Overall system design

The M-AUE system is designed to measure time series of 3D ambient currents or to mimic the vertical swimming behaviours of plankton. The overall design goal was to create a portable, easily deployed system that could provide 3D localizations at reasonable update rates in a relevant volume of water. An update rate of 1 min−1, 10s of vehicles and an areal coverage of at least 1 km2 was determined necessary for sampling internal waves and other submesoscale dynamics. The system consists of two basic components: small, freely drifting subsurface vehicles that can adjust their buoyancy to control depth and whose 3D trajectories can be measured underwater (Fig. 1a), and a set of moored global positioning system (GPS)-localized and synchronized spar buoy surface floats that produce a timed acoustic signal for underwater vehicle navigation (Fig. 1b).

Figure 1: M-AUE and Spar Buoy Pinger. (a) The 1.5 litre M-AUE in the ocean at an approximate depth of 3 m. (b) The pinger of the GPS-localized spar buoy with a 30 cm ruler at the base for scale. Full size image

M-AUE underwater vehicle localization

Typically, underwater vehicles are localized by responding acoustically to the interrogation of a known source, allowing measurement of separation distances via travel times. Unfortunately, generating this acoustic response requires significant energy that would increase the size and cost of the M-AUEs. Instead, acoustic pings generated by the GPS-localized surface floats are passively sensed by the subsurface M-AUEs. Each of the five surface floats transmits their ping in sequence, at precisely controlled times in a ‘round-robin’ manner. At the M-AUE, the set of sensed pings is recorded and subsequently combined—via measurement of their send–receive time intervals—with the known positions of the surface float at the time of the ping to estimate the temporally evolving set of M-AUE positions. Vertical positions are obtained via the pressure sensors on the M-AUEs.

The surface float’s ping waveform was a broadband chirp with frequency range from 8–15 kHz. The ith set of pings was transmitted with an interfloat pulse interval of Δt=2 s: the pinger on float (1, 2, 3, 4, 5) transmitted the pulse with start time T i seconds at times (T i , T i +Δt, T i +2Δt, T i +3Δt, T i +4Δt). A GPS-synchronized clock on the surface float was used to ensure microsecond transmit-time accuracy. This sequence is repeated continuously throughout the deployment. The 2-s interpulse interval ensures that the signal received at the M-AUEs can be uniquely assigned to the appropriate surface float.

The M-AUEs recorded the pings using a high-fidelity hydrophone and analogue-to-digital circuits for waveform recording. Postprocessing with a correlation receiver19 allowed estimation of the arrival time of the set of surface pings at each M-AUE with no ambiguity in assigning pings to their respective surface float. In addition, we note that it was generally easy to pick out the direct arrival from the matched filtered M-AUE hydrophone output, eliminating the need for more advanced environmental (sound speed) modelling or matched field processing.

Matched filtered acoustic data from each M-AUE were then processed to yield the two-dimensional (2D) locations of the vehicles in latitude and longitude. This was then combined with the vehicle’s measured depth to yield tracks of position in depth, latitude and longitude. The tracking is essentially an underwater analogue to GPS localization using a probabilistic framework. Our tracking method constructs a factor-graph representation of the joint probability density function for the lateral locations of the M-AUEs and surface pingers over the duration of the experiment given estimates of distance to the pingers and bounds on the velocity of the M-AUEs. The Maximum Likelihood estimates of the 2D locations of the M-AUEs are computed by running the sum-product algorithm on the factor-graph as described in our previous work20,21. This algorithm was tested at sea using a GPS-localized hydrophone suspended at a known depth (an M-AUE mimic) and the five surface-float pingers described above22. The algorithm showed very low bias in hydrophone locations, with s.e. on the order of a few metres laterally over a 2-km drift track.

The surface float pinger

The surface float pinger is a 1.5-m long spar buoy with a submerged acoustic transducer (Fig. 1b). The surface floats receive satellite GPS location information that is time-encoded for postmission processing. For the field experiments, the spar buoys were clipped to a simple, easily deployed and recovered mooring made from a 1/4-inch single braid line with 2:1 scope and a 10-kg shackle as an anchor. More details can be found in the Methods section.

The M-AUE vehicle

The M-AUE (Fig. 2) is a self-ballasting, cylindrical, 1.5-litre volume subsurface drifter that can be tracked underwater in 3D. The small size maximizes the surface area to volume ratio, increasing the vehicle’s ability to drift with the currents. The vehicle has active buoyancy control to execute vertical movements. To maintain the small size, no propulsion system was incorporated. The M-AUE’s electronic and mechanical components were designed to achieve the following mission requirements: it must be hand-deployable from a small boat, acoustically record the surface pings with adequate signal-to-noise ratio to estimate arrival times, execute preprogrammed vertical movements—including depth holding—using buoyancy control, be sufficiently buoyant at the surface to elevate the antenna far enough out of the water for satellite communication, and record depth and temperature. The vehicles need to surface for recovery, then obtain and communicate its GPS position to a retrieving party via satellite, internet or cell phone and have a radio beacon and light-emitting diode strobe to aid in visual recovery. Each vehicle must have sufficient battery energy to perform missions up to several days with a limited number of vertical excursions and have adequate memory to store all vehicle sensor information including the acoustic records, as well as information about the internal state of the vehicle.

Figure 2: An exploded view of the M-AUE vehicle. (a) The M-AUE in closed position. (b) The two concentric shells of the M-AUE separated to reveal the internal components. Full size image

The housing of the M-AUE consists of two concentric, syntactic foam cylinders forming inner and outer sleeves that can slide over each other to significantly increase or decrease the vehicle’s volume (Fig. 2). This large change in volume allows the vehicle to raise its antenna far enough above the sea surface, when surfaced, so that the satellite links for GPS and the Globalstar network are functional (Supplementary Fig. 1). The vehicle also uses a smaller piston to create incremental changes in vehicle volume while fully submerged to produce the small changes in density necessary for the vehicle to regulate its depth. The total change in volume that is possible with the small piston is ±0.4% with 12,000 increments over the entire piston range. A geared motor whose shaft is equipped with an optical encoder rotates a threaded rod that controls the small piston. When the piston reaches the end of its translation, the threaded rod then pushes the cylinders apart (Supplementary Fig. 1). In a range of density stratifications off San Diego, USA, the combined system was found to provide adequate control of depth in the upper 50 m of the water column while also providing enough buoyancy at the surface to acquire satellite links.

Vehicle depth-control algorithm

The M-AUE moves vertically solely via buoyancy control; thus control of vehicle density—and hence position in the water column—is critical. To use the swarm of M-AUEs to measure the horizontal strain of the internal wave field, simple vertical profiling was augmented with the more stringent requirement of depth holding.

Maintaining a given depth requires an algorithm to change the vehicle’s buoyancy when ambient currents or changes in density move it vertically. We use the PID control algorithm23, which has three adjustable coefficients: the proportional gain, the derivative gain, and the integral gain. These are used to actuate the piston to minimize the difference between the desired depth and the actual depth, with the goal of ultimately converging to the target depth. Although it would be optimal to fix the vehicle’s density to achieve a desired density surface, in practice, this is nearly impossible for a compressible vehicle. To accommodate vehicle compressibility, a two-state PID controller was developed: one set of control gains was used at the surface, transitioning to another set when a given target set of conditions was met at depth. In subsequent sea trials, the vehicles were programmed to hold 10 m depth in 40 m of water off San Diego, CA, USA. Over 5 h, the vehicles remained at 10±1.02 m, even during the passage of significant high-frequency nonlinear internal waves (Fig. 3).

Figure 3: Depth-holding ability of the 16 M-AUEs for the 5-hour at-sea experiment. Once at depth, the M-AUEs maintained their target of 10 m with an s.e. of ± 1.02 m using small motions of the piston to counteract vertical currents and density changes caused by internal waves. Black lines show depths of individual M-AUEs. Red vertical lines show the times of panels a–f in figure 5, and gray shaded area shows the time period of panels g and h in figure 5. Full size image

Internal wave measurements by the M-AUE swarm

Upon completion of vehicle construction, tank tests and initial sea tests, an experiment was conducted 3 km west of Torrey Pines beach near San Diego, CA, USA over several days in late September–early October 2013. To test accumulation of depth-holding plankton in internal waves, 16 M-AUE vehicles were deployed inside a 3-km diameter pentagonal array of moored surface-float pingers and programmed to maintain depth at 10 m for 5 h (Fig. 4). 3D locations were obtained every 12 s with an estimated s.d. of ±1 m horizontally and <1 cm vertically. An animation of the estimated vehicle positions over the course of the experiment is shown in Supplementary Movie 3. A moored wirewalker24 equipped with a CTD provided environmental context through vertical profiles every 7 min.

Figure 4: An overview of the field site off Torrey Pines in San Diego. (a) The locations of the 5 pingers P1–P5 are shown relative to the local bathymetry. The white box contains a plan view of the measured trajectories of the 16 M-AUEs during the 5-hour deployment. (b) The trajectories of the 16 M-AUE once they had reached the target depth of 10 m. Each trajectory is colored according to the time since deployment. Full size image

To identify high-frequency internal waves, temperature anomalies were calculated as residuals from the 5-h quadratic loess-smoothed temperature records from the individual M-AUEs using a window of 15% of the data. Spatial contours of the temperature anomalies clearly show high-frequency internal waves propagating through the M-AUE swarm (Fig. 5, Supplementary Movie 4).

Figure 5: M-AUE swarm showing accumulation in internal wave troughs. (a–f) Alongshore/cross-shore maps of the temperature anomaly within the M-AUE swarm. Black circles are M-AUE locations in a coordinate system centred at the centre of mass of the swarm. Warm colours indicate internal wave troughs, cold colours the crests. (g,h) Section of the 5-h time series of average temperature in the M-AUE swarm and the M-AUE concentration (numbers m−2), showing changes owing to internal waves propagating through the depth-holding swarm. Red line denotes the data and black line the model (see text for details). Vertical black lines show times corresponding to the six upper panels. Accumulation of M-AUEs over the warm waters of the wave trough supports the model predictions. Full size image

Theoretical models13,14,16,17,18 predict that depth-holding objects in the upper water column should accumulate over the troughs of internal waves (that is, in warm water) and disperse over the wave crests (cold water). Changes in concentration of the M-AUEs were calculated from changes in the area of the swarm: smaller areas indicate higher concentrations (Fig. 5). As predicted by theory, the swarm concentrated over wave troughs and dispersed over wave crests. The changes in M-AUE concentration of ∼30% during the 40-min period shown in Fig. 5 were consistent with linear theory14; however, the up to 2 × changes in M-AUE concentration over the course of the ∼5-h deployment are indicative of nonlinear high-frequency internal wave activity.

The depth-holding M-AUE swarm acted as a 2D sensing array, enabling accurate detection and quantification of the underlying flows. In particular, the swarm can resolve the wave direction, phase speed, amplitude or the presence of multiple waves with different properties. The wavelength, frequency and phase speed of the dominant (onshore-propagating) waves were diagnosed from cross-correlations of temperature fluctuations in time and space among the M-AUEs (Supplementary Fig. 2). A model of depth-holding objects in a linear internal wave in a linear density gradient25 parameterized with these data gave excellent agreement with the changes observed in the M-AUE swarm (Fig. 5). The simple linear theory explained 92% of the observed temperature variance and 88% of the variance of the M-AUE concentration during the 40-min period shown in Fig. 5.