Improved Acoustic Tracking of RAFOS-Enabled Profiling Floats through the New Software Package artoa4argo
1. Introduction
The Argo program, which started in 1999 with regional arrays of profiling floats, now comprises over 3000 active floats globally, allowing for the continuous autonomous sampling of the subsurface ocean temperature and salinity profiles without the need for ships or moorings. Argo floats generally drift at 1000-m depth—that is, their parking depth—for 7–10 days, then sink to 2000 m and profile up to the surface. At the surface the profile and drift data are transmitted via satellite before the Argo float sinks back to its parking depth.
At high latitudes, such as the Weddell Sea, seasonal sea ice coverage prevents Argo floats from surfacing and transmitting data during winter months. In fact, to avoid potential ice damage, high-latitude Argo floats are often deployed with temperature-controlled sea ice avoidance firmware (Klatt et al. 2007), instructing them to stay subsurface until ice-free conditions are available for surfacing and data transmission. Since standard Argo floats are tracked solely through satellite positional (SAT) data at the surface, under-ice profiles lack SAT data. During postprocessing, profile position data for Argo floats trapped under ice are usually obtained by linear interpolation (Wong and Riser 2011) or by following contours of planetary-geostrophic vorticity (PV; Reeve et al. 2016) between two known positions. Unfortunately, this introduces errors in profile locations, as well as underestimates float speed and displacement. Chamberlain et al. (2018) quantified the maximum position uncertainty, over 8 months of position loss, due to using linear interpolation for longitude–latitude and PV coordinates, to be 116 ± 148 km and 92 ± 121 km, respectively. This is worrisome, as horizontal mapping of temperature and salinity (Reeve et al. 2016), derived quantities (Reeve et al. 2019), and surface boundary information (D’Ortenzio et al. 2014; Wong and Riser 2011) from Argo profiles are dependent on the quality of the float’s positional data. In addition, estimates of lateral eddy diffusivity using Argo GPS position data (Roach et al. 2016, 2018) at 10-day intervals are difficult to calculate.
One way to improve this situation is to acoustically track Argo floats subsurface using RAFOS technology. Developed in the 1980s (Rossby et al. 1986), standard RAFOS floats have seen great success over the last 40 years in ice-free regions such as the North Atlantic (e.g., Owens 1984, 1991; Zenk et al. 1992; Bower and von Appen 2008; Bower et al. 2011; Rudnickas et al. 2019), the South Atlantic (e.g., Ollitrault 1999; Boebel et al. 1999; Richardson and Garzoli 2003; Ollitrault et al. 2006), the Gulf of Mexico (e.g., Furey et al. 2018; Pérez-Brunius et al. 2018; Hancock et al. 2022), and the Antarctic Circumpolar Current and greater Agulhas Current System (e.g., Boebel et al. 2003; Richardson et al. 2003; Balwada et al. 2016, 2021). Standard RAFOS floats are equipped with an acoustic receiver designed to listen for well-defined acoustic signals (RAFOS sweep) from an array of moored sound sources (Fig. 1, along with Table A1 in the appendix). The RAFOS float listens for these signals by correlating the incoming sound with the nominal RAFOS sweep, saving the times of arrival (toas) of the six highest correlations, along with their correlation height (corr). Using the speed of sound in seawater, this allows for the float’s position to retroactively be determined by triangulation. Using the software package ARTOA3 (Furey 2005), an updated version of ARTOA-II (Wooding et al. 2005), the toas are visualized graphically along with the expected time of arrival (eta) of each sound sources’ signal at float deployment and surfacing positions (Fig. 1; Table A1). The toas of a given source thereby line up, forming a toa trace spanning long periods of the float deployment. Using the launch and surfacing etas, toa traces are assigned to the respective sound sources and corrected for float clock offsets. These toa traces are then used to calculate the range between the float and each sound source. When multiple sound sources are identified, the float can be tracked employing common methods of navigation, specifically least squares and circular tracking (Fig. 1).
Diagram illustrating the RAFOS technique, for a RAFOS-enabled Argo float in a region with a preexisting network of subsurface sound sources (SoSo). Abbreviations are as follows (see appendix Table A1 for definitions of all RAFOS/ARTOA3/arto4argo terminology used in the paper): (a) corr is the correlation of the heard signal to the nominal signal, (b) toa is the time of arrival of the signal in seconds from the float’s listening window, (c) SAT is any satellite positional data, (d) metadata include any data associated with float deployment and recovery, (e) RFB is the input file for artoa4argo, (f) SoSo is the sound source, and (g) eta is the theoretical time of arrival (in seconds) of a RAFOS signal as estimated from the distance between a sound source and a float’s SAT location.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
Up until recently, the ARTOA3 software package had been modified only incrementally to address problems and limitations. However, no major overhaul of ARTOA had been performed so far. The initial ARTOA, ARTOA-II, and ARTOA3 software packages were created with the original RAFOS float in mind, which remains submerged for its entire mission with only two associated surface locations, the RAFOS float’s deployment, obtained from the ships position, and its surfacing location, acquired from Argos Satellite Services. These were used to correctly assign float toa traces to available sound sources, as well as to calculate any offset in the sound source and float clocks. Profiling floats, on the other hand, are programmed to surface at set intervals to transfer data, including SAT data for positional information. In ice-covered oceans, this usually occurs only during summer months, when the float encounters open water conditions. The subsequent SAT data acquired during surfacing are a valuable aid when acoustically tracking RAFOS-enabled profiling floats. These midtrajectory surface positions have been used in ARTOAII and ARTOA3 to aid in tracking, but not fully exploited and formally integrated with the software and tracking process, as in this new artoa4argo software package.
At midlatitudes, acoustic transmission ranges are large (>1000 km), due to a broad and deep SOFAR channel, and RAFOS floats often hear 3 or more sound sources for extended periods of time. Thus, while making the warranted assumption of constant clock drifts, any missing sound source clock offsets can be calculated using initial and final toas from multiple floats. However, in ice-covered regions such as the Weddell Sea the effective acoustic surface duct is relatively narrow and shallow, forcing sound to travel close to the sea surface. This introduces multiple interactions with sea ice and the sea surface, which reduces transmission ranges to 300 km (Klatt et al. 2007) or less, depending on sea ice coverage and roughness. With such reduced transmission ranges, resulting in fewer sound source signals received, the postprocessing method of empirically removing any unknown clock offsets fails. Successful float tracking depends on the availability of sound source clock offsets, which requires the recovery of sound sources. It is often operationally difficult to recover sound sources in heavily ice-covered oceans, resulting in missing sound source clock information.
Weddell Sea floats often drift for 3–4 years, covering several thousands of kilometers, passing a dozen or so sound sources during their lifetime. Given the limited acoustic ranges, toa traces from some sound sources will unavoidably not connect to a float’s deployment and/or surfacing location’s etas, hampering the assignment of such toa traces to a specific sound source. In addition, during winter it is not unusual for Weddell Sea floats to receive no toas from a specific source. This results in gaps in the toa traces between deployment and final surfacing positions and possibly free floating toa-trace segments (i.e., unconnected to launch and final surfacing etas). From a tracking point of view, such gaps are problematic as correctly assigning subsequent toas to a specific sound source becomes difficult.
Since the quality of the trajectory is directly related to the quality of the toa traces and their proper assignment to a specific source, unidentified clock offsets and/or incorrectly assigned toas are among the largest sources of tracking errors.
To address these tracking problems, a Kalman smoothing method was developed by Chamberlain et al. (2022) and used to track 22 RAFOS-enabled Argo floats in the Weddell Sea. The Kalman smoother, a minimum mean-square error estimator, was designed to solve the entire float equation system simultaneously. It treats float position, float velocities, and sound source clock offsets as state variables and inputs SAT positions and all acoustic ranging data (i.e., toas and corrs). State variables and covariances are saved on the forward pass and applied during the backward pass to compute improved state estimates. Regardless of how many toas are available per time step, the Kalman smoother provides an estimate of float position for each time step.
In 2020, the Alfred Wegener Institute for Polar and Marine Research (AWI), in collaboration with Emirror-de (https://emirror.de), developed a new version of ARTOA, named artoa4argo, which expands the functionality and addresses the shortcomings, described below, of the original ARTOA3 software. The new software underwent preliminary testing in collaboration with Florida State University (FSU) in 2021 and is currently being used to track RAFOS-enabled profiling floats in the Weddell Sea. The artoa4argo fully exploits available SAT data to (i) ease identification and assignment of toa traces to specific sound sources, (ii) resolve sound source and float clock offsets, and (iii) calculate offsets between the current track and SAT positions (named tracking errors hereinafter).
The Weddell Gyre is an ideal location to test artoa4argo, as (i) AWI has maintained an extensive array of sound sources since 2008 (e.g., Boebel et al. 2017, 2019), (ii) seasonal ice coverage drastically reduces the number of float profiles with position data, and (iii) transmission ranges are reduced seasonally to 300 km or less. To evaluate the success of the artoa4argo software, we compare resultant trajectories of 21 RAFOS-enabled profiling floats deployed in the Weddell Gyre, which have previously been tracked using the Kalman smoother (Chamberlain et al. 2022) and a new multiconstraint method (Oke et al. 2022).
This paper is structured as follows. Section 2 describes the main features of the artoa4argo software. Data used are outlined in section 3. In section 4, artoa4argo trajectories are compared with trajectory outputs from the Kalman smoother and the multiconstraint method, and the discussion and conclusions are presented in section 5.
2. artoa4argo
a. ARTOA history
Acoustically tracked subsurface floats have been in use since the 1970s and include SOFAR floats, RAFOS floats, and RAFOS-enabled profiling floats. As of today, 2571 subsurface floats, from over 55 different field programs, have been acoustically tracked, with most of the tracks stored in a new repository at the National Oceanic and Atmospheric Administration’s Atlantic Oceanographic and Meteorological Laboratory (AOML; Ramsey et al. 2018).
RAFOS tracked floats were invented in 1986 by Tom Rossby at the University of Rhode Island (URI; Rossby et al. 1986). The original tracking software, used to calculate positions from toas of sound signals emitted from moored sound sources, was developed at the Graduate School of Oceanography at URI. This software was composed of five modules: Redit, Setup, Argot, Artoa, and Artrk (König and Zenk 1992). Running on early computers, Artoa allowed assigning toas to sources via a basic text-mode pseudographic with alphanumeric symbols representing toas. In the early 1990s, these Fortran versions were transcribed to MATLAB code at the Institute of Marine Science in Kiel (IfM Kiel); however, they were still on a nongraphic display.
Starting in 1997, a MATLAB-based tracking software package was created, featuring the first true graphic user interface, representing a complete overhaul of previous program suites. ARTOA-II became a single integrated package of MATLAB routines, allowing the user to track a float in a single session. This development started at IfM Kiel and continued at Woods Hole Oceanographic Institution (WHOI) (Wooding et al. 2005), URI, and the French Research Institute for Exploration of the Sea (IFREMER). An updated version, ARTOA3 (Furey 2005), includes modifications to ease tracking by (i) color coding assigned toas in the toa window, (ii) increasing the maximum number of sound sources used during tracking to five, (iii) including bathymetry in the trajectory plot, and (iv) plotting residuals between least squares fit and individual sound source toa records. Several other modifications have been implemented over the years to address issues as they occur, one of which was accommodating for different sound signal schedules.
In addition to traditional RAFOS floats described above, RAFOS-enabled profiling floats were originally used in RAFOS field programs to monitor sound source arrays over time. RAFOS-enabled profiling floats were first tracked using ARTOA-II (modified by H. Furey) in the 1996/97 ACCE program (Furey et al. 2001). The first use of RAFOS-enabled profiling floats to achieve science objectives of a field program was in the BOBBER program (Fratantoni et al. 2010), this time using ARTOA3. Midtrajectory SAT locations were used to visually guide the float tracking; the user could adjust tracking parameters to ensure the resultant track aligned with the surface SAT fixes, if needed. Later, ARTOA3 was modified at AWI around 2016 to not only display SAT fixes in the tracking window, but also their corresponding etas in the toa window.
b. artoa4argo
Like ARTOA-II and ARTOA3, artoa4argo is a single integrated package of MATLAB routines, which permits the user to track a float in a single session. In comparison with the earlier versions, this allows the user to identify and rectify tracking errors at any point in the process. That said, the fundamental concept of artoa4argo is in exploiting the quantitative comparison of toas with corresponding etas to the best of our ability.
The current version of artoa4argo software (Boebel et al. 2023) runs on MATLAB versions 2020a–2022b and is published online (https://doi.org/10.5281/zenodo.7588848). A basic users’ guide is currently being developed by AWI, FSU, and Emirror-de and is available through the GitLab repository (https://gitlab.awi.de/argotools/artoa4argo). The artoa4argo features a toa and a tracking window, each with multiple embedded plots and numerical input/output (I/O) panels, displaying all available input and calculated output data as needed for a successful tracking session. Data in both windows are linked, such that selections in either view are readily identified in the other. Several functionalities described below are available in both artoa4argo and ARTOA3. Specific improvements to ARTOA3 are noted in both the text and Table 1. Appendix Table A1 is a glossary and defines any RAFOS, ARTOA3, and artoa4argo specific terminology used in the paper.
Main features of ARTOA3 and artoa4argo.
1) Input data
The artoa4argo requires float SAT data, acoustic (RAFOS) data, and sound source information provided in specific ASCII formats. Once these files have been created and loaded, selecting valid temperature and pressure data points enables the program to calculate a nominal, plausible speed of sound (Spiesecke 2018). This speed of sound is needed to calculate the eta as corresponding to the float’s launch and surfacing positions and plot them in the toa window, as well as eta-type estimates for any available SAT data.
2) Assigning toas
Several modifications have been implemented to artoa4argo’s toa window to create a user-friendly interface. Specifically, all information, features and parameter selections that affect float tracking, are contained in a comprehensive display and integrated with numerical I/O panels displaying information on tracking settings as well as float and sound source clock offsets and sound speeds.
The floats’ toa data (y axis) are presented as a function of date (x axis), and color coded by their respective corr to indicate signal quality in the toa window. The artoa4argo maps corrs onto a continuous grayscale, with the option of interactively setting upper and lower corrs limits (Fig. 2, note the increased discernability at 4300s). This allows maximizing the contrast between valid toas and noise, while simultaneously plotting toas assigned to a specific sound source in sound source specific colors, something ARTOA3 also allows (Fig. 3).
The artoa4argo’s toa window, showing unassigned toas (gray dots) for Argo float WMO 5901743 with a (a) full (0–255) and (b) modified (35–66) corr range. The corr range is highlighted by the yellow box in Fig. 3b, below. The toas (y axis) and message date (x axis) have units of seconds and days, respectively. Filled circles indicate etas for the launch position, and open circles indicate etas associated with SAT data. Maps are MATLAB-based dynamic figures, which allow the user to zoom in while labels retain their font size. Note the increased discernability between (a) and (b) for the trace at 4300 s.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
The artoa4argo’s toa window, showing (a) unassigned and (b) assigned toa traces for Argo float WMO 5901743, where the color coding of the assigned sound sources is found in the top-left corner (blue box). Not all sound sources are heard by the float, in which case they are unassigned, and uncolored. The toas (y axis) and message date (x axis) have units of seconds and days, respectively. A histogram of the corr range (yellow box) identifies the current range in use, with the option to adjust the upper and lower bounds (see Fig. 2 for an example). The green box lists any duplicate assigned toas. It is currently empty, because there are no duplicates for any of the sound sources. Maps are MATLAB-based dynamic figures, which allow the user to zoom in while labels retain their font size.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
A major improvement over previous versions of ARTOA is artoa4argo’s ability to actively integrate SAT data in the tracking process of RAFOS-enabled Argo floats. SAT data are added to the (.rfb) input data file and their corresponding etas are displayed in the toa window to ease correct assignment of toas to specific sound sources (Fig. 3). Generally, toa data are assigned to specific sound sources on the basis of toas fitting a given source’s eta at launch and surface time. However, decreasing acoustic ranges in sea ice–covered oceans during winter can result in toa traces to fade out, resulting in isolated toa traces. As Fig. 3 illustrates, SAT data-based etas allow the user to easily identify toas from the same sound source across the entire float deployment [see (1) in section 2b(4), below, on how etas are calculated].
In the toa window the user allocates toa data to the appropriate sound source, where each sound source is then color coded for user ease (Fig. 3b). In artoa4argo both toas and etas associated with a sound source are color coded, informing the user where the subsequent toas should be located. The color coding is displayed in a separate legend located to the left of the toa window (Fig. 3b, blue box). This facilitates toa allocation to the correct sound source, as floats often drift for several years, covering a few thousand kilometers and passing, on average, a dozen or so sound sources.
Another modification relates to how artoa4argo deals with multiple toas picked for the same sound source with the same date stamp. Neither ARTOA3 nor artoa4argo allows more than one toa for each sound source for a specific date stamp. ARTOA3 would relay error messages when attempting to track, indicating sound source and date stamp of the inconsistency. The user would then have to return to the toa window and manually find them. The artoa4argo, on the other hand, displays this information in a separate window to the left of the toa window (Fig. 3b, green box). By simply clicking on the respective toa duplet artoa4argo takes the user to the specific location in the toa window to identify and remedy the inconsistencies before attempting to track.
Some floats exhibited episodic, erratic clock drifts, i.e., a sudden increase in clock speed for a limited time period (Fig. 4). Such errors cannot be accounted for through initial offsets and constant drifts, but rather need to be addressed on an individual basis. The artoa4argo (and ARTOA3) allows the user to manipulate sections of toas in the toa window to correct these errors. Since shifting the toa essentially changes the input data, the user should always attempt to correct errors using the clock start offset and drift first. Careful examination of the section in question, including between different floats, needs to happen prior to applying a shift, preferably through a calculation of mean toa changes at each event for each sound source.
The artoa4argo’s toa window, showing jumps in toas that are due to a malfunctioning float clock (the steep toa-trace sections, detectible concurrently for all sound source traces), (a) before and (b) after correctional shifts have been applied. The toas (y axis) and message date (x axis) have units of seconds and days, respectively. Maps are MATLAB-based dynamic figures, which allow the user to zoom in while labels retain their font size.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
3) Tracking
Upon correctly assigning toas to their respective sound sources, the next source of potential tracking error is associated with uncertainties in offsets in the float and sound sources clocks. Subject to relative sound source and float positions, these can result in substantial tracking errors, or even render segments of the trajectory untraceable, particularly when the float and sources are lined up in a row. To minimize such mistakes and resulting tracking errors, artoa4argo offers two tools: direct visual control and manual manipulation of (known) clock offsets applied, as well as numerically solving for remaining unknown clock offsets.
In the toa window, the user can toggle between offsets being ignored and applied in the eta calculations of each sound source (Fig. 5, note how circles and dots match when clock offsets are applied). Using the toa window’s zoom function, the user can check the plausibility of an offset to less than 1 s resolution and modify it if necessary.
The artoa4argo’s toa window, showing assigned toas from Argo float WMO 5901743 with sound source and float clock offsets (a) excluded and (b) included. toas (y axis) and message date (x axis) have units of seconds and days, respectively. Colored dots and circles indicate toas and SAT based etas (labeled by sound source name), respectively. Maps are MATLAB-based dynamic figures, which allow the user to zoom in while labels retain their font size.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
Clock-offset information derives from several sources. 1) “Direct” measurement of clock offsets (usually on board the ship prior to deployment and after recovery) are ideal and should be recorded in the associated sound source file. 2) “Empirical” estimates of sound source clock offsets, often based on user experience during previous float tracking, are also to be included in the sound source file and thus uploaded into artoa4argo. Notably, this is the place to save parameters calculated by simultaneous inversions of multiple float data [see section 2b(4), below]. With artoa4argo (and ARTOA3) offering the option to reload the sound source file, these entries can be modified therein and used at any time in the tracking effort. The artoa4argo can also calculate “optimal” offsets internally, to best fit SAT based etas with associated toa data [see section 2b(4), below]. This is particularly helpful in situations where clock-offset information is missing.
Clock offsets are unique to each source, requiring the user to make a selection among the three types “direct,” “empirical,” and “optimal.” This is facilitated in artoa4argo by simultaneously displaying all data in a numerical I/O panel, within which the user may copy any of these offsets into the panel’s “applied” field, which furthermore may be manually edited.
Before tracking, the user needs to select (i) tracking method, (ii) sound source velocity calculation method, (iii) interpolation algorithm and interval, (iv) whether to incorporate a Doppler shift correction, (v) sound source combinations and date intervals, and (vi) a tracking reference position. The artoa4argo, as the antecedent ARTOA3, currently offers two tracking methods, least squares and circular tracking. Circular tracking requires two sound sources’ toas and finds track location through intersecting circles of r = toa/c, located on a baseline (the great circle passing through both sources’ position) between the respective sound sources. Least squares tracking also uses two sound sources’ toas and determine float positions by minimizing (etasn − toafm), where etasn is the time (s) between the last known position and the sound source sn, for sn ∈ {1, …, N}, and toafm is the recorded toa (s) on day m, after clock corrections. This is performed iteratively for all possible sound source toa pairs, where a prediction is suggested and each iteration improves upon the initial prediction until the difference is less than 1 km. Hyperbolic tracking, requiring concurrent toas from at least 3 sources, is currently not implemented in artoa4argo but is available in ARTOA3.
A fourth tracking method, single-source tracking, will be implemented with the next version of artoa4argo, for segments during which toa data from only a single source are available. Single-source tracking estimates a plausible trajectory commensurate with the toa, that is, distance, from this single sound source and additional constraints made by the user (e.g., topographic data if the float grounded or constant speed, with, however, various degrees of robustness/reliability).
Critical to achieving good tracks is the appropriate choice of a reference position. Tracking solutions usually involve an ambiguity regarding which side of two sources’ baseline the trajectory resides. This becomes particularly important when the float crosses a baseline. To determine the most plausible (continuous) trajectory, artoa4argo (and ARTOA3) allows concurrent tracking and display of multiple tracking attempts, featuring different tracking methods, time periods, sound source configurations, reference positions, and potentially small adjustments to the clock corrections. Although ARTOA3 allows concurrent tracking using different sound source combinations and sound velocities in different segments, the user cannot simultaneously track overlapping segments with different parameter setups. Neither does ARTOA3 allow the user to change the method of tracking between segments for the same float within the same ARTOA3 session, an improvement made in artoa4argo. These improvements allow the artoa4argo user to easily identify the optimum track for each segment and meld them together into a coherent trajectory within artoa4argo itself.
Another issue that regularly occurs in high-latitude oceans, such as the Weddell Sea, are periods when no sound source is heard (Fig. 3). If the time gap between two isolated toa traces becomes too large, tracking the latter portion becomes difficult. A solution for this, which artoa4argo employs, is to allow the user to track any segment forward or backward in time. The only stipulation is that the user must specify a suitable starting reference location for each section.
Once the toas have been assigned and offsets applied, artoa4argo will calculate the float trajectory according to the users specified sound source combination and tracking method for each segment. The resultant trajectory is visualized in a separate tracking window, on a map with bathymetry and sound source locations. Each section of the trajectory will be color coded by sound source combinations used during tracking (Fig. 6), with calculated velocities and eta versus toa differences as separate figures in the tracking window. eta versus toa differences are calculated for each sound source, based on available SAT data. Hence, whenever SAT data are missing, no error can be calculated. Trajectory plausibility is revealed by (i) the distance between deployment and recovery SAT data and trajectory start and end points, (ii) the distance between SAT data and the equivalent track position, (iii) differences between eta and toa for each sound source, and (iv) plausibility checks regarding, e.g., bathymetry.
The artoa4argo trajectory panel displaying essential tracking results. (right) Trajectory window, showing final track for Argo float WMO 5901743. The trajectory is color coded by segment, where colored dots show tracked positions and gray dots show SAT locations with a date stamp. Sound sources are labeled and denoted by black dots, and bathymetry is shown in green. (left) Deviations between GPS based etas and associated toas for (top) each sound source used during tracking in seconds and (middle) horizontal velocities and (bottom) vertical velocity, both given in meters per second. The message date has units of days. Maps are MATLAB-based dynamic figures, which allow the user to zoom in while labels retain their font size.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
4) Resolving for unknown clock offsets and sound speed
In this equation the following nomenclature was used:
The robustness of the solution x increases as the number of unknowns decreases. We can incorporate additional information to simplify the problem and reduce the number of unknowns.
-
Usually, float and sound source clocks are set (relative to UTC) at the time of instrument deployment, resulting in start offsets equaling zero or at least a known value. This is accounted for in (3) by removing the corresponding columns of “minus ones” in
and corresponding start offsets stroffsn in x and adding the offset to the equation’s left-hand side eta. This reduces the number of unknows by N (sound sources), leaving us with 2N + 2 unknowns. -
Drifts of some sound sources are known in the case of successful postrecovery clock checks. As above, the corresponding known drift can be accounted for by adding
to the left side of (3) and removing the corresponding columns and rows on the right-hand side. -
In many oceanographic settings it is reasonable to assume that the effective sound speed is only dependent on the sound source and not on the eta’s SAT position, reducing the number of unknowns to N + 3 (minus known drifts).
-
One can even assume one universal sound speed c for the entire study area. This collapses the set of cs to one universal c and leaves us with N (sound source offsets) + 2 (float offset and drift) + 1 (sound speed) = N + 3 unknowns. All but the first column of rs in (3) needs to be removed from
which is appended with the rs of all eta–toa combinations. -
The only remaining unknowns that might be known are float start offset and drift. Unfortunately, at 1-s accuracy, the RAFOS window start times are a somewhat obscure parameter in profiling float technology because these are state-controlled rather than time-controlled instruments. Different manufactures chose different approaches, and it is left to the discretion of the analyst as to whether it is appropriate to make any assumptions on its start offset and drift. If taken, these would reduce the number of unknowns to N + 1, that is, the sound sources’ drifts and the sound speed.
The above approach provides a solution exclusively tailored to the toa/eta duplets of a single float. Independent execution for another float might result in deviating drift estimates for a given sound source. Typically, a dozen or so floats receive sound signals from different subsets of the concurrently moored sound sources to which unique clock start offsets and drifts should be assigned, regardless of the float used in their calculation. To be able to execute a “grand” inversion of all active floats and sound sources together, artoa4argo offers the export of the above matrices and vectors, from which an external script forms a grand matrix
5) Limitations
There are some limitations to the artoa4argo software, the main one being its dependence on assigned toas from multiple sound sources. Currently, if only one sound source can be received by the float, artoa4argo cannot produce a trajectory.
Single-source tracking will be added as an option in an updated version of artoa4argo; however, at this time, it is unknown how successfully it will track. In addition, even when multiple sound sources are received and assigned in the toa window, if the software does not converge, no trajectory is produced. Thus, unlike the Kalman smoother and multiconstraint method, the final trajectories from artoa4argo often include missing sections.
artoa4argo is sensitive to several parameters, which require careful consideration by the user. As mentioned earlier, the trajectory is heavily dependent on the clock corrections applied to both the float and sound sources. In addition, the starting location of each trajectory is crucial, especially if the float’s position in relation to sound sources is close to their respective baseline.
3. Data
Raw acoustic data and GPS positions from 21 RAFOS-enabled profiling floats deployed by the University of Washington in the Weddell Sea during 2008–12 were used for a comparison of the different tracking methods. Deployment and recovery information for each float can be found in Table 2. Prior to tracking, preprocessing of the raw acoustic data was necessary to correct float clock offsets in the toa data, and format data to create artoa4argo compatible input files. Equivalent trajectories created by the Kalman smoother (Chamberlain et al. 2022) and the multiconstraint method (Oke et al. 2022) were downloaded from AOML (2022) and Rykova and Oke (2022), respectively.
Overview of RAFOS-enabled profiling floats tracked using artoa4argo (see Table 3 procedure A), the Kalman smoother (see Table 3 procedure B), and the multiconstraint method. Since both the Kalman smoother and the multiconstraint method produce positions for all time steps between float deployment and recovery (i.e., 100% tracked), they have not been included in this table. Here, ID is identifier.
4. Results
To assess the success of artoa4argo, 21 RAFOS-enabled profiling floats (Table 2) were tracked and compared with previous trajectories using the Kalman smoother (Chamberlain et al. 2022) and a new multiconstraint method (Oke et al. 2022). Both the trajectory path itself, as well as zonal and meridional velocities, were compared to evaluate artoa4argo’s performance in relation to other tracking methods.
a. artoa4argo versus linearly interpolated GPS fixes
During sea ice conditions, Argo floats are typically trapped under ice for 6–8 months. Figure 7 shows linearly interpolated GPS fixes (black line) and RAFOS (red line) positions for Argo float WMO 5901731, during its deployment from February 2008 to May 2010. Note the straight lines during winters of 2008 and 2009 (yellow dashed line), indicating when the float could not surface to acquire a GPS position. If no other tracking data were available, all profiles completed by the float during this time would be positioned on the straight line using linear interpolation (not great circle) of latitude and longitude, introducing a positional error of 5–100 km (Fig. 7, insert), when compared with the artoa4argo trajectory. However, using artoa4argo to track the float (Table 3, procedure A), we are able to resolve both sub- and mesoscale motions and significantly reduce float position errors relative to linear interpolation (Fig. 8). In addition, we gain daily meridional and zonal velocity estimates, where GPS only provides a single mean (Fig. 7). The positional errors from linearly interpolating across missing winter GPS data for all 21 RAFOS-enabled profiling floats over their 4-yr deployment ranges from 5 to 660 km with a mean and median of 186 ± 149 km and 130 ± 149 km (Fig. 9), respectively, in comparison with the respective artoa4argo trajectories.
(a) Track according to GPS (black line) and artoa4argo (red line) for Argo float WMO 5901731. Yellow/black dashed segments indicate the periods when the float was under the sea ice. Gray contour lines show bathymetry. (top left inset) Calculated distance between linearly interpolated GPS positions and the artoa4argo trajectory (km) during winter of 2008 (blue) and 2009 (red). (b) Distribution of zonal and meridional velocities calculated from the trajectory in (a) during winter 2008 (blue) and 2009 (red). The yellow dots denote velocity as calculated from GPS positions in (a), during winter 2008 (zonal and meridional: −0.012 and −0.003 m s−1, respectively) and 2009 (zonal and meridional: −0.006 and −0.006 m s−1, respectively).
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
The four procedures currently available for acoustic float tracking.
Probability density function of tracking error for all 21 RAFOS enabled profiling floats. Tracking errors were calculated by comparing artoa4argo track with the equivalent GPS positions. Mean and standard deviations are 5 and 11 km, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
Probability density function of tracking error due to linear interpolation between GPS locations during ice-covered seasons for all 21 RAFOS-enabled profiling floats deployed in the Weddell Sea between 2008 and 2012. Only GPS gaps of 1 month or longer were included in this analysis. Mean, median, and standard deviation of the tracking error are 186, 130, and 149 km, respectively.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
b. artoa4argo versus Kalman smoother
Figure 10 shows daily and 7-day averaged speed for Argo float WMO 5901731 as calculated by artoa4argo (Fig. 10a) and the Kalman smoother (Fig. 10b). We clearly see more large velocity spikes in the time series produced by the Kalman smoother as compared with artoa4argo (solid boxes in Fig. 10). Interestingly, these tend to occur during periods of GPS position data (black dots in Fig. 10). This could be due to the Kalman smoother weighting these data points more heavily, forcing the float to these positions. One could attempt to address this by modifying the weighting of GPS data; however, as this is a complex system, it will likely affect other parts of the trajectory in an unknown fashion. Note also that the Kalman smoother produces slightly larger speeds, with a mean of 0.05 ± 0.05 m s−1 (Table 4) as compared with 0.03 ± 0.03 m s−1 from artoa4argo. This is particularly evident in the power spectral density of speed (Fig. 11) as calculated by the two methods. The Kalman smoother trajectory shows anomalously large peaks in the 2–14-day period, likely a result of the Kalman smoother’s algorithm and weighting scheme. These results are not isolated to Argo float WMO 5901731 but occur, to some degree, in all the trajectories as illustrated by the probability density function for the normalized meridional and zonal velocities of all 21 trajectories (Fig. 12). At values greater than ±4 standard deviations, the Kalman smoother has longer, and fatter tails relative to artoa4argo, a result of the numerous velocity spikes seen in Fig. 10b. If we examine the first 330 days of track for each method (Fig. 13), we observe a noticeably smoother trajectory with artoa4argo, as well as one eddy the Kalman smoother failed to resolve.
Daily (blue) and 7-day-averaged (red) speed (m s−1) for Argo float WMO 5901731 tracked by (a) artoa4argo, (b) the Kalman smoother, and (c) the multiconstraint method, from March 2008 to May 2010. Black solid and dashed boxes identify time periods of large velocity spikes and smoothed velocities, respectively. Black dots indicate GPS fixes. The multiconstraint method has a default time step of 7 days, as compared with artoa4argo and the Kalman smoother, which both have a 1-day time step.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
Mean, median, and standard deviation of speed as calculated from the Argo float WMO 5901713 trajectory, using artoa4argo, the Kalman smoother, and the multiconstraint method.
Power spectral density of speed for Argo float WMO 5901731 as calculated using the multitaper method (Lilly and Elipot 2021) from trajectories produced by artoa4argo (red), the Kalman smoother (blue), the multiconstraint method (orange), and 7-day interpolated GPS data (black). Power spectral density units are meters squared per second per day, and frequency units are cycles per day (cpd). Temporal resolution for artoa4argo and the Kalman smoother data is 1 day as compared with the multiconstraint method and interpolated GPS data, which are 7 days.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
The probability density function for meridional (squares) and zonal (circles) normalized velocities for artoa4argo (red), the Kalman smoother (blue), and the multiconstraint method (orange). Velocities have been normalized by removing the mean and dividing by the standard deviation. The black line is the probability density function for a Gaussian distribution. All 21 Argo floats were used in this analysis.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
First 330 days of track for Argo float WMO 5901731 from artoa4argo (red), the Kalman smoother (blue), and the multiconstraint method (orange). The black dots indicate GPS positions, the gray dots are a trajectory’s starting point, and gray contours are bathymetry. The artoa4argo does not produce track for the first 5 days and therefore starts at a different location than the Kalman smoother and multiconstraint method.
Citation: Journal of Atmospheric and Oceanic Technology 41, 1; 10.1175/JTECH-D-23-0020.1
c. artoa4argo versus multiconstraint method
Both Chamberlain et al. (2018) and Yamazaki et al. (2020) reported that using a single constraint, such as conservation of potential vorticity, to estimate a float’s trajectory over GPS position gaps can fail in regions of complex bathymetry, where, between two GPS fixes, no path of bottom depth or potential vorticity exists. To solve this problem, Oke et al. (2022) used a multiconstraint method, requiring several relevant oceanographic properties to be conserved. Thus, when one constraint fails another can be used instead. In such a manner, the multiconstraint method produces trajectories for the entire float deployment, with a 7-day time step. The properties used by Oke et al. (2022) are time invariant and include (i) potential vorticity (f/H, where f is the Coriolis parameter and H is bottom depth), (ii) mean sea level (MSL), and (iii) potential density σ1 at 1000-m depth. Maps for each of the properties were created using climatological data (bathymetry and σ1) or long runs of an eddy-resolving ocean–sea ice model (MSL). The Argo trajectory is further constrained by the top 50th percentile of average gridded Argo drift speeds (1° × 1° grid), which was calculated using all Argo data south of 60°S. It is worth mentioning, since Oke et al. (2022) only use time-invariant properties, the effect of eddies, meandering currents, and waves are not represented. In regions where these dominate, this multiconstraint method may incur large positional errors. Some additional weariness remains in applying this approach, as using modeled or climatological data to derive float positions might introduce biases toward these, i.e., generate self-fulfilling prophecies.
Figure 10 shows the daily (blue) and 7-day (red) averaged speed for Argo float WMO 5901731 as calculated by artoa4argo (Fig. 10a) and the multiconstraint method (Fig. 10c). During under-ice periods (dashed boxes) velocity variations are significantly dampened using the multiconstraint method (Fig. 10c), with a mean of 0.02 ± 0.02 m s−1 (Table 4). The multiconstraint spectrum is reduced but comparable to artoa4argo for low frequencies; however, it drops off in the higher frequency bands and is remarkably similar to the 7-day linearly interpolated GPS data (Fig. 11). When comparing trajectories for the first 330 days from both methods, the use of time-invariant properties in the multiconstraint method is evident in its overly smoothed track and lack of eddy activity (Fig. 13). Similar to the Kalman smoother, the probability density function for the normalized meridional and zonal velocities for all 21 trajectories (Fig. 12) has fatter tails for the multiconstraint method (orange) at values greater than ±4 standard deviations as compared with artoa4argo (red).
5. Discussion and conclusions
We have shown that artoa4argo improves acoustic tracking of RAFOS-enabled profiling floats in locations such as the Weddell Sea, relative to other methods such as the Kalman smoother, where seasonal ice cover prevents the acquisition of SAT data in winter and significantly reduces acoustic transmission ranges. It needs to be noted that, at the time of their analysis, Chamberlain et al. (2022) did not have complete clock offsets and drifts for all sound sources (Table 3, procedure B). As the Kalman smoother has no way of estimating unresolved clock errors, this likely contributed to errors in their trajectories (Fig. 13) and associated velocities (Figs. 10–12 and Table 4). The artoa4argo solved this problem by employing SAT data to set sound source and float clock corrections, resulting in relatively small, 5 ± 11 km, positional errors (Table 3, procedure A). Since most tracking errors are associated with systematic clock offsets, minimizing these creates both longer and improved float trajectories. When incorrect clock offsets are used for tracking, artoa4argo can fail to converge on a track, decreasing total trajectory length. Improved float trajectories result in more accurate profile positions, which is essential when creating horizontal maps of temperature, salinity, derived quantities (Reeve et al. 2016, 2019), and surface boundary information (D’Ortenzio et al. 2014; Wong and Riser 2011).
Not only does artoa4argo increase trajectory length and reduce tracking inaccuracies, but it also gives rise to improved Lagrangian statistics relative to the Kalman smoother and multiconstraint methods. Mesoscale and submesoscale motions, in particular eddy detection, are significantly improved by high-quality trajectory data. In addition, accurate trajectories are essential when calculating ocean properties such as transport estimates (Zilberman et al. 2017). Other quantities, such as dispersion and absolute diffusivity, which can be calculated from Lagrangian trajectories, are of importance to the modeling community to accurately parameterize subscale motions. Though robust estimates of horizontal mixing have been calculated using GPS positions from Argo floats (Roach et al. 2016; Roach and Speer 2019), the Weddell Sea’s extensive sea ice coverage during large parts of the year drastically decreases available GPS data. Thus, in these environments, acoustically tracked floats are necessary to produce reliable estimates of horizontal mixing.
The artoa4argo does have limitations, such as its dependency on available toa data and sensitivity to clock offsets. These not only increase the burden on the user but result in missing portions of track as well (Table 3, procedure A). Introduction of single-source tracking, with a forthcoming version of artoa4argo, should expand trajectory length farther; however, that will probably not solve the problem in all situations. The Kalman smoother, on the other hand, is not confined to the availability of toas as it produces positions for every time step (Table 3, procedure B). To maximize the use of available data, particularly in data-scarce areas like the Weddell Sea, we propose to create trajectories in three steps, thereby utilizing the strengths of both artoa4argo and the Kalman smoother successively (Table 3, procedure D). The artoa4argo should be employed first to perform the grand inversion of etas versus toas across all concurrently active floats and sound sources, to obtain a unique and consistent set of applicable clock start offsets and drifts. Second, with this information, each float should be tracked in artoa4argo as completely as possible. Then, the partial artoa4argo float trajectory, along with (unused) acoustic and SAT data, as well as the updated sound source clock offsets, could be employed by the Kalman smoother to fill gaps in the track. In this way, a robust, consistent, and complete trajectory for every RAFOS-enabled float would be ensured.
Note that SAT fixes and toas cannot occur simultaneously, because floats need to be at depth while listening for RAFOS signals and at the surface for SAT fixes.
Acknowledgments.
Development of artoa4argo was conceived and initiated by Olaf Boebel at the Alfred Wegener Institute (AWI) and coded by Emirror-de (https://emirror.de). The original Fortran float tracking code (including ARTOA) was rerendered in MATLAB by Kathy Schultz Tokos in the early 1990s. ARTOA-II was initiated by Olaf Boebel and created piecewise by Martin Menzel, Claudia Schmid, Christine Wooding, Heather Furey, and Marguerite Pacheco between 1997 and 2005. An updated version, ARTOA3, was created by Heather Furey, Thierry Reynaud, and Sandra Fontana in 2005. ARTOA’s history has been pieced together from multiple secondary sources and includes, to the best of our knowledge, all substantial contributions by institutions and personnel. We thank Heather Furey for her assistance with piecing together ARTOA’s history. Acoustic data from the 21 RAFOS-enabled profiling floats used in this analysis were generously supplied by Steve Riser at the University of Washington. Paul Chamberlain, at the Scripps Institution of Oceanography, generously supplied the Kalman smoother trajectories.This work was funded by the National Science Foundation Office of Polar Programs through Grant Award 2148517 and the Alfred Wegener Institute Helmholtz Center for Polar and Marine Research. The authors declare no conflicts of interest.
Data availability statement.
The artoa4argo software (version used for this publication) is freely available (https://zenodo.org/record/7588848#.Y9k8Ja2ZOvw; Boebel et al. 2023). The most recent version of artoa4argo is available online (https://gitlab.awi.de/argotools/artoa4argo). The jLab software used for the spectral analysis of velocities in this paper is freely available (https://www.jmlilly.net/software; Lilly and Elipot 2021). Data used for this paper—artoa4argo trajectories (https://doi.org/10.15784/601652; Hancock 2023), Kalman smoother trajectories (https://www.aoml.noaa.gov/phod/float_traj/data.php; AOML 2022), and multiconstraint trajectories (https://doi.org/10.5281/zenodo.6571146; Rykova and Oke 2022)—are freely available online.
APPENDIX
Glossary
Table A1 provides explanations of the RAFOS, ARTOA3, and artoa4argo specific terms as used in the paper.
Glossary of RAFOS, ARTOA3 and artoa4argo specific terms.
REFERENCES
AOML, 2022: RAFOS-enabled Argo trajectories in the Weddell Sea during 2008–2012, produced using a Kalman smoother. Atlantic Oceanographic and Meteorological Laboratory, accessed 12 October 2022, https://www.aoml.noaa.gov/phod/float_traj/data.php.
Balwada, D., K. G. Speer, J. H. LaCasce, W. B. Owens, J. Marshall, and R. Ferrari, 2016: Circulation and stirring in the southeast Pacific Ocean and the Scotia Sea sectors of the Antarctic Circumpolar Current. J. Phys. Oceanogr., 46, 2005–2027, https://doi.org/10.1175/JPO-D-15-0207.1.
Balwada, D., J. H. LaCasce, K. G. Speer, and R. Ferrari, 2021: Relative dispersion in the Antarctic Circumpolar Current. J. Phys. Oceanogr., 51, 553–574, https://doi.org/10.1175/JPO-D-19-0243.1.
Boebel, O., R. E. Davis, M. Ollitrault, R. G. Peterson, P. L. Richardson, C. Schmid, and W. Zenk, 1999: The intermediate depth circulation of the western South Atlantic. Geophys. Res. Lett., 26, 3329–3332, https://doi.org/10.1029/1999GL002355.
Boebel, O., T. Rossby, J. Lutjeharms, W. Zenk, and C. Barron, 2003: Path and variability of the Agulhas Return Current. Deep-Sea Res. II, 50, 35–56, https://doi.org/10.1016/S0967-0645(02)00377-6.
Boebel, O., and Coauthors, 2017: The Expedition PS103 of the Research Vessel POLARSTERN to the Weddell Sea in 2016/2017. Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung Rep., 160 pp., https://doi.org/10.2312/BzPM_0710_2017.
Boebel, O., and Coauthors, 2019: The Expedition PS117 of the Research Vessel POLARSTERN to the Weddell Sea in 2018/2019. Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung Rep., 205 pp., https://doi.org/10.2312/BzPM_0732_2019.
Boebel, O., L. Probst, and C. Hancock, 2023: artoa4argo software package for acoustic tracking of RAFOS-enabled Argo floats, version 4.318. Zenodo, https://doi.org/10.5281/zenodo.7588848.
Bower, A. S., and W.-J. von Appen, 2008: Interannual variability in the pathways of the North Atlantic current of the Mid-Atlantic Ridge and the impact of topography. J. Phys. Oceanogr., 38, 104–120, https://doi.org/10.1175/2007JPO3686.1.
Bower, A. S., S. Lozier, and S. Gray, 2011: Export of Labrador Sea Water from the subpolar North Atlantic: A Lagrangian perspective. Deep-Sea Res. II, 58, 1798–1818, https://doi.org/10.1016/j.dsr2.2010.10.060.
Chamberlain, P. M., L. D. Talley, M. R. Mazloff, S. C. Riser, K. Speer, A. R. Gray, and A. Schwartzman, 2018: Observing the ice-covered Weddell Gyre with profiling floats: Position uncertainties and correlation statistics. J. Geophys. Res. Oceans, 123, 8383–8410, https://doi.org/10.1029/2017JC012990.
Chamberlain, P. M., B. Cornuelle, L. D. Talley, K. Speer, C. Hancock, and S. Riser, 2022: Acoustic float tracking with the Kalman smoother. J. Atmos. Oceanic Technol., 40, 15–35, https://doi.org/10.1175/JTECH-D-21-0063.1.
D’Ortenzio, F., and Coauthors, 2014: Observing mixed layer depth, nitrate and chlorophyll concentrations in the northwestern Mediterranean: A combined satellite and NO3 profiling floats experiment. Geophys. Res. Lett., 41, 6443–6451, https://doi.org/10.1002/2014GL061020.
Fratantoni, D. M., T. K. McKee, B. A. Hodges, H. H. Furey, and J. M. Lund, 2010: CLIMODE bobber data report: July 2005–May 2009. WHOI Tech. Rep. WHOI-2010-03, 153 pp., https://apps.dtic.mil/sti/citations/ADA520794.
Furey, H., 2005: RAFOS float processing at the Woods Hole Oceanographic Institution. WHOI Tech. Rep. WHOI-02-2005 ARTOA 3 April 2005 Addendum, 4 pp., https://www.whoi.edu/science/PO/rafos/ARTOA3%20Addendum.pdf.
Furey, H., A. S. Bower, and P. L. Richardson, 2001: Warm water pathways in the northeastern North Atlantic: ACCE RAFOS float data report: November 1996–November 1999. WHOI Tech. Rep. WHOI-01-17, 161 pp., https://apps.dtic.mil/sti/tr/pdf/ADA398539.pdf.
Furey, H., A. S. Bower, P. Perez-Brunius, P. Hamilton, and R. Leben, 2018: Deep eddies in the Gulf of Mexico observed with floats. J. Phys. Oceanogr., 48, 2703–2719, https://doi.org/10.1175/JPO-D-17-0245.1.
Hancock, C., 2023: Under ice trajectories for RAFOS-enabled profiling floats in the Weddell Gyre. USAP Data Center, accessed 9 January 2023, https://doi.org/10.15784/601652.
Hancock, C., K. Speer, J. M. A. de Souza, and S. L. Morey, 2022: Dispersion of subsurface Lagrangian drifters in the northeastern Gulf of Mexico. Front. Mar. Sci., 9, 949338, https://doi.org/10.3389/fmars.2022.949338.
Klatt, O., O. Boebel, and E. Fahrbach, 2007: A profiling float’s sense of ice. J. Atmos. Oceanic Technol., 24, 1301–1308, https://doi.org/10.1175/JTECH2026.1.
König, H., and W. Zenk, 1992: Principles of RAFOS technology at the Institut für Meereskunde Kiel. Berichte aus dem Institut für Meereskunde an der Christian-Albrechts-Universität Kiel 222, 99 pp., https://oceanrep.geomar.de/id/eprint/24672/.
Lilly, J., and S. Elipot, 2021: jLab: A data analysis package for MATLAB, version1.7.1. Zenodo, accessed 1 June 2023, https://doi.org/10.5281/zenodo.4547006.
Oke, P. R., T. Rykova, G. S. Pilo, and J. L. Lovell, 2022: Estimating Argo float trajectories under ice. Earth Space Sci., 9, e2022EA002312, https://doi.org/10.1029/2022EA002312.
Ollitrault, M., 1999: MARVOR floats reveal intermediate circulation in the western equatorial and tropical South Atlantic (30°S to 5°N). International WOCE Newsletter, No. 34, WOCE International Project Office, Southampton, United Kingdom 7–10.
Ollitrault, M., M. Lankhorst, D. Frantantoni, P. Richardson, and W. Zenk, 2006: Zonal intermediate currents in the equatorial Atlantic Ocean. Geophys. Res. Lett., 33, L05605, https://doi.org/10.1029/2005GL025368.
Owens, W. B., 1984: A synoptic and statistical description of the Gulf Stream and subtropical gyre using SOFAR floats. J. Phys. Oceanogr., 14, 104–113, https://doi.org/10.1175/1520-0485(1984)014<0104:ASASDO>2.0.CO;2.
Owens, W. B., 1991: A statistical description of the mean circulation and eddy variability in the northwestern Atlantic using SOFAR floats. Prog. Oceanogr., 28, 257–303, https://doi.org/10.1016/0079-6611(91)90010-J.
Pérez-Brunius, P., H. Furey, A. Bower, P. Hamilton, J. Candela, P. Garcia-Carrillo, and R. Leben, 2018: Dominant circulation patterns of the deep Gulf of Mexico. J. Phys. Oceanogr., 48, 511–529, https://doi.org/10.1175/JPO-D-17-0140.1.
Ramsey, A. L., H. H. Furey, and A. S. Bower, 2018: Deep floats reveal ocean circulation patterns. Eos, 99, https://doi.org/10.1029/2018EO105549.
Reeve, K. A., O. Boebel, T. Kanzow, V. Strass, G. Rohards, and E. Fahrbach, 2016: A gridded data set of upper-ocean hydrographic properties in the Weddell Gyre obtained by objective mapping of Argo float measurements. Earth Syst. Sci. Data, 8, 15–40, https://doi.org/10.5194/essd-8-15-2016.
Reeve, K. A., O. Boebel, V. Strass, T. Kanzow, and R. Gerdes, 2019: Horizontal circulation and volume transports in the Weddell Sea derived from Argo float data. Prog. Oceanogr., 175, 263–283, https://doi.org/10.1016/j.pocean.2019.04.006.
Richardson, P. L., and S. L. Garzoli, 2003: Characteristics of intermediate water flow in the Benguela Current as measured with RAFOS floats. Deep-Sea Res. II, 50, 87–118, https://doi.org/10.1016/S0967-0645(02)00380-6.
Richardson, P. L., J. R. E. Lutjeharms, and O. Boebel, 2003: Introduction to the “Inter-ocean exchange around southern Africa.” Deep-Sea Res. II, 50, 1–12, https://doi.org/10.1016/S0967-0645(02)00376-4.
Roach, C. J., and K. Speer, 2019: Exchange of water between the Ross Gyre and ACC assessed by Lagrangian particle tracking. J. Geophys. Res. Oceans, 124, 4631–4643, https://doi.org/10.1029/2018JC014845.
Roach, C. J., D. Balwada, and K. Speer, 2016: Horizontal mixing in the Southern Ocean from Argo float trajectories. J. Geophys. Res. Oceans, 121, 5570–5586, https://doi.org/10.1002/2015JC011440.
Roach, C. J., D. Balwada, and K. Speer, 2018: Global observations of horizontal mixing from Argo float and surface drifter trajectories. J. Geophys. Res. Oceans, 123, 4560–4575, https://doi.org/10.1029/2018JC013750.
Rossby, T., D. Dorson, and J. Fontaine, 1986: The RAFOS system. J. Atmos. Oceanic Technol., 3, 672–679, https://doi.org/10.1175/1520-0426(1986)003<0672:TRS>2.0.CO;2.
Rudnickas, D., Jr., J. Palter, D. Hebert, and H. T. Rossby, 2019: Isopycnal mixing in the North Atlantic oxygen minimum zone revealed by RAFOS floats. J. Geophys. Res. Oceans, 124, 6478–6497, https://doi.org/10.1029/2019JC015148.
Rykova, T., and P. Oke, 2022: Argo trajectories under ice (Southern Hemisphere, version 2022.05). Zenodo, accessed 10 December 2022, https://doi.org/10.5281/ZENODO.6571146.
Spiesecke, S., 2018: Analysis and modelling of RAFOS signal propagation under the Antarctic sea-ice for positioning Argo floats. M.S. thesis, Dept. of Electronics Engineering, Hochschule Bremen City University of Applied Sciences and Alfred Wegener Institute, 78 pp., https://epic.awi.de/id/eprint/46737/1/2018_Spiesecke_Analysis_and%20modelling_of_RAFOS_signal_propagation.pdf.
Wong, A. P. S., and S. C. Riser, 2011: Profiling float observations of the upper ocean under sea ice off the Wilkes Land coast of Antarctica. J. Phys. Oceanogr., 41, 1102–1115, https://doi.org/10.1175/2011JPO4516.1.
Wooding, C. M., H. H. Furey, and M. A. Pachece, 2005: RAFOS float processing at the Woods Hole Oceanographic Institution. WHOI Tech. Rep. WHOI-2005-02, 35 pp., https://hdl.handle.net/1912/55.
Yamazaki, K., S. Aoki, K. Shimada, T. Kobayashi, and Y. Kitade, 2020: Structure of the subpolar gyre in the Australian-Antarctic Basin derived from Argo floats. J. Geophys. Res. Oceans, 125, e2019JC015406, https://doi.org/10.1029/2019JC015406.
Zenk, W., K. S. Topkos, and O. Boebel, 1992: New observations of meddy movement south of the Tejo Plateau. Geophys. Res. Lett., 19, 2389–2392, https://doi.org/10.1029/92GL02139.
Zilberman, N. V., D. H. Roemmich, and S. T. Gille, 2017: The East Pacific Rise Current: Topographic enhancement of the interior flow in the South Pacific Ocean. Geophys. Res. Lett., 44, 277–285, https://doi.org/10.1002/2016GL069039.
