waves signature to assess the sea state bias in wide-swath interferometric altimetry. 2018 IEEE Int. Geoscience and Remote Sensing Symp., Valencia, Spain, IEEE, 3789–3792, https://doi.org/10.1109/IGARSS40696.2018.
Fu, L. L., and P.-Y. Le Traon, 2006: Satellite altimetry and ocean dynamics. C. R. Geosci., 338, 1063–1076, https://doi.org/10.1016/j.crte.2006.05.015.
Fu, Y., J. T. Freymueller, and T. van Dam, 2012: The effect of using inconsistent ocean tidal loading models on GPS coordinate solutions. J. Geod., 86, 409–421, https://doi.org/10.1007/s00190-011-0528-1.
Gaspar, P., F. Ogor, P.-Y. Le Traon, and O.-Z. Zanife, 1994: Estimating the sea state bias of the TOPEX and Poseidon altimeters from crossover differences. J. Geophys. Res., 99, 24 981–24 994, https://doi.org/10.1029/94JC01430.
Grigorieva, V. G., S. I. Badulin, and S. K. Gulev, 2022: Global validation of SWIM/CFOSAT wind waves against voluntary observing ship data. Earth Space Sci., 9, e2021EA002008, https://doi.org/10.1029/2021EA002008.
Guillot, S., A. Ollivier, and V. Quet, 2022: Level-2+ off-nadir products (L2PBOX) from SWIM instrument of CFOSAT. CNES Doc. SALP-MU-P1-OP-23553-CLS, 26 pp., https://www.aviso.altimetry.fr/fileadmin/documents/data/tools/CFOSAT_L2PBOX_handbook_SALP.pdf.
Hasselmann, S., C. Brüning, K. Hasselmann, and P. Heimbach, 1996: An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra. J. Geophys. Res., 101, 16 615–16 629, https://doi.org/10.1029/96JC00798.
Hauser, D., C. Tison, T. Amiot, L. Delaye, N. Corcoral, and P. Castillan, 2017: SWIM: The first spaceborne wave scatterometer. IEEE Trans. Geosci. Remote Sens., 55, 3000–3014, https://doi.org/10.1109/TGRS.2017.2658672.
Hauser, D., and Coauthors, 2021: New observations from the SWIM radar on-board CFOSAT: Instrument validation and ocean wave measurement assessment. IEEE Trans. Geosci. Remote Sens., 59, 5–26, https://doi.org/10.1109/TGRS.2020.2994372.
Hermozo, L., and Coauthors, 2022: CFOSAT: Latest improvements in the swim products and contributions in oceanography. 2022 IEEE Int. Geoscience and Remote Sensing Symp., Kuala Lumpur, Malaysia, IEEE, 6768–6771, https://doi.org/10.1109/IGARSS46834.2022.9883958.
Jiang, H., A. Mironov, L. Ren, A. V. Babanin, J. Wang, and L. Mu, 2022: Validation of wave spectral partitions from SWIM instrument on-board CFOSAT against in situ data. IEEE Trans. Geosci. Remote Sens., 60, 4204013, https://doi.org/10.1109/TGRS.2021.3110952.
Johnson, D., 2012: DIWASP, Directional Wave Spectra Toolbox for MATLAB: User Manual, version 1.4. MetOcean Solutions Doc., 23 pp.
Legresy, B., C. Watson, J. Beardsley, B. Zhou, and M. King, 2022: Altimeter validation results from the Bass Strait validation facility, Australia. OSTST Meeting, Venice, Italy, EUMETSAT and CNES, https://doi.org/10.24400/527896/A03-2022.3358.
Li, B., J. Li, J. Liu, S. Tang, W. Chen, P. Shi, and Y. Liu, 2022: Calibration experiments of CFOSAT wavelength in the southern South China Sea by artificial neural networks. Remote Sens., 14, 773, https://doi.org/10.3390/rs14030773.
Liang, G., J. Yang, and J. Wang, 2021: Accuracy evaluation of CFOSAT SWIM L2 products based on NDBC buoy and Jason-3 altimeter data. Remote Sens., 13, 887, https://doi.org/10.3390/rs13050887.
Loyer, S., F. Perosanz, F. Mercier, H. Capdeville, and J.-C. Marty, 2012: Zero-difference GPS ambiguity resolution at CNES–CLS IGS Analysis Center. J. Geod., 86, 991–1003, https://doi.org/10.1007/s00190-012-0559-2.
Lyard, F. H., D. J. Allain, M. Cancet, L. Carrère, and N. Picot, 2021: FES2014 global ocean tide atlas: Design and performance. Ocean Sci., 17, 615–649, https://doi.org/10.5194/os-17-615-2021.
Meredith, M. P., 2016: Understanding the structure of changes in the Southern Ocean eddy field. Geophys. Res. Lett., 43, 5829–5832, https://doi.org/10.1002/2016GL069677.
Moreau, T., N. Tran, J. Aublanc, C. Tison, S. Le Gac, and F. Boy, 2018: Impact of long ocean waves on wave height retrieval from SAR altimetry data. Adv. Space Res., 62, 1434–1444, https://doi.org/10.1016/j.asr.2018.06.004.
Orsi, A. H., T. Whitworth, and W. D. Nowlin, 1995: On the meridional extent and fronts of the Antarctic Circumpolar Current. Deep-Sea Res. I, 42, 641–673, https://doi.org/10.1016/0967-0637(95)00021-W.
Oruba, L., D. Hauser, S. Planes, and E. Dormy, 2022: Ocean waves in the South Pacific: Complementarity of SWIM and SAR observations. Earth Space Sci., 9, e2021EA002187, https://doi.org/10.1029/2021EA002187.
Passaro, M., M. A. Hemer, G. D. Quartly, C. Schwatke, D. Dettmering, and F. Seitz, 2021: Global coastal attenuation of wind-waves observed with radar altimetry. Nat. Commun., 12, 3812, https://doi.org/10.1038/s41467-021-23982-4.
Peral, E., E. Rodríguez, and D. Esteban-Fernández, 2015: Impact of surface waves on SWOT’s projected ocean accuracy. Remote Sens., 7, 14 509–14 529, https://doi.org/10.3390/rs71114509.
Plant, W. J., 2009: The ocean wave height variance spectrum: Wavenumber peak versus frequency peak. J. Phys. Oceanogr., 39, 2382–2383, https://doi.org/10.1175/2009JPO4268.1.
Pujol, M.-I., Y. Faugère, G. Taburet, S. Dupuy, C. Pelloquin, M. Ablain, and N. Picot, 2016: DUACS DT2014: The new multi-mission altimeter data set reprocessed over 20 years. Ocean Sci., 12, 1067–1090, https://doi.org/10.5194/os-12-1067-2016.
Pujol, M.-I., P. Schaeffer, Y. Faugère, M. Raynal, G. Dibarboure, and N. Picot, 2018: Gauging the improvement of recent mean sea surface models: A new approach for identifying and quantifying their errors. J. Geophys. Res. Oceans, 123, 5889–5911, https://doi.org/10.1029/2017JC013503.
Quartly, G. D., and A. A. Kurekin, 2020: Sensitivity of altimeter wave height assessment to data selection. Remote Sens., 12, 2608, https://doi.org/10.3390/rs12162608.
Raghukumar, K., G. Chang, F. Spada, C. Jones, T. Janssen, and A. Gans, 2019: Performance characteristics of “Spotter,” a newly developed real-time wave measurement buoy. J. Atmos. Oceanic Technol., 36, 1127–1141, https://doi.org/10.1175/JTECH-D-18-0151.1.
Rapizo, H., A. V. Babanin, E. Schulz, M. A. Hemer, and T. H. Durrant, 2015: Observation of wind-waves from a moored buoy in the Southern Ocean. Ocean Dyn., 65, 1275–1288, https://doi.org/10.1007/s10236-015-0873-3.
Rapizo, H., T. H. Durrant, and A. V. Babanin, 2018: An assessment of the impact of surface currents on wave modeling in the Southern Ocean. Ocean Dyn., 68, 939–955, https://doi.org/10.1007/s10236-018-1171-7.
RINEX Working Group, 2018: The Receiver Independent Exchange Format: Version 3.04. IGS Doc., 100 pp., http://acc.igs.org/misc/rinex304.pdf.
Scharroo, R., 2022: RADS user manual, version 4.3.7. RADS Doc., 52 pp.
Schlembach, F., and Coauthors, 2020: Round robin assessment of radar altimeter low resolution mode and delay-Doppler retracking algorithms for significant wave height. Remote Sens., 12, 1254, https://doi.org/10.3390/rs12081254.
Schulz, E. W., M. A. Grosenbaugh, L. Pender, D. J. M. Greenslade, and T. W. Trull, 2011: Mooring design using wave-state estimate from the Southern Ocean. J. Atmos. Oceanic Technol., 28, 1351–1360, https://doi.org/10.1175/JTECH-D-10-05033.1.
Schulz, E. W., S. A. Josey, and R. Verein, 2012: First air-sea flux mooring measurements in the Southern Ocean. Geophys. Res. Lett., 39, L16606, https://doi.org/10.1029/2012GL052290.
Selle, C., and S. Desai, 2016: Optimization of tropospheric delay estimation parameters by comparison of GPS-based precipitable water vapor estimates with microwave radiometer measurements. IGS Workshop, Sydney, Australia, IGS, http://acc.igs.org/workshop2016/presentations/Plenary_05_03.pdf.
Sepulveda, H. H., P. Queffeulou, and F. Ardhuin, 2015: Assessment of SARAL/AltiKa wave height measurements relative to buoy, Jason-2, and CryoSat-2 data. Mar. Geod., 38, 449–465, https://doi.org/10.1080/01490419.2014.1000470.
Storer, B. A., M. Buzzicotti, H. Khatri, S. M. Griffies, and H. Aluie, 2022: Global energy spectrum of the general oceanic circulation. Nat. Commun., 13, 5314, https://doi.org/10.1038/s41467-022-33031-3.
Talley, L. D., G. L. Pickard, and W. J. Emery, Eds., 2011: Descriptive Physical Oceanography: An Introduction. 6th ed. Academic Press, 555 pp.
Tison, C., and D. Hauser, 2018: SWIM products user guide. CNES Doc. CF-GSFR-MU-2530-CNES, 95 pp.
Wang, J., and Coauthors, 2022: On the development of SWOT in situ calibration/validation for short-wavelength ocean topography. J. Atmos. Oceanic Technol., 39, 595–617, https://doi.org/10.1175/JTECH-D-21-0039.1.
Waseda, T., and Coauthors, 2014: Deep water observations of extreme waves with moored and free GPS buoys. Ocean Dyn., 64, 1269–1280, https://doi.org/10.1007/s10236-014-0751-4.
Watson, C. S., 2005: Satellite altimeter calibration and validation using GPS buoy technology. Ph.D. thesis, University of Tasmania, 264 pp.
Watson, C. S., R. Coleman, N. White, J. Church, and R. Govind, 2003: Absolute calibration of TOPEX/Poseidon and Jason-1 using GPS buoys in Bass Strait, Australia. Mar. Geod., 26, 285–304, https://doi.org/10.1080/714044522.
Wunsch, C., and D. Stammer, 1997: Atmospheric loading and the oceanic “inverted barometer” effect. Rev. Geophys., 35, 79–107, https://doi.org/10.1029/96RG03037.
Wynn-Edwards, C. A., D. M. Davies, P. Jansen, E. H. Shadwick, and T. W. Trull, 2020: IMOS—Southern Ocean Time Series (SOTS)—Annual reports: 2019/2020. IMOS, https://doi.org/10.26198/V7KC-GT27.
Wynn-Edwards, C. A., T. W. Trull, and E. H. Shadwick, 2022: IMOS—Southern Ocean Time Series (SOTS)—Annual reports: 2020/2021. IMOS, https://doi.org/10.26198/WSF3-9R77.
Yang, J., and J. Zhang, 2019: Validation of Sentinel-3A/3B satellite altimetry wave heights with buoy and Jason-3 data. Sensors, 19, 2914, https://doi.org/10.3390/s19132914.
Yang, L., X. Zhou, S. P. Mertikas, L. Zhu, L. Yang, and N. Lei, 2017: First calibration results of Jason-2 and SARAL/AltiKa satellite altimeters from the Qianli Yan permanent Cal/Val facilities, China. Adv. Space Res., 59, 2831–2842, https://doi.org/10.1016/j.asr.2017.02.044.
Young, I. R., E. Fontaine, Q. Liu, and A. V. Babanin, 2020: The wave climate of the Southern Ocean. J. Phys. Oceanogr., 50, 1417–1433, https://doi.org/10.1175/JPO-D-20-0031.1.
Zhou, B., C. Watson, B. Legresy, M. A. King, J. Beardsley, and A. Deane, 2020: GNSS/INS-equipped buoys for altimetry validation: Lessons learnt and new directions from the Bass Strait validation facility. Remote Sens., 12, 3001, https://doi.org/10.3390/rs12183001.
Zumberge, J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins, and F. H. Webb, 1997: Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res., 102, 5005–5017, https://doi.org/10.1029/96JB03860.