Editorial Type:
Article
Article Type:
Research Article

Swish Floats: An Inexpensive Neutrally Buoyant Float to Monitor Dispersion in Coastal Seas

Samuel W. Stevens aDepartment of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

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https://orcid.org/0000-0003-1108-6578
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Rich Pawlowicz aDepartment of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

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Online Publication:
22 Nov 2023
Print Publication:
01 Nov 2023
DOI:
https://doi.org/10.1175/JTECH-D-23-0045.1
Page(s):
1493–1508
Free access

Abstract

Neutrally buoyant floats have been widely used to measure flows in the ocean, but deploying them in large numbers can be costly and impractical. This is particularly true near coastlines due to the elevated risk of instrument grounding or vessel collisions, resulting in a lack of subsurface Lagrangian measurements in coastal regions. Here, we describe an inexpensive neutrally buoyant satellite-tracked float (named “Swallow-ish,” or “Swish” floats) that has been designed and tested as a cost-effective strategy to measure subsurface dispersion in coastal areas on time scales up to a month. These autonomous instruments are inexpensive, constructed at a material cost of CAD $300 per unit; lightweight, with a mass of 5.4 kg; isopycnal; and constructed from commercially available components, using recently available global navigation satellite system technology to provide the user with a point-to-point measure of subsurface transport. We describe the float design, ballasting techniques, and the governing equations that determine their behavior. Further, through 29 deployments in two coastal seas, we calculate an uncertainty budget and determine a ballasting error of ±1.6 g, corresponding to a local depth targeting error of 16–30 m, analyze the float resurfacing data to calculate subsurface dispersion coefficients, and examine the float depth records to quantify the local internal wave field. Finally, we evaluate surface dispersion using the postresurfacing trajectories. Our findings indicate that Swish floats offer a cost-effective alternative for Lagrangian measurements of subsurface flows in coastal regions.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Samuel W. Stevens, sstevens@eoas.ubc.ca

Abstract

Neutrally buoyant floats have been widely used to measure flows in the ocean, but deploying them in large numbers can be costly and impractical. This is particularly true near coastlines due to the elevated risk of instrument grounding or vessel collisions, resulting in a lack of subsurface Lagrangian measurements in coastal regions. Here, we describe an inexpensive neutrally buoyant satellite-tracked float (named “Swallow-ish,” or “Swish” floats) that has been designed and tested as a cost-effective strategy to measure subsurface dispersion in coastal areas on time scales up to a month. These autonomous instruments are inexpensive, constructed at a material cost of CAD $300 per unit; lightweight, with a mass of 5.4 kg; isopycnal; and constructed from commercially available components, using recently available global navigation satellite system technology to provide the user with a point-to-point measure of subsurface transport. We describe the float design, ballasting techniques, and the governing equations that determine their behavior. Further, through 29 deployments in two coastal seas, we calculate an uncertainty budget and determine a ballasting error of ±1.6 g, corresponding to a local depth targeting error of 16–30 m, analyze the float resurfacing data to calculate subsurface dispersion coefficients, and examine the float depth records to quantify the local internal wave field. Finally, we evaluate surface dispersion using the postresurfacing trajectories. Our findings indicate that Swish floats offer a cost-effective alternative for Lagrangian measurements of subsurface flows in coastal regions.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Samuel W. Stevens, sstevens@eoas.ubc.ca
Keywords: Lagrangian circulation/transport; Ocean circulation; In situ oceanic observations; Instrumentation/sensors

1. Introduction

The direct measurement of subsurface ocean currents using neutrally buoyant floats has been a common practice among oceanographers for decades (Gould 2005). These free-floating instruments track the movement of water parcels and can provide a kinematic description of a system. Following the neutrally buoyant “Swallow floats” of the 1950s (Swallow 1955), floats have been deployed to measure the paths, structures, and variability of features such as mesoscale eddies (Prater 2002; Shoosmith et al. 2005), internal waves (D’Asaro 2003; Goodman and Levine 1990), Rossby waves (Hamilton 2009), and basin-scale current systems (Bower et al. 2011; Lozier et al. 2022). When using neutrally buoyant floats for these purposes, it is preferable to gather many individual observations of a flow to improve the statistical significance of any determinations of a mean flow over a period of time. Collecting a large number of these observations can be costly, however, and it is therefore desirable to find ways to reduce the cost of each individual measurement. While various low-cost surface drifter systems have been developed that implement inexpensive tracking devices to measure surface flows (e.g., Pawlowicz et al. 2019; Pawlowicz 2021; Novelli et al. 2017; Meyerjürgens et al. 2019; Page et al. 2019), less attention has been given to the production of an inexpensive float system for subsurface flows.

Many coastal and inland seas have deep circulation that is not well known and could benefit greatly from an inexpensive measure of their internal dynamics. While the number of subsurface Lagrangian observations in the open ocean has been growing in the past few decades as a result of global initiatives such as the Argo program (Wong et al. 2020), observations in coastal and marginal seas remain limited as they are often a more complicated and riskier proposition. This is largely due to strong tides, challenges with float buoyancy control as a result of increased water column density variability, and a heightened probability that expensive instrumentation will run aground or collide with ships and other vessels (Pawlowicz 2021). Moreover, access to the usual frameworks for underwater telemetry such as acoustic sources or hydrophones (like those employed in RAFOS floats; Richardson et al. 1981) is often unavailable or hard to establish due to elevated levels of low-frequency ambient noise in areas of increased vessel traffic (e.g., Bassett et al. 2012).

Examples of floats deployed for the specific purpose of coastal monitoring are scarce, although efforts have been made to develop floats to measure coastal upwelling (Hebert et al. 1997), and to deploy profiling floats in Arctic (Sandby et al. 2021) and marginal seas (e.g., the Mediterranean Sea and the Black Sea; Korotaev et al. 2006; Poulain et al. 2007). Other modern Lagrangian methodologies such as the release and recapture of magnetically attractive particles (Hrycik et al. 2013) offer comparable frameworks to track dispersion but require further development and testing on larger space and time scales. This lack of measurements highlights the utility of low-cost Lagrangian solutions where the financial risk is reduced and no single instrument is pivotal to the monitoring scheme.

In this paper, we describe a simple neutrally buoyant satellite-tracked float that has been developed to measure subsurface dispersion in coastal regions at a material cost of CAD $300 per unit. The initial motivation for the float design outlined here is the need to better understand flows in a layer at depths of 50–200 m in the Strait of Georgia, Canada (Stevens et al. 2021), but similar problems also arise in other regions where shipping traffic can result in a significant risk factor for unattended deployment of Lagrangian instruments with a surface element, and where layered flows exist but bathymetry is complex enough that current meters are not always useful [e.g., the Gulf of Saint Lawrence (Han et al. 1999), the Chiloé Inner Sea (Strub et al. 2019), and a number of other fjordal areas worldwide]. Our floats share some passing similarities with the original Swallow floats; thus, they are nicknamed “Swallow-ish,” or Swish floats. Here, we describe the Swish float design, including the construction materials, engineering principles, and testing of the float components; outline the equations that govern a float’s behavior during its drift period; discuss the ballasting procedure; and present the results from initial deployments in coastal waters to evaluate performance and provide examples of possible analysis techniques.

2. Objectives

The scientific goal of the Swish floats is to measure subsurface flows for periods up to 1 month. To achieve this, the floats must sink to a preselected depth following deployment at a known time and location, after which they become neutrally buoyant and drift with the prevailing currents for a period of time. Although their location is not known during this drift, after a predetermined time, the floats then jettison a sufficient mass to become positively buoyant, resurface, and automatically begin reporting a global navigation satellite system (GNSS)-derived position via a satellite telemetry link. The exactly known time and distance between the deployment and the resurfacing position provide a single-point Lagrangian displacement that is the integral of the in situ motions while drifting at depth (Rossby and Dorson 1983). The neutral buoyancy depth of the float during its drift is dependent on the float mass; the float volume, which varies dynamically throughout the deployment due to in situ pressure and temperature changes; and the prevailing isopycnal structure of the water column. The floats can be treated as single-use expendable instruments or, in certain circumstances, can be recovered once resurfaced—in this case, the floats can be used as a limited platform for internally recording sensors and/or reused. Secondarily, the floats provide a surface trajectory upon resurfacing until the GNSS unit loses power.

To achieve this scientific goal, the following design criteria were specified:

  1. Affordability and ease of construction: To increase the statistical significance of drift measurements, it is desirable to maximize the number of measurements and minimize the expense associated with collecting these measurements. Thus, at every level of the design process, simplicity of manufacturing and reduction of cost is emphasized. This specification promotes the use of off-the-shelf components that require limited customization by the user.

  2. Reliability of operation: The float housing must be watertight and resistant to crushing at target pressures, large enough to accommodate the necessary electronics, relatively resistant to the elastic effects of pressure and thermal expansion, resistant to plastic deformation, and resistant to corrosion. The resurfacing mechanism must be reliable and configurable for a variety of time scales.

  3. Accuracy of positioning: As the primary goal of this float is to consider transport on time scales up to 1 month, a simple point-to-point measure of float travel between deployment at time = t and resurfacing at t + Δt suffices for a basic understanding of the advective and diffusive characteristics of a system. This geolocation is easily achieved using commercially available GNSS units. To allow GNSS communication, the float must be permeable to electromagnetic radiation and the surface expression of the float must be upright with an appropriate freeboard to ensure that the GNSS unit is orientated skyward with an unobstructed view.

3. Design

a. GNSS unit

The modern technology that allows us to economically communicate the surface positions of the floats is the now widely available commercial asset tracker. These trackers can return position data at frequent intervals using either cell phone or low-Earth-orbit satellite systems. We use the SPOT Trace (SPOT LLC, Louisiana) at a cost of CAD $150–$190 per unit. The units have a waterproof case, are powered internally by four lithium AA cells, are 7 cm × 5 cm × 2 cm in size, and weigh 90 g. These units have been tested at length during various surface drifter experiments (Pawlowicz et al. 2019; Pawlowicz 2021) and have been found to transmit reliable GNSS locations via the Globalstar constellation of low-Earth-orbit satellites with lifetimes of weeks to months. Tests on land find that the standard error in positions from the units is about 2.5 m, uncorrelated from fix to fix. The systems can be programmed to transmit every 5, 10, 30, or 60 min and are vibration activated, meaning that they cannot be mounted in a stationary manner: to combat this, the GNSS units are hung by a line within the housing (see schematic in Fig. 1) so that when the float surfaces, the wave-induced movement of the hanging unit causes vibration due to contact with the hull, activating the system. The units can be programmed for increased sensitivity to further promote activation; however, in calm sea states, the GNSS transmission can pause for periods until surface wave energy increases sufficiently to reactivate the unit. The surface battery life of these units suggests that no significant activation occurs while the floats are submerged.

Fig. 1.
Fig. 1.

(left) Swish float schematic with coarse measurements (cm; 2:1 vertical to horizontal scale), (center) an internal view of a float, and (right) a labeled photograph of two Swish floats. Note the previously deployed and recovered red float (rightmost) with a temperature–depth (TD) sensor attachment and a bridle to aid recovery from a vessel.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

b. Housing

The float housing design consists of a cylindrical hull and watertight top and bottom endcaps (Fig. 1). The hull must be wide enough to contain the satellite communications package and long enough relative to its width to float upright when surfaced. This requires a hull with an inside width of about 10 cm for our asset tracker, and thus a length of at least 50 cm or so (i.e., a volume of about 5 L), as an initial size specification. In addition, the float must be sufficiently rigid so that it will not crumple at the pressures of interest, nor should its volume decrease too quickly under pressure loading so that it would sink to the bottom uncrumpled. The compressibility of a volume V of seawater due to changes in pressure P is about γw = −4.4 × 10−6 dbar−1 and so float compressibilities should be of that magnitude or less. However, we also want to reduce material costs as much as possible, which implies that optimal design properties will tend toward to greatest compressibility within that design range.

To select materials with the appropriate properties, we first approximate the overall compressibility of a float by calculating the contribution of each external component to the compressibility. If we class the float cylindrical hull as an intermediate length thin-walled pressure vessel (i.e., length/radius = 0.1–100 and radius ≫ hull wall thickness), we can model its pressure response as follows (ASME 2019):
ϵΘ=−PREt(1−υ2),
ϵz=−PREt(12−υ),
γ=−1Vh∂Vh∂P=2ϵΘ+ϵz=−PREt(5−4υ2),
where γ is the compressibility coefficient; Vh is the hull volume; P is the external pressure; ϵΘ is the hoop strain; ϵz is the longitudinal stress; and R, t, E, and υ are the radius, wall thickness, Young’s modulus, and Poisson ratio of the hull material, respectively.
The endcap contribution to a float’s compressibility will be due primarily to the inward bowing of the endcaps due to axial stress. If we class the endcap as a simply supported thin circular plate under a uniformly distributed load (Budynas and Sadegh 2020), we can model the endcap inward displacement as a function of pressure. While the endcaps do not perfectly meet the criteria of a thin plate (i.e., thickness/radius ≤ 0.1), this basic approximation will suffice for a first-order estimate of endcap bowing. For a cylinder of height H and an endcap with thickness l, we can integrate the circular plate displacement function to obtain the endcap contribution to compressibility by inward bowing as follows:
γe=116PE(1−υ)(5+υ)R4Hl3.
In addition to having an adequate rigidity, we also need to make sure that catastrophic failure will not occur at the pressures of interest. The first mode of failure in a cylindrical pressure vessel will likely be due to an elastic buckling of the hull (Sharp 1981). We can calculate the buckling pressure of the hull to determine the maximum useful depth of the floats:
Pb=2E1−υ2(t2R)3.
It has been shown in pressure tank experiments that this theoretical buckling pressure Pb of cylindrical hulls is a good estimate of actual buckling pressure (Ikeda et al. 2013).

After considering and testing various options, we decided to construct the hull from aluminum 6061 T6 alloy tubing. This material was chosen as it is, among other things, inexpensive, purchased from a local supplier for CAD $13 per foot; easily machined; easily sealed using a simple plug style endcap; relatively incompressible; and relatively resistant to mass changes due to corrosion (D’Asaro 2003). While borosilicate glass is sometimes favored for float construction (Rossby and Dorson 1983), it is significantly more expensive, costing (locally) almost 8 times as much as an aluminum tube of similar dimensions. Plastics such as polyvinyl chloride (PVC) and acrylonitrile butadiene (ABS) are less expensive materials that are sometimes used for low-cost pressure housings; however, the relatively high compressibility of cylindrical hulls constructed from these materials in easily available thicknesses precludes them from being an effective float hull material, even though they may be resistant to buckling.

A H = 61 cm (2 ft; where appropriate, design measurements will be provided with imperial conversions in parentheses as these are often the standard units used in purchasing and manufacturing) length of aluminum tube was chosen as roughly the shortest—and therefore least expensive and easiest to handle—hull that could float upright at the surface. Note that we specify “tube” here as opposed to “pipe,” the difference being that tubing has a lower manufacturing tolerance on the outer diameter (OD), which we found more suitable for design and machining purposes, whereas pipe has a lower tolerance on the inner diameter (ID).

From Eqs. (1)–(3), it follows that doubling the hull wall thickness t or halving the hull radius R will halve the hull compressibility γ; thus, it is necessary to carefully select the wall thickness and the radius of the hull to construct a float with the desired compressibility. Although a number of standard wall thickness options ranging from t = 0.12–1.9 cm are available for tubes of this diameter, a wall thickness of t = 0.32 cm (1/8 in.) was judged to be best for the hulls. While thicker-walled tubes would produce less compressible hulls (which, as we show below, would have some advantages), we found hulls with t > 0.32 cm to be harder to machine in addition to being more expensive. The narrowest standard-sized t = 0.32-cm aluminum tube available from local suppliers that could accommodate the GNSS unit was nominally listed with an OD = 10.2 cm (4 in.) and an ID = 9.9 cm. Per Eqs. (1)–(3), a hull with r = 5.1 cm, t = 0.32 cm, E = 69 × 105 Pa, and υ = 0.33 (material properties from Dexter 1972) yields an estimated compressibility of γ = −4.3 × 10−6 dbar−1. These hulls have a volume Vh = 4.93 × 10−3 m3 and a buckling pressure Pb = 472 dbar, which is sufficient for most coastal regions.

Flanged plug-style endcaps were manufactured with a recessed O-ring on the inner flange to seal the float and to allow endcap expansion without cracking or leaking (see Fig. 1). The top endcap is a 3.3 cm (1.3 in.) thick, 10.2 cm (4 in.) OD plug constructed from PVC and firmly seated using a latch mechanism composed of steel wire and a small hose clamp. It is constructed from PVC to allow GNSS signal transmission through the housing. The bottom endcap is a 3.3 cm (1.3 in.) thick, 10.2 cm (4 in.) OD aluminum plug which is glued permanently shut upon assembly, designed to bolster the incompressibility of the float. For the PVC top endcap, γet=−0.2×10−6 dbar−1, while for the aluminum bottom endcap, γeb=−0.001×10−6 dbar−1. This gives a cumulative compressibility for the Swish float of γd=γ+γet+γeb=−4.5×10−6dbar−1, whereby the endcap contribution to the overall compressibility is 5%. Note that the floats are slightly more compressible than seawater (γd < γw); we shall show that in a stably stratified ocean, this compressibility will be sufficient to achieve neutral buoyancy. We provide an engineering drawing of a Swish float housing at https://doi.org/10.5281/zenodo.8173038.

c. Pressure testing

While section 3b provides an approximation of housing compression and buckling that aids in the selection of construction materials, it is beneficial for accurate ballasting to directly measure these properties. To achieve this, the float housings were tested in a pressure tank facility where they were pressurized to at least 250 dbar to (i) ensure the structural integrity of the floats to ocean depths of at least 240 m and (ii) to directly measure housing compressibility γm to compare with γd. We can directly measure the coefficient γm of a float by pressurizing the housing and measuring the internal pressure Pi and absolute temperature Ti response as a function of external pressure Pe. These measurements were achieved using an Arduino BMP180 sensor placed inside the housing. Assuming the air inside the cylinder behaves as an ideal gas, we can approximate γm for small displacements as follows:
γm=1V∂V∂Pe≈1ΔPe(ΔTiTi−ΔPiPi).
The volume response and γm of eight individual housings were measured by pressure cycling each housing between 30 and 250–300 dbar a number of times (Fig. 2). The coefficient γm ranged from −8.0 × 10−6 to −4.3 × 10−6 dbar−1 with a mean of γm¯=−6.4×10−6 dbar−1, which is 30% larger than γd. As a directly measured property of the float housing, we use γm¯ as the overall float compressibility during ballasting and analysis. Pressure testing also showed that the latch mechanism increases γm by 0.3 × 10−6 dbar−1 (i.e., makes the float less compressible). This phenomenon is likely related to the seating of the top endcap O-ring, which is precompressed when the endcap is securely latched.
Fig. 2.
Fig. 2.

Swish float compression (a) measured in pressure tank experiments as a function of external pressure Pe (blue scatter points) and (b) derived γm.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

d. Thermal expansion

One drawback of using metal for the float hull, in contrast to glass, is that it can undergo significant thermal expansion. Thus, we must also consider the change in float volume due to this thermal expansion. Making direct measurements of a float’s thermal expansion coefficient α is difficult; however, the thermal expansion coefficient of a float can be estimated by taking the volume-weighted average of the coefficients of its external components:
α=1V∂V∂T=Vaαa+VpαpVa+Vp,
where T is the float temperature and subscripts a and p refer to the aluminum (αa = 71 × 10−6 °C−1) and PVC (αp = 80 × 10−6 °C−1) components that are in direct contact with the water (Dexter 1972). For the Swish floats, this yields α = 71 × 10−6 °C−1 which is functionally identical to αa due to the large proportion of external aluminum and similarity in αa and αp.

e. Release mechanism

To return the floats to the surface at the end of their deployments, a release mechanism is required to jettison the drop weight after a set duration. An inexpensive (CAD $3–$15 per unit), reliable, and commercially available solution is a galvanic timed release (GTR; also known as pop-up release): a simple sacrificial link that consists of two plated cathodic wire eyes seated in precisely machined anodic metal alloy cylinders (Fig. 1). Most commonly used for fishing, the GTRs electrochemically degrade when placed in seawater and release after a preset period of time that depends primarily on (i) the amount of galvanic material in the alloy cylinder, ranging in volume from VGTR 0.4 to 4.8 cm3; and (ii) the temperature of the ambient water (warmer water increases the rate of degradation and vice versa). The time scales of the GTRs range from 1 to 30 days with a nominal manufacturing accuracy of ±2.5% of the GTR duration. The drop weight weighs 1.1 kg and is made from a 7.6-cm length of 5.1-cm diameter hot-rolled steel bar with a hole drilled through the center for ease of attachment; once released, the float will have significant positive buoyancy.

Tests have shown that the in situ lifespan of the GTRs is often less predictable than the manufacturer-stated accuracy due to two main reasons: 1) the ambient water may be warmer or colder than anticipated, decreasing or increasing the lifespan of a release, respectively; and 2) prior to deployment, the GTRs are submerged in saltwater for a varying amount of time during the ballasting process, reducing the in situ lifespan of the release.

Another characteristic of the GTRs’ gradual loss of galvanic material is a reduction in the mass of the float coupled with a loss in volume and therefore buoyancy. The density of the galvanic alloy is approximately ρGTR = 1600 kg m−3; therefore, any loss of galvanic material will increase the buoyancy of the float. This buoyancy increase can be calculated as MGTR = VGTR(ρ − ρGTR) in seawater of density ρ and ranges from 0.2 g for the shorter releases to 2.8 g for the longest releases. The consequences of this for float behavior will be discussed later.

f. Other design features

Some other important design features are listed here and labeled in Fig. 1. Externally, stainless steel D-rings are fastened to the housing using a stainless steel hose clamp to serve as attachment points and for ease of handling. The release mechanism is attached to these D-rings using nylon monofilament line, which is then threaded through the drop weight and tied to a stainless steel washer to secure the weight. The line is held in place on either side of the hull using two smaller stainless steel D-rings attached with glue or epoxy resin.

A handful of the floats were designed for recovery from a vessel—these floats are spray-painted red for visibility, have a short wire lanyard and steel clip to attach small sensors, and have a 1.2-m-long wire bridle to aid recovery. Internally, a 7.6 cm long × 5.1 cm radius hot-rolled steel bar weighing approximately 1.2 kg is glued to the inner-bottom endcap to ensure that the floats are upright at the surface with the GNSS unit sufficiently above sea level when drifting; in this configuration, the floats extend 18 cm above the waterline.

4. Principles of operation

Assuming conditions of hydrostatic balance, a float will be neutrally buoyant when its mass Mf is equal to the mass Mt of water it displaces (Swift and Riser 1994). The mass of displaced water is
Mt(S,T,P)=ρ(S,T,P)V(T,P),
where P, S, T, and ρ(S, T, P) are the in situ pressure, salinity, temperature, and density of the ambient water.
We can determine the float mass Mf required to target a depth by calculating the mass of water the float displaces at that target depth:
Mf(S,T,P)=M0+V0[ρc(S,T,P)−ρ0]+ρc(S,T,P)ΔV,
where
ΔV=V0[α(T0−T)+γP].
The required float mass Eq. (9) consists of three terms: the first term is the mass of a float M0 that is neutrally buoyant in a fluid with density ρ0 (say, in a ballasting tank). The second term applies a mass correction using the initial float volume V0 and the difference between the ballasting density ρ0 and the in situ ocean density ρc(S, T, P) to correct the mass (note that small corrections to these density terms are discussed in the following section). The third term is a further mass correction that uses the ballasting tank temperature T0 and the in situ ocean temperature T and pressure P to account for in situ changes in float volume ΔV due to compression and thermal expansion. To implement Eq. (9), the user must first ballast the float to neutral buoyancy in a fluid of known density, have an understanding of the compressibility and thermal expansion properties of the float (previously discussed in sections 3b–d), and have prior knowledge of the temperature and density structure of the body of water into which the floats are being deployed.

5. Ballasting

a. Ballasting tank

Practically implementing Eq. (9) requires careful ballasting of a float in a tank of fluid. As we shall discuss below, a target accuracy for this ballasting process is about 0.1 kg m−3. In contrast, the accuracy of ballasting calculations for ocean gliders is typically an order of magnitude less stringent as they have a buoyancy engine which can change their effective density by O(10) kg m−3. The floats are ballasted using a 227-L (60 gallon) drum of freshwater that is tuned to density close to that of the target ocean by the addition of Instant Ocean, a readily available aquarium-grade salt mixture that dissolves freely into the freshwater. The temperature T0 and conductivity of the tank are measured frequently during the ballasting process using a CTD, and tank density is derived from these measurements.

As the ionic composition of Instant Ocean does not perfectly mimic that of seawater, its density will differ from that of seawater of the same conductivity. In the language of the Thermodynamic Equation of Seawater—2010 (TEOS-10) standard (IOC et al. 2010), there is an Absolute Salinity anomaly δSA associated with the density error δρA that occurs when ρ0 is calculated from CTD measurements using formulas that are associated with the specific chemical composition of seawater. One problem with commercial salt preparations is that their composition can vary widely (Atkinson and Bingman. 1997) and so their TEOS-10 Absolute Salinity anomaly is not known. Thus, we supplement the frequent CTD measurements by direct density determinations using an Anton Paar DMA 5000 benchtop density meter to measure the density of water samples to an accuracy of ±0.01 kg m−3. The difference between these measurements is used to calculate a calibration term Δρ. This term is applied to calibrate the tank density ρ0 = ρ′ + Δρ, where ρ′ is the measured tank density.

We found that this calibration varies not only between different commercial preparations but also between seawaters made from different batches of the same product. Seawaters made from one batch had a measured Absolute Salinity anomaly δSA = 0.05 g kg−1 leading to a density error δρA = 0.04 kg m−3, whereas the seawaters made from a second batch had an Absolute Salinity anomaly δSA = −0.20 g kg−1 leading to a density error δρA = −0.15 kg m−3. This indicates that δρA should be measured regularly.

In addition to inaccurate conductivity-derived densities of the ballast tank seawater, note that the TEOS-10 Absolute Salinity anomaly for seawater in coastal areas may also be nonzero. Calculated values vary from δρA = 0.02 to 0.3 kg m−3 in different coastal regions (Pawlowicz 2015). A density anomaly correction term δρA = 0.02 kg m−3 was calculated for both the Strait of Georgia and Gulf of Saint Lawrence Intermediate Waters based on the ionic composition of the relevant water masses and applied to the in situ density term ρc(S, T, P) = ρ′(S, T, P) + δρA, where ρ′(S, T, P) is the measured or estimated in situ density.

Finally, experience has shown that tuning tank density ρ0 close to target density ρc(S, T, P) is desirable, as any error present in the ballasting procedure will scale as ρc(S, T, P) − ρ0 increases. Thus, it is necessary to use an artificial seawater in this procedure, in spite of the extra complications that ensue, over using (say) tap water for which an equation of state is known to much greater precision.

b. Ballasting procedure

To roughly ballast the float, links of small gauge scrap chain are added until the float mass is approximately 5.5 kg. The float is placed into the ballasting tank, and the mass of the float in water (Mw) is fine-tuned using 4.5-mm caliber steel ball bearing (BB) pellets weighing 0.35 ± 0.003 g each until the float is neutrally buoyant within the tank. This neutral buoyancy point is identified by hanging the float from the underfloor weighing mechanism of a balance and iteratively adding/removing ballast inside the float until the float is approximately neutrally buoyant (i.e., the float weight in water Mw = 0). To confirm the neutral buoyancy point, a calibration mass of known weight in water (Mc) is placed on top of the float; the float ballasting is complete when the combined weight Mw + Mc = Mc. Note that using a balance with a readability of order 0.01 g enables the user to distinguish the differences in ballasting due to individual BB pellets.

Then, the float mass in air M′ is measured with a benchtop balance with a readability of 0.5 g. To determine M0, a mass correction ΔM must be applied to M′ to account for the buoyancy of the float in air. This correction is ΔM=V¯ρa, where V¯=5.22×10−3 m3 is the approximate float volume based on the geometry and ρa = 1.18 kg m−3 is the approximate density of air in the ballasting laboratory based on temperature and pressure measurements; the correction ΔM accounts for approximately 6.2 g difference between the weight and the mass of the float.

Once neutral buoyancy has been achieved, the float volume V0 is calculated as follows:
V0=(M′+ΔM)(ρ′+Δρ)=M0ρ0.
Equation (11) uses the calibrated float mass M0 ballasted to neutral buoyancy in a tank of water of calibrated density ρ0 to calculate the float volume V0 in laboratory conditions. We can then employ Eqs. (9) and (10) to calculate the final mass of the float Mf for a target depth with salinity S, temperature T, pressure P, and density ρ(S, T, P), taking into account the in situ compressive and thermal effects on volume ΔV [Eq. (10)]. Per Eqs. (9) and (10), we require the in situ density ρ(S, T, P) and temperature T to ballast the floats in the laboratory. We can estimate these properties using a recent CTD cast from the deployment region; in the case that no such data are available, we estimate ρ(S, T, P) from local property climatologies or from regional models.

In practice, however, we have found that climatologies are often not accurate enough to reveal the actual water properties at deployment to sufficient precision. Thus, to fine-tune the ballasting to the in situ physical conditions, a final ballasting step occurs whereby a CTD profile is collected immediately before a deployment, Mf is recalculated, and the ballast is adjusted according to the instantaneous in situ measurements of ρ(S, T, P) and T. These mass adjustments can be made on the fly without the use of scales or balances by adjusting the number of steel BB pellets in the float housing. In our deployments so far we have found that the final adjustments are generally <2 g, depending on the accuracy of estimates of ρ(S, T, P) and temperature T.

6. Uncertainty budget

Errors in ballasting will be manifested as a mistargeting of the float in depth (Swift and Riser 1994). When preparing a float to target a certain depth, it is important to understand how the errors will propagate in the ballasting Eqs. (9)–(11) and the impact it will have on depth targeting. To evaluate the impact of these errors, we calculated an uncertainty budget using a Monte Carlo resampling error analysis (Table 1).

Table 1.

Uncertainty budget for depth targeting. Uncertainty and error are presented with a coverage factor k = 2. Depth error is provided for the intermediate waters of the Strait of Georgia [dρ/dz = 0.11 kg m−3 (10 m)−1] and the Gulf of Saint Lawrence in parentheses [dρ/dz = 0.18 kg m−3 (10 m)−1].
Table 1.

For this analysis, we assigned uncertainty to terms in the ballasting equations; these uncertainty limits are defined by the accuracy of our laboratory measurement techniques, the precision of our measurement equipment, and the manufacturing tolerances of the hull. Equations (9)–(11) were then computed 1000 times with simulated errors in each of the terms to calculate the 95% confidence limits for our determinations of float mass and density. Doing this, we can isolate the impact of uncertainty in each individual parameter in addition to combined uncertainty. Finally, we used an average layer density stratification from our two test regions—the Strait of Georgia Intermediate Waters (0.11 kg m−3 per 10-m depth between 50 and 200 m; Stevens et al. 2021) and the Gulf of Saint Lawrence Intermediate Waters (0.18 kg m−3 per 10-m depth between 50 and 150 m; Galbraith et al. 2022)—to estimate the neutral buoyancy depth variability based on this uncertainty.

The uncertainty budget yields global 95% confidence limits of ±1.60 g and ±0.30 kg m−3, resulting in a neutral buoyancy depth variability of ± ∼29 m for the Strait of Georgia and ± ∼16 m for the Gulf of Saint Lawrence. The largest contributor to the global float error stems from the determination of V0. To produce the uncertainty estimate for V0, we determined V0 thirty times using Eq. (11) for three different floats while varying tank density ρ0 and calculated the confidence limits for this determination (Table 1). While a small portion of this error originates from the laboratory measurements of M0 and ρ0, a seemingly larger portion originates from uncontrolled uncertainty in the ballasting process.

A likely origin of this uncertainty could be the trapping and formation of air bubbles around the hull. Various other studies (Rossby and Dorson 1983; D’Asaro et al. 1996) have found that the presence of air bubbles trapped and/or formed on float external components can cause a buoyancy variability of a few grams, which would have a significant and unpredictable impact on determining V0 that we are unable to control for using the simple ballasting setup described in section 5. Other significant sources of uncertainty stem from temperature of the float in the ballasting tank, in which T0 can lag ambient laboratory temperature by approximately 1°C, and the manufacturing tolerances of the aluminum hull (OD = 1.3 mm; t = 0.3 mm), which produces uncertainty in γ.

As discussed in section 3e, the GTRs degrade during the course of a deployment, causing a float to gain buoyancy and impacting its neutral buoyancy depth. The degradation of the shorter releases used in the Strait of Georgia (from 1 day to 1 week) results in a 0.2–0.9-g buoyancy gain and a shallowing of the neutral buoyancy depth of 3–15 m. The longer 1-month release employed in the Gulf of Saint Lawrence, however, will cause a 2.8-g buoyancy gain and a shallowing of the neutral buoyancy depth of 29 m.

7. Float behavior

Neutrally buoyant floats can be classed as isopycnal or isobaric. This classification refers to the equilibrium surface on which they will settle: an ideal isopycnal float would settle and remain on a specified density surface, whereas an ideal isobaric float would do the same on a specified pressure surface. Upon reaching the equilibrium surface, three factors can cause the floats to deviate from that surface: internal waves, water mass changes, and variations in float mass (Garfield et al. 1999). The response of a float to any of these three forcings will depend on its physical properties and the background stratification; therefore, we must have a strong understanding of these to understand a float’s behavior during a deployment.

In a coordinate system where z is the vertical position taken as positive upward, we can define the position of a float at rest on an equilibrium surface as Ze = Zf = Zρ, where Ze is the depth of the equilibrium surface, Zf is the depth of the float, and Zρ is the depth of the equilibrium isopycnal ρe. The response of a float to vertical perturbations from this equilibrium surface can be defined by the ratio r = ϵr/ϵw, which compares the vertical displacement of the float from ρe (ϵr = Zρ − Zf) to the vertical displacement of ρe from the equilibrium depth (ϵw = Zρ − Ze). Following Goodman and Levine (1990), we can then define r:
r=ϵr/ϵw≈(1−s)/(1−s+N2),
N=Ncg−1,
N=−gρdρdz.
Here, s=γm¯/γw is a ratio comparing the float compressibility to the compressibility of seawater γw, and N is the local buoyancy frequency N normalized by cg−1 ≈ 3.8 cycles per hour, where c is the speed of sound in water and g = 9.81 m2 s−1 is the acceleration due to gravity. From this formulation, it follows that a perfectly isopycnal float with an identical compressibility to seawater would have the same vertical displacement as the isopycnal displacement (s = 1, r = 0) whereas a perfectly isobaric float that is much more incompressible than seawater would remain at the equilibrium depth regardless of the isopycnal displacement (s ≈ 0, r = 1). Floats that are more compressible than seawater (s > 1, r < 0) will have vertical displacements which are amplifications of isopycnal displacements.

In the deployment regions of this study, the floats typically have a response ratio ranging from r ≈ −0.5 to r ≈−0.2, suggesting that the floats will behave isopycnally with a vertical response that will be an amplification of isopycnal displacements. This strong response to isopycnal displacements occurs largely due to the slightly higher compressibility of the floats compared to seawater (s = 1.45), meaning that the floats will compress more than the ambient seawater for any given vertical displacement.

In more homogeneous water masses, there is a risk that the background density gradient δρ/δz is less than the float density gradient δρf/δz. We can define a stability criterion:
δρδz>δρf(S,T,P)δz,
where
δρf(S,T,P)δz=1MtΔVδz=1MtV0[α(T0−T)+γP]δz.
In water columns where this stability criterion is met, a float will be stable on an equilibrium surface; i.e., it will return to an equilibrium surface following vertical perturbations from that surface. If the stability criterion is not achieved, the float will become unstable, resulting in uncontrolled vertical excursions of the float from its intended target depth; the practical consequence of an unstable float is that it sinks to the seafloor. Therefore, the stability criterion must be taken into account when considering which regions and water masses to target and in the case that the user would target a surface where the float might become unstable, measures should be taken to reduce the compressibility of the float by, for example, increasing the wall thickness.

8. Ocean performance

Here, we present data from initial Swish float deployments to evaluate their performance and illustrate the types of data that the floats produce.

a. Deployments

Three deployments of between four and six floats occurred in the Strait of Georgia, British Columbia, Canada, in June (D1), July (D2), and September (D3) 2022 to initiate an ongoing regional monitoring program (Fig. 3). These floats were deployed immediately offshore of a large wastewater treatment outfall with the goal of tracking pollutant dispersal in the regional intermediate layer (50–200-m depth; Stevens et al. 2021). The release mechanisms had time scales of 1–5 days, and all deployed floats resurfaced successfully. The GNSS units were configured to transmit every 5 or 10 min—upon resurfacing, the units had an average battery life of 8.5 days. Of the 15 floats deployed in total, 7 were designed to be retrieved at the surface and were recovered with a 100% success rate. Four of the remaining floats were found and returned by members of the public on the beaches of British Columbia; this 50% recovery rate from public findings (to date) is in line with recovery rates from surface drifter programs in the region (Pawlowicz et al. 2019).

Fig. 3.
Fig. 3.

Results from the Strait of Georgia float deployments. (a) Circular markers represent pop-up positions colored by resurfacing time scale t, the gold pentagram the deployment site. As a point of reference, gray lines represent 24 h of surface drifter trajectories passing within 2 km of the deployment site (Pawlowicz 2021). (b) A zoomed out map of the region and (c) a histogram of float resurfacing time scales t.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

Additionally, to test the long-term reliability of the floats on scales up to a month, two deployments of eight and six floats occurred in the Gulf of Saint Lawrence, Canada, in October 2021 and June 2022, respectively (Fig. 4). These floats targeted the 110-m isobath to track the initial dispersion of a chemical tracer. The release mechanisms had time scales of 1–5 weeks, and all but one of the deployed floats resurfaced successfully. The GNSS units were configured to transmit every hour and had an average postresurfacing battery life of 12 days. Of the 14 floats deployed, four were recovered on beaches and returned by the general public; all four of the recovered floats were recovered from the second deployment (Fig. 4c) on the Newfoundland coastline.

Fig. 4.
Fig. 4.

Results from the Gulf of Saint Lawrence float deployments. (a) A map of the deployment region where the black and gray pentagrams are the deployment sites of two deployments in October 2021 and June 2022, respectively. (c),(d) Circular markers represent pop-up positions and gray contours are bathymetry; (b),(e) histograms of float resurfacing time scales t (all are colored by resurfacing time scale t).

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

Figure 5 shows the average climatological temperature and density properties of the two deployment regions of this study and indicates in which portions of the water column the stability criterion [Eq. (15)] is achieved. In the intermediate layers of the deployment regions, the floats are generally stable due to the relatively large density stratification; this stability criterion was met in all of the above deployments for the targeted water masses and is only not achieved at intermediate depths in 2.0% of the historical Strait of Georgia profiles and 0.8% of the historical Gulf of Saint Lawrence profiles.

Fig. 5.
Fig. 5.

Mean climatological ρ (solid black lines) and temperature (red lines) profiles from (a) the Strait of Georgia and (b) the Gulf of Saint Lawrence; shading represents ±σ limits. Dashed black lines are the variation in float density ρf throughout the water column calculated from Eq. (16) for a typical float ballasted for neutral buoyancy at z = 100 m; shading represents ±2σ limits based on the variability of temperature profiles in the climatologies. Dotted black lines show the density of a water parcel with the volume of a typical float, a constant compressibility coefficient of γw = −4.4 × 10−6 dbar−1, and a variable thermal expansion coefficient calculated for the water column (αw ≈ 1.5 × 10−4 °C−1). Gray shaded regions of the profile depict depth ranges where the stability criterion [Eq. (15)] is not achieved (δρ/δz < δρf/δz); unshaded depth ranges depict where it is achieved (δρ/δz > δρf/δz).

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

b. Neutral buoyancy

To evaluate the in situ depth variability, a handful of the floats deployed in the Strait of Georgia (Fig. 3) were equipped with Star-Oddi DST milli-TD external temperature–depth (TD) sensors to record depth every 30 s (Fig. 6). These 12-g, 13 mm × 39 mm (length × diameter) sensors were attached prior to ballasting and are internally logging, accurate to ±0.3 m, and have an online battery life of >1 year. Note that as the sensors have a small volume (∼16 mL, or 0.3% of float volume) and are contained in a very incompressible ceramic housing, their contribution to float compression and thermal expansion is deemed to be negligible.

Fig. 6.
Fig. 6.

Strait of Georgia float depth records from the June (D1; black), July (D2; blue), and September (D3; red) 2022 deployments. “Pair A” is denoted by darker red lines. Pink circles denote the initial neutral buoyancy depth of floats. (a) The entire drift depth record and (b) only the initial descent.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

The time and space variability of the isopycnal field experienced by each float will impact neutral buoyancy depth during its drift period; however, the initial neutral buoyancy depth of a float (pink circles in Fig. 6) is a good indicator of ballasting accuracy due to the in situ ballasting step that fine-tunes a float’s ballast to the water column properties at the time of deployment. The initial neutral buoyancy depths of the six floats fitted with sensors range from 75 to 152 m, with an average depth of z¯=109 m and a standard deviation zσ = 27 m. The floats deployed in D1 had a wide range of neutral buoyancy depths (black lines in Fig. 6); following some improvements in the ballasting protocol, neutral buoyancy depths in deployments D2 and D3 were less variable (z¯=103 m, zσ = 20 m). These deviations in depth are comparable to the calculated uncertainty budget error for depth targeting in the Strait of Georgia (29 m; section 6 and Table 1), suggesting that we have identified the significant error sources. Further, this level of depth targeting error is comparable to other float designs that do not feature buoyancy compensating mechanisms (Garfield et al. 1999).

In addition to monitoring the buoyant depth, these records also provide information on the fall and rise rate of the floats. The average float descent rate ranges from 1.6 to 3.2 m min−1, taking anywhere between 24 and 53 min to reach neutral buoyancy (Fig. 6b), while the ascent rate ranges from 39 to 73 m min−1. It should be noted that relatively strong surface currents will be integrated into the Lagrangian displacement of a float, almost entirely during the slower descent period. The slowest sinking float cumulatively spends 6 min of its 22-h deployment in the upper 20 m (Fig. 6b)—for an upper limit estimate of this effect, a strong 1 m s−1 current in the surface 20 m would displace this float 360 m, which is small compared to the kilometer/tens of kilometers scale resurfacing displacements seen in these deployments.

c. Lateral motion

The positions of the floats when they resurface can provide information about the dispersive characteristics of a system. Here, we achieve this for the Strait of Georgia Intermediate Water mass by aggregating the individual deployments (Fig. 3) into a single dataset to represent the average transport and dispersion over the 3-month observation period. To achieve this, we use single and multiple particle statistics to calculate dispersion in both absolute and relative terms [see LaCasce (2008) for a detailed overview of Lagrangian statistics].

We can calculate the mean float drift speed of n floats to provide an advection speed for the targeted water mass:
U¯=1n∑i=1n(xi−x0t),
where xi are the resurfacing positions, x0 is the deployment site, and t is the time interval until surfacing. The float drift speeds range from 1.9 to 7.9 cm s−1 with U¯=5.2cms−1 (or 4.5 km day−1; Fig. 7), which is consistent with observed and modeled current speeds in the same region (Stevens et al. 2021).
Fig. 7.
Fig. 7.

Lateral transport of floats. (a) Circular gray points show the float resurfacing distances. (b) Circular gray points show the separation distances of float pairs. The 2Kt is also depicted for various values of K: K = 170 m2 s−1 from the Swish floats is plotted with 95% confidence limits (gray shading); K = 88–167 m2 s−1 is the intermediate layer diffusivity estimated by Stevens et al. (2021); and K = 4000–7000 m2 s−1 is the surface layer diffusivity estimated by Pawlowicz et al. (2019), plotted for reference.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

The relative dispersion describes the mean square separation of float pairs over time. As the resurfacing periods of the floats are not identical, we can match any floats that resurface with time scales t ± 12 h. There are 43 unique pairs that fit this criterion. We calculate the relative dispersion:
D(t)=12N(N−1)∑i≠j[xi(t)−xj(t)]2.
Here, t is the average resurfacing time scale of the float pair and i and j are the float indices. The relative diffusivity is then
K=12ddtD.
If we assume the diffusivity K is constant, the root-mean-square separation distance D should increase with time t as 2Kt (Fig. 7b; Pawlowicz 2021). The separation of the floats yields a relative diffusivity of K = 170 m2 s−1, which is comparable to diffusivities of 88–167 m2 s−1 estimated from Lagrangian simulations of the regional intermediate water mass (Stevens et al. 2021).

Certain float pairs deployed at the same time do not separate as much as expected (Fig. 7b). One such pair is “Pair A” (purple diamond in Fig. 7b), which was neutrally buoyant on approximately the same isobar (thick red lines in Fig. 6) and had a separation of 1 km after 22 h, yielding a separation rate of just 1.2 cm s−1. It has been found that floats that equilibrate on the same equilibrium surface tend to stay closer together due to a reduced influence of vertical shear (Rossby et al. 2021). Pair A, along with other pairs that fall well below the predicted separation rate, is likely an example of this reduced isopycnal dispersion.

d. Vertical motion

Vertical velocities in the ocean interior are typically very small compared to the horizontal velocity field. Neutrally buoyant floats offer an ideal platform to observe these small vertical motions by maintaining a near-zero relative horizontal velocity with respect to the surrounding water, effectively isolating the weaker vertical component of motion from the much larger horizontal velocities (Rossby 2007). When a float is on an equilibrium surface, dynamic vertical forcing is largely the result of isopycnal displacement by the internal wave field (Goodman and Levine 1990). The response of a float to this isopycnal displacement is determined by both the float properties and the water properties (see section 7). With a full description of these properties, it is possible to use the vertical displacement of a float as a reliable measure of the internal wave field, including motions such as diurnal and semidiurnal internal tides, near-inertial motions, and nonlinear internal waves. Measuring an internal wave field directly through high-resolution observations of vertical displacements, as demonstrated here, is uncommon, as neutrally buoyant instruments are not often able to sample and/or telemeter their vertical position at high enough frequencies to resolve the full bandwidth of the internal wave spectrum.

The Garrett–Munk (GM) spectrum (Garrett and Munk 1972, 1975) is an effective description of the oceanic internal wave field that we can compare to the vertical motions of the Swish floats (Fig. 8). The GM model predicts that spectral energy will be concentrated in a band between a lower limit of f = 2Ω sinϕ, the local Coriolis forcing frequency, and an upper limit of N, the local buoyancy frequency. The natural frequency of a float (ω0; Goodman and Levine 1990), which represents the oscillation frequency of a float derived from the buoyancy force per unit mass between the float and the water surrounding the float, is as follows:
ω02=N2+ρt+g2(γw−γm)−gα(dTdz).
As the float is isopycnal (section 7), we expect its natural frequency ω0 to be approximately equal to the local buoyancy frequency N. We analyze three depth signals from D3 (red lines in Fig. 6) using a multitaper power spectral density method to provide a power spectrum of vertical displacement (Fig. 8). Additionally, we can approximate the internal wave spectrum using the GM76 model (calculated using the GM MATLAB toolbox). The float spectra, which agree well with the GM76 estimate in spite of the coastal environment, are red in the frequency band between f = 0.06 cycles per hour and ω0 = 6.13 cycles per hour. The local buoyancy frequency is N = 5.99 cycles per hour (dot–dashed line in Fig. 8). At higher frequencies, the spectra rapidly fall through four orders of magnitude to the instrument noise floor. The float spectra from D1 and D2 (not shown) have a similar agreement with their respective GM76 spectra.
Fig. 8.
Fig. 8.

Three float frequency spectra from D3 (gray lines) in cycles per hour (CPH). The dashed line is the GM76 spectrum, the solid vertical line is f, and the dot–dashed vertical line is N.

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

These results suggest that the Swish floats are able to measure the full dynamic range of internal waves. They can achieve this as their response ratio is r < 0 (section 7). This characteristic means that the floats will amplify isopycnal displacements, allowing them to capture weaker vertical motions effectively. Further, due to their isopycnal behavior, their natural frequency ω0 will approximately match the local neutral buoyancy frequency N. Thus, the floats will respond in near dynamic equilibrium to the internal wave forcing frequencies band bounded by f and N (Goodman and Levine 1990).

e. Surface trajectories

While the primary goal of the Swish floats is to measure subsurface dispersion, upon resurfacing, the floats also produce a dataset of surface trajectories (Figs. 9a,c) which can be used to provide information on surface transport characteristics. As the Swish floats are not designed to be optimal Lagrangian surface followers, it is important to first evaluate how effectively a Swish float follows surface currents. This is necessary as drifters are subject to processes such as wind slip (Niiler and Paduan 1995) and Stokes drift (Curcic et al. 2016) that influence their trajectories.

Fig. 9.
Fig. 9.

Surface trajectories from resurfaced floats in (a) the Strait of Georgia and (c) the Gulf of Saint Lawrence; scatter points along trajectories represent the GNSS position fixes. (b) Surface separation of Strait of Georgia float pairs that resurface <3 km from one another (gray lines) and separation 2KRt using an average diffusivity for the first 24 h of KR = ∼45892 s−1 (black dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 40, 11; 10.1175/JTECH-D-23-0045.1

A simple technique to evaluate the efficacy of a surface drifter is to calculate the drag ratio Rd of the drogued (i.e., submerged) cross-sectional area to the area above-water components (Niiler et al. 1995). The Swish floats have a drag ratio Rd = 2.6; this is not dissimilar to some early undrogued drifter designs (Niiler and Paduan 1995) but falls well short of the canonical Rd = 40 ratio that defines a “modern drifter” (Niiler et al. 1987). To improve the surface following capabilities of the Swish floats, future designs could feasibly incorporate a drogue to increase the underwater surface area of the float.

While the Swish floats do not represent perfectly Lagrangian surface followers, they can still provide information on dispersion processes at the surface (Fig. 9b). Pair separation can be calculated from Strait of Georgia float pairs that resurface within 3 km of one another, and we can again employ Eqs. (18) and (19) to calculate surface relative dispersion and diffusivity, where t is equal to time since resurfacing. In total, there are 91 unique pairs of postresurfacing floats that meet the resurfacing distance criterion; as all three deployments are used in this analysis, properties derived here are representative mean conditions over the June–September 2023 deployment period. These surface-float pairs yield an absolute diffusivity of 4589 m2 s−1 over the first 24 h postresurfacing, which compares well to absolute diffusivity measurements from surface drifters in the same region (4000–7000 m2 s−1; Pawlowicz et al. 2019).

9. Conclusions

The data presented in section 8 suggest that Swish floats are an effective tool to investigate a number of ocean processes in coastal regions. We have shown that the floats can be used as expendable units to track lateral dispersion (section 8c), or as a limited platform for small internally logging sensors to acquire additional datasets and quality control information (sections 8b and 8d), although the requirement for recovery does preclude such floats from being expendable instruments.

The simplicity of the design means that the floats can be constructed from easily available materials, require limited resources to manufacture, can be assembled by hand, can be ballasted in any workshop that can house a 227-L (60 gallon) drum, and can be easily deployed from most vessels. These properties might make them attractive to other researchers in coastal areas or enclosed bodies of water such as estuaries or fjords—indeed, much of the initial Swish float testing was performed with some success in the smaller fjords of British Columbia, proving that these instruments could feasibly be deployed in areas where the usage of more expensive Lagrangian floats is impractical.

However, this design simplicity does come with certain concessions, some significant ones being the lack of a compensating mechanism to improve depth targeting via automated adjustments in the float volume/buoyancy, some form of underwater positioning that would enable the floats to record subsurface trajectories (although this might be affordably achieved in certain regions by incorporating recently available “fish-chip” hydrophones; Fischer et al. 2017), or a telemetry framework to transfer data collected by the float.

Most importantly, these datasets can be acquired at a fraction of the cost of other float platforms—for context, the average material cost after building several dozen Swish floats is about CAD $300 each, compared to the USD $20,000 cost of a single profiling float in the Argo program (https://argo.ucsd.edu/faq). In this regard, Swish floats provide an opportunity to collect information in a similar fashion to any number of increasingly common expendable surface drifter studies (e.g., Novelli et al. 2017; Pawlowicz et al. 2019; Page et al. 2019; van Sebille et al. 2021), where large numbers of Lagrangian measurements are used to study regional kinematics.

Acknowledgments.

Thanks to J. Unger for machining services; E. Cunningham for assistance in building, testing, ballasting, and deploying the floats; K. Stankov for assistance in preparing GNSS units; W. Nesbitt, C. Boutot, and the TReX research team for coordinating and assisting with Gulf of Saint Lawrence deployments; L. Pakhomova, C. Payne (R/V Kraken), and the crews of the R/V Coriolis II, CCGH Moytel, and CCGH Siyay for field operations; and B. Beutel for discussions concerning the manuscript preparation. Funding for this work was provided by Metro Vancouver and the Natural Sciences and Engineering Research Council of Canada under Grant ALLRP 566475-21 and the Marine Environmental Observation, Prediction and Response (MEOPAR) Network Center of Excellence program and Réseau Québec Maritime (RQM) for the Gulf of Saint Lawrence Tracer Experiment, as well as a UBC Four-Year Fellowship to SWS. The GM toolbox was created by J. Klymak (http://jklymak.github.io/GarrettMunkMatlab/). We thank two anonymous reviewers for their helpful and constructive comments on earlier versions of this manuscript.

Data availability statement.

The float datasets and an engineering drawing of the float hull and endcaps can be accessed at https://doi.org/10.5281/zenodo.8173038. The Strait of Georgia surface drifter dataset can be accessed at https://doi.org/10.5683/SP2/C8MJOA. The historical Strait of Georgia hydrography data used here are compiled from data archived by the Fisheries and Oceans Canada Institute of Ocean Sciences at waterproperties.ca and by Ocean Networks Canada at https://data.oceannetworks.ca—a large portion of the data are obtained from the Pacific Salmon Foundation Citizen Science dataset, described here: https://sogdatacentre.ca/atlas/. The historical Gulf of Saint Lawrence hydrography data used here are archived by the National Oceanic and Atmospheric Administration and are available through the World Ocean Database at https://www.ncei.noaa.gov/products/world-ocean-database.

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  • Galbraith, P. S., J. Chassé, J. Dumas, J.-L. Shaw, C. Caverhill, D. Lefaivre, and C. Lafleur, 2022: Physical oceanographic conditions in the Gulf of St. Lawrence during 2021. DFO Canadian Science Advisory Secretariat Research Doc. 2022/034, 87 pp., https://publications.gc.ca/collections/collection_2022/mpo-dfo/fs70-5/Fs70-5-2022-034-eng.pdf.

  • Garfield, N., C. A. Collins, R. G. Paquette, and E. Carter, 1999: Lagrangian exploration of the California Undercurrent, 1992–95. J. Phys. Oceanogr., 29, 560–583, https://doi.org/10.1175/1520-0485(1999)029<0560:LEOTCU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Garrett, C., and W. Munk, 1972: Space-time scales of internal waves. Geophys. Fluid Dyn., 3, 225–264, https://doi.org/10.1080/03091927208236082.

    • Search Google Scholar
    • Export Citation

  • Garrett, C., and W. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80, 291–297, https://doi.org/10.1029/JC080i003p00291.

    • Search Google Scholar
    • Export Citation

  • Goodman, L., and E. R. Levine, 1990: Vertical motion of neutrally buoyant floats. J. Atmos. Oceanic Technol., 7, 38–49, https://doi.org/10.1175/1520-0426(1990)007<0038:VMONBF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Gould, W. J., 2005: From swallow floats to Argo—The development of neutrally buoyant floats. Deep-Sea Res. II, 52, 529–543, https://doi.org/10.1016/j.dsr2.2004.12.005.

    • Search Google Scholar
    • Export Citation

  • Hamilton, P., 2009: Topographic Rossby waves in the Gulf of Mexico. Prog. Oceanogr., 82, 1–31, https://doi.org/10.1016/j.pocean.2009.04.019.

    • Search Google Scholar
    • Export Citation

  • Han, G., J. W. Loder, and P. C. Smith, 1999: Seasonal-mean hydrography and circulation in the Gulf of St. Lawrence and on the eastern Scotian and southern Newfoundland shelves. J. Phys. Oceanogr., 29, 1279–1301, https://doi.org/10.1175/1520-0485(1999)029<1279:SMHACI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Hebert, D., M. Prater, J. Fontaine, and T. Rossby, 1997: Results from the test deployments of the Coastal Ocean Lagrangian (COOL) float. University of Rhode Island GSO Tech. Rep. 97-2, 27 pp., https://apps.dtic.mil/sti/citations/ADA331390.

  • Hrycik, J. M., J. Chassé, B. R. Ruddick, and C. T. Taggart, 2013: Dispersal kernel estimation: A comparison of empirical and modelled particle dispersion in a coastal marine system. Estuarine Coastal Shelf Sci., 133, 11–22, https://doi.org/10.1016/j.ecss.2013.06.023.

    • Search Google Scholar
    • Export Citation

  • Ikeda, C. M., J. Wilkerling, and J. H. Duncan, 2013: The implosion of cylindrical shell structures in a high-pressure water environment. Proc. Roy. Soc., 469A, 20130443, https://doi.org/10.1098/rspa.2013.0443.

    • Search Google Scholar
    • Export Citation

  • IOC, SCOR, and IAPSO, 2010: The International Thermodynamic Equation of Seawater—2010: Calculations and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides 56, 218 pp., https://www.teos-10.org/pubs/TEOS-10_Manual.pdf.

  • Korotaev, G., T. Oguz, and S. Riser, 2006: Intermediate and deep currents of the Black Sea obtained from autonomous profiling floats. Deep-Sea Res. II, 53, 1901–1910, https://doi.org/10.1016/j.dsr2.2006.04.017.

    • Search Google Scholar
    • Export Citation

  • LaCasce, J., 2008: Statistics from Lagrangian observations. Prog. Oceanogr., 77, 1–29, https://doi.org/10.1016/j.pocean.2008.02.002.

  • Lozier, M. S., A. S. Bower, H. H. Furey, K. L. Drouin, X. Xu, and S. Zou, 2022: Overflow water pathways in the North Atlantic. Prog. Oceanogr., 208, 102874, https://doi.org/10.1016/j.pocean.2022.102874.

    • Search Google Scholar
    • Export Citation

  • Meyerjürgens, J., T. H. Badewien, S. P. Garaba, J.-O. Wolff, and O. Zielinski, 2019: A state-of-the-art compact surface drifter reveals pathways of floating marine litter in the German Bight. Front. Mar. Sci., 6, 58, https://doi.org/10.3389/fmars.2019.00058.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., and J. D. Paduan, 1995: Wind-driven motions in the northeast Pacific as measured by Lagrangian drifters. J. Phys. Oceanogr., 25, 2819–2830, https://doi.org/10.1175/1520-0485(1995)025<2819:WDMITN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., R. E. Davis, and H. J. White, 1987: Water-following characteristics of a mixed layer drifter. Deep-Sea Res., 34A, 1867–1881, https://doi.org/10.1016/0198-0149(87)90060-4.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., A. S. Sybrandy, K. Bi, P. M. Poulain, and D. Bitterman, 1995: Measurements of the water-following capability of holey-sock and TRISTAR drifters. Deep-Sea Res. I, 42, 1951–1964, https://doi.org/10.1016/0967-0637(95)00076-3.

    • Search Google Scholar
    • Export Citation

  • Novelli, G., C. M. Guigand, C. Cousin, E. H. Ryan, N. J. M. Laxague, H. Dai, B. K. Haus, and T. M. Özgökmen, 2017: A biodegradable surface drifter for ocean sampling on a massive scale. J. Atmos. Oceanic Technol., 34, 2509–2532, https://doi.org/10.1175/JTECH-D-17-0055.1.

    • Search Google Scholar
    • Export Citation

  • Page, S., C. Hannah, T. Juhasz, D. Spear, and H. Blanken, 2019: Surface circulation tracking drifter data for the Kitimat Fjord System in northern British Columbia and adjacent continental shelf for April, 2014 to July, 2016. Canadian Data Rep. of Hydrography and Ocean Science, Vol. 206, 33 pp.

  • Pawlowicz, R., 2015: The absolute salinity of seawater diluted by riverwater. Deep-Sea Res. I, 101, 71–79, https://doi.org/10.1016/j.dsr.2015.03.006.

    • Search Google Scholar
    • Export Citation

  • Pawlowicz, R., 2021: The grounding of floating objects in a marginal sea. J. Phys. Oceanogr., 51, 537–551, https://doi.org/10.1175/JPO-D-20-0183.1.

    • Search Google Scholar
    • Export Citation

  • Pawlowicz, R., C. Hannah, and A. Rosenburger, 2019: Lagrangian observations of estuarine residence times, dispersion, and trapping in the Salish Sea. Estuarine Coastal Shelf Sci., 225, 106246, https://doi.org/10.1016/j.ecss.2019.106246.

    • Search Google Scholar
    • Export Citation

  • Poulain, P.-M., and Coauthors, 2007: MedArgo: A drifting profiler program in the Mediterranean Sea. Ocean Sci., 3, 379–395, https://doi.org/10.5194/os-3-379-2007.

    • Search Google Scholar
    • Export Citation

  • Prater, M. D., 2002: Eddies in the Labrador Sea as observed by profiling RAFOS floats and remote sensing. J. Phys. Oceanogr., 32, 411–427, https://doi.org/10.1175/1520-0485(2002)032<0411:EITLSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Richardson, P. L., J. F. Price, W. B. Owens, W. J. Schmitz, H. T. Rossby, A. M. Bradley, J. R. Valdes, and D. C. Webb, 1981: North Atlantic Subtropical Gyre: SOFAR floats tracked by moored listening stations. Science, 213, 435–437, https://doi.org/10.1126/science.213.4506.435.

    • Search Google Scholar
    • Export Citation

  • Rossby, T., 2007: Evolution of Lagrangian methods in oceanography. Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics, A. Griffa et al., Eds., Cambridge University Press, 1–38, https://doi.org/10.1017/CBO9780511535901.002.

  • Rossby, T., and D. Dorson, 1983: The deep drifter—A simple tool to determine average ocean currents. Deep-Sea Res., 30A, 1279–1288, https://doi.org/10.1016/0198-0149(83)90085-7.

    • Search Google Scholar
    • Export Citation

  • Rossby, T., M. Omand, J. Palter, and D. Hebert, 2021: On rates of isopycnal dispersion at the submesoscale. Geophys. Res. Lett., 48, e2021GL093526, https://doi.org/10.1029/2021GL093526.

    • Search Google Scholar
    • Export Citation

  • Sandby, L. M., J. E. B. Mejdahl, S. H. Bjerregaard, C. Melvad, and S. Rysgaard, 2021: A cost-efficient low-weight autonomous profiler for measurements in polar coastal waters and other regions with strong density gradients. HardwareX, 10, E00207, https://doi.org/10.1016/j.ohx.2021.e00207.

    • Search Google Scholar
    • Export Citation

  • Sharp, A. G., 1981: Design curves for oceanographic pressure-resistant housings. WHOI Tech. Memo. 3-81, 44 pp., https://doi.org/10.1575/1912/1427.

  • Shoosmith, D. R., P. L. Richardson, A. S. Bower, and H. T. Rossby, 2005: Discrete eddies in the northern North Atlantic as observed by looping RAFOS floats. Deep-Sea Res. II, 52, 627–650, https://doi.org/10.1016/j.dsr2.2004.12.011.

    • Search Google Scholar
    • Export Citation

  • Stevens, S. W., R. Pawlowicz, and S. E. Allen, 2021: A study of intermediate water circulation in the Strait of Georgia using tracer-based, Eulerian, and Lagrangian methods. J. Phys. Oceanogr., 51, 1875–1893, https://doi.org/10.1175/JPO-D-20-0225.1.

    • Search Google Scholar
    • Export Citation

  • Strub, P. T., C. James, V. Montecino, J. A. Rutllant, and J. L. Blanco, 2019: Ocean circulation along the southern Chile transition region (38°–46°S): Mean, seasonal and interannual variability, with a focus on 2014–2016. Prog. Oceanogr., 172, 159–198, https://doi.org/10.1016/j.pocean.2019.01.004.

    • Search Google Scholar
    • Export Citation

  • Swallow, J. C., 1955: A neutral-buoyancy float for measuring deep currents. Deep-Sea Res., 3, 74–81, https://doi.org/10.1016/0146-6313(55)90037-X.

    • Search Google Scholar
    • Export Citation

  • Swift, D. D., and S. C. Riser, 1994: RAFOS floats: Defining and targeting surfaces of neutral buoyancy. J. Atmos. Oceanic Technol., 11, 1079–1092, https://doi.org/10.1175/1520-0426(1994)011<1079:RFDATS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • van Sebille, E., E. Zettler, N. Wienders, L. Amaral-Zettler, S. Elipot, and R. Lumpkin, 2021: Dispersion of surface drifters in the tropical Atlantic. Front. Mar. Sci., 7, 607426, https://doi.org/10.3389/fmars.2020.607426.

    • Search Google Scholar
    • Export Citation

  • Wong, A. P. S., and Coauthors, 2020: Argo data 1999–2019: Two million temperature-salinity profiles and subsurface velocity observations from a global array of profiling floats. Front. Mar. Sci., 7, 700, https://doi.org/10.3389/fmars.2020.00700.

    • Search Google Scholar
    • Export Citation
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Journal of Atmospheric and Oceanic Technology

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  • Galbraith, P. S., J. Chassé, J. Dumas, J.-L. Shaw, C. Caverhill, D. Lefaivre, and C. Lafleur, 2022: Physical oceanographic conditions in the Gulf of St. Lawrence during 2021. DFO Canadian Science Advisory Secretariat Research Doc. 2022/034, 87 pp., https://publications.gc.ca/collections/collection_2022/mpo-dfo/fs70-5/Fs70-5-2022-034-eng.pdf.

  • Garfield, N., C. A. Collins, R. G. Paquette, and E. Carter, 1999: Lagrangian exploration of the California Undercurrent, 1992–95. J. Phys. Oceanogr., 29, 560–583, https://doi.org/10.1175/1520-0485(1999)029<0560:LEOTCU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Garrett, C., and W. Munk, 1972: Space-time scales of internal waves. Geophys. Fluid Dyn., 3, 225–264, https://doi.org/10.1080/03091927208236082.

    • Search Google Scholar
    • Export Citation

  • Garrett, C., and W. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80, 291–297, https://doi.org/10.1029/JC080i003p00291.

    • Search Google Scholar
    • Export Citation

  • Goodman, L., and E. R. Levine, 1990: Vertical motion of neutrally buoyant floats. J. Atmos. Oceanic Technol., 7, 38–49, https://doi.org/10.1175/1520-0426(1990)007<0038:VMONBF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Gould, W. J., 2005: From swallow floats to Argo—The development of neutrally buoyant floats. Deep-Sea Res. II, 52, 529–543, https://doi.org/10.1016/j.dsr2.2004.12.005.

    • Search Google Scholar
    • Export Citation

  • Hamilton, P., 2009: Topographic Rossby waves in the Gulf of Mexico. Prog. Oceanogr., 82, 1–31, https://doi.org/10.1016/j.pocean.2009.04.019.

    • Search Google Scholar
    • Export Citation

  • Han, G., J. W. Loder, and P. C. Smith, 1999: Seasonal-mean hydrography and circulation in the Gulf of St. Lawrence and on the eastern Scotian and southern Newfoundland shelves. J. Phys. Oceanogr., 29, 1279–1301, https://doi.org/10.1175/1520-0485(1999)029<1279:SMHACI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Hebert, D., M. Prater, J. Fontaine, and T. Rossby, 1997: Results from the test deployments of the Coastal Ocean Lagrangian (COOL) float. University of Rhode Island GSO Tech. Rep. 97-2, 27 pp., https://apps.dtic.mil/sti/citations/ADA331390.

  • Hrycik, J. M., J. Chassé, B. R. Ruddick, and C. T. Taggart, 2013: Dispersal kernel estimation: A comparison of empirical and modelled particle dispersion in a coastal marine system. Estuarine Coastal Shelf Sci., 133, 11–22, https://doi.org/10.1016/j.ecss.2013.06.023.

    • Search Google Scholar
    • Export Citation

  • Ikeda, C. M., J. Wilkerling, and J. H. Duncan, 2013: The implosion of cylindrical shell structures in a high-pressure water environment. Proc. Roy. Soc., 469A, 20130443, https://doi.org/10.1098/rspa.2013.0443.

    • Search Google Scholar
    • Export Citation

  • IOC, SCOR, and IAPSO, 2010: The International Thermodynamic Equation of Seawater—2010: Calculations and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides 56, 218 pp., https://www.teos-10.org/pubs/TEOS-10_Manual.pdf.

  • Korotaev, G., T. Oguz, and S. Riser, 2006: Intermediate and deep currents of the Black Sea obtained from autonomous profiling floats. Deep-Sea Res. II, 53, 1901–1910, https://doi.org/10.1016/j.dsr2.2006.04.017.

    • Search Google Scholar
    • Export Citation

  • LaCasce, J., 2008: Statistics from Lagrangian observations. Prog. Oceanogr., 77, 1–29, https://doi.org/10.1016/j.pocean.2008.02.002.

  • Lozier, M. S., A. S. Bower, H. H. Furey, K. L. Drouin, X. Xu, and S. Zou, 2022: Overflow water pathways in the North Atlantic. Prog. Oceanogr., 208, 102874, https://doi.org/10.1016/j.pocean.2022.102874.

    • Search Google Scholar
    • Export Citation

  • Meyerjürgens, J., T. H. Badewien, S. P. Garaba, J.-O. Wolff, and O. Zielinski, 2019: A state-of-the-art compact surface drifter reveals pathways of floating marine litter in the German Bight. Front. Mar. Sci., 6, 58, https://doi.org/10.3389/fmars.2019.00058.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., and J. D. Paduan, 1995: Wind-driven motions in the northeast Pacific as measured by Lagrangian drifters. J. Phys. Oceanogr., 25, 2819–2830, https://doi.org/10.1175/1520-0485(1995)025<2819:WDMITN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., R. E. Davis, and H. J. White, 1987: Water-following characteristics of a mixed layer drifter. Deep-Sea Res., 34A, 1867–1881, https://doi.org/10.1016/0198-0149(87)90060-4.

    • Search Google Scholar
    • Export Citation

  • Niiler, P. P., A. S. Sybrandy, K. Bi, P. M. Poulain, and D. Bitterman, 1995: Measurements of the water-following capability of holey-sock and TRISTAR drifters. Deep-Sea Res. I, 42, 1951–1964, https://doi.org/10.1016/0967-0637(95)00076-3.

    • Search Google Scholar
    • Export Citation

  • Novelli, G., C. M. Guigand, C. Cousin, E. H. Ryan, N. J. M. Laxague, H. Dai, B. K. Haus, and T. M. Özgökmen, 2017: A biodegradable surface drifter for ocean sampling on a massive scale. J. Atmos. Oceanic Technol., 34, 2509–2532, https://doi.org/10.1175/JTECH-D-17-0055.1.

    • Search Google Scholar
    • Export Citation

  • Page, S., C. Hannah, T. Juhasz, D. Spear, and H. Blanken, 2019: Surface circulation tracking drifter data for the Kitimat Fjord System in northern British Columbia and adjacent continental shelf for April, 2014 to July, 2016. Canadian Data Rep. of Hydrography and Ocean Science, Vol. 206, 33 pp.

  • Pawlowicz, R., 2015: The absolute salinity of seawater diluted by riverwater. Deep-Sea Res. I, 101, 71–79, https://doi.org/10.1016/j.dsr.2015.03.006.

    • Search Google Scholar
    • Export Citation

  • Pawlowicz, R., 2021: The grounding of floating objects in a marginal sea. J. Phys. Oceanogr., 51, 537–551, https://doi.org/10.1175/JPO-D-20-0183.1.

    • Search Google Scholar
    • Export Citation

  • Pawlowicz, R., C. Hannah, and A. Rosenburger, 2019: Lagrangian observations of estuarine residence times, dispersion, and trapping in the Salish Sea. Estuarine Coastal Shelf Sci., 225, 106246, https://doi.org/10.1016/j.ecss.2019.106246.

    • Search Google Scholar
    • Export Citation

  • Poulain, P.-M., and Coauthors, 2007: MedArgo: A drifting profiler program in the Mediterranean Sea. Ocean Sci., 3, 379–395, https://doi.org/10.5194/os-3-379-2007.

    • Search Google Scholar
    • Export Citation

  • Prater, M. D., 2002: Eddies in the Labrador Sea as observed by profiling RAFOS floats and remote sensing. J. Phys. Oceanogr., 32, 411–427, https://doi.org/10.1175/1520-0485(2002)032<0411:EITLSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Richardson, P. L., J. F. Price, W. B. Owens, W. J. Schmitz, H. T. Rossby, A. M. Bradley, J. R. Valdes, and D. C. Webb, 1981: North Atlantic Subtropical Gyre: SOFAR floats tracked by moored listening stations. Science, 213, 435–437, https://doi.org/10.1126/science.213.4506.435.

    • Search Google Scholar
    • Export Citation

  • Rossby, T., 2007: Evolution of Lagrangian methods in oceanography. Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics, A. Griffa et al., Eds., Cambridge University Press, 1–38, https://doi.org/10.1017/CBO9780511535901.002.

  • Rossby, T., and D. Dorson, 1983: The deep drifter—A simple tool to determine average ocean currents. Deep-Sea Res., 30A, 1279–1288, https://doi.org/10.1016/0198-0149(83)90085-7.

    • Search Google Scholar
    • Export Citation

  • Rossby, T., M. Omand, J. Palter, and D. Hebert, 2021: On rates of isopycnal dispersion at the submesoscale. Geophys. Res. Lett., 48, e2021GL093526, https://doi.org/10.1029/2021GL093526.

    • Search Google Scholar
    • Export Citation

  • Sandby, L. M., J. E. B. Mejdahl, S. H. Bjerregaard, C. Melvad, and S. Rysgaard, 2021: A cost-efficient low-weight autonomous profiler for measurements in polar coastal waters and other regions with strong density gradients. HardwareX, 10, E00207, https://doi.org/10.1016/j.ohx.2021.e00207.

    • Search Google Scholar
    • Export Citation

  • Sharp, A. G., 1981: Design curves for oceanographic pressure-resistant housings. WHOI Tech. Memo. 3-81, 44 pp., https://doi.org/10.1575/1912/1427.

  • Shoosmith, D. R., P. L. Richardson, A. S. Bower, and H. T. Rossby, 2005: Discrete eddies in the northern North Atlantic as observed by looping RAFOS floats. Deep-Sea Res. II, 52, 627–650, https://doi.org/10.1016/j.dsr2.2004.12.011.

    • Search Google Scholar
    • Export Citation

  • Stevens, S. W., R. Pawlowicz, and S. E. Allen, 2021: A study of intermediate water circulation in the Strait of Georgia using tracer-based, Eulerian, and Lagrangian methods. J. Phys. Oceanogr., 51, 1875–1893, https://doi.org/10.1175/JPO-D-20-0225.1.

    • Search Google Scholar
    • Export Citation

  • Strub, P. T., C. James, V. Montecino, J. A. Rutllant, and J. L. Blanco, 2019: Ocean circulation along the southern Chile transition region (38°–46°S): Mean, seasonal and interannual variability, with a focus on 2014–2016. Prog. Oceanogr., 172, 159–198, https://doi.org/10.1016/j.pocean.2019.01.004.

    • Search Google Scholar
    • Export Citation

  • Swallow, J. C., 1955: A neutral-buoyancy float for measuring deep currents. Deep-Sea Res., 3, 74–81, https://doi.org/10.1016/0146-6313(55)90037-X.

    • Search Google Scholar
    • Export Citation

  • Swift, D. D., and S. C. Riser, 1994: RAFOS floats: Defining and targeting surfaces of neutral buoyancy. J. Atmos. Oceanic Technol., 11, 1079–1092, https://doi.org/10.1175/1520-0426(1994)011<1079:RFDATS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • van Sebille, E., E. Zettler, N. Wienders, L. Amaral-Zettler, S. Elipot, and R. Lumpkin, 2021: Dispersion of surface drifters in the tropical Atlantic. Front. Mar. Sci., 7, 607426, https://doi.org/10.3389/fmars.2020.607426.

    • Search Google Scholar
    • Export Citation

  • Wong, A. P. S., and Coauthors, 2020: Argo data 1999–2019: Two million temperature-salinity profiles and subsurface velocity observations from a global array of profiling floats. Front. Mar. Sci., 7, 700, https://doi.org/10.3389/fmars.2020.00700.

    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    (left) Swish float schematic with coarse measurements (cm; 2:1 vertical to horizontal scale), (center) an internal view of a float, and (right) a labeled photograph of two Swish floats. Note the previously deployed and recovered red float (rightmost) with a temperature–depth (TD) sensor attachment and a bridle to aid recovery from a vessel.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Swish float compression (a) measured in pressure tank experiments as a function of external pressure Pe (blue scatter points) and (b) derived γm.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Results from the Strait of Georgia float deployments. (a) Circular markers represent pop-up positions colored by resurfacing time scale t, the gold pentagram the deployment site. As a point of reference, gray lines represent 24 h of surface drifter trajectories passing within 2 km of the deployment site (Pawlowicz 2021). (b) A zoomed out map of the region and (c) a histogram of float resurfacing time scales t.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Results from the Gulf of Saint Lawrence float deployments. (a) A map of the deployment region where the black and gray pentagrams are the deployment sites of two deployments in October 2021 and June 2022, respectively. (c),(d) Circular markers represent pop-up positions and gray contours are bathymetry; (b),(e) histograms of float resurfacing time scales t (all are colored by resurfacing time scale t).

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Mean climatological ρ (solid black lines) and temperature (red lines) profiles from (a) the Strait of Georgia and (b) the Gulf of Saint Lawrence; shading represents ±σ limits. Dashed black lines are the variation in float density ρf throughout the water column calculated from Eq. (16) for a typical float ballasted for neutral buoyancy at z = 100 m; shading represents ±2σ limits based on the variability of temperature profiles in the climatologies. Dotted black lines show the density of a water parcel with the volume of a typical float, a constant compressibility coefficient of γw = −4.4 × 10−6 dbar−1, and a variable thermal expansion coefficient calculated for the water column (αw ≈ 1.5 × 10−4 °C−1). Gray shaded regions of the profile depict depth ranges where the stability criterion [Eq. (15)] is not achieved (δρ/δz < δρf/δz); unshaded depth ranges depict where it is achieved (δρ/δz > δρf/δz).

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Strait of Georgia float depth records from the June (D1; black), July (D2; blue), and September (D3; red) 2022 deployments. “Pair A” is denoted by darker red lines. Pink circles denote the initial neutral buoyancy depth of floats. (a) The entire drift depth record and (b) only the initial descent.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Lateral transport of floats. (a) Circular gray points show the float resurfacing distances. (b) Circular gray points show the separation distances of float pairs. The 2Kt is also depicted for various values of K: K = 170 m2 s−1 from the Swish floats is plotted with 95% confidence limits (gray shading); K = 88–167 m2 s−1 is the intermediate layer diffusivity estimated by Stevens et al. (2021); and K = 4000–7000 m2 s−1 is the surface layer diffusivity estimated by Pawlowicz et al. (2019), plotted for reference.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Three float frequency spectra from D3 (gray lines) in cycles per hour (CPH). The dashed line is the GM76 spectrum, the solid vertical line is f, and the dot–dashed vertical line is N.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Surface trajectories from resurfaced floats in (a) the Strait of Georgia and (c) the Gulf of Saint Lawrence; scatter points along trajectories represent the GNSS position fixes. (b) Surface separation of Strait of Georgia float pairs that resurface <3 km from one another (gray lines) and separation 2KRt using an average diffusivity for the first 24 h of KR = ∼45892 s−1 (black dashed line).

Fig. 1.

(left) Swish float schematic with coarse measurements (cm; 2:1 vertical to horizontal scale), (center) an internal view of a float, and (right) a labeled photograph of two Swish floats. Note the previously deployed and recovered red float (rightmost) with a temperature–depth (TD) sensor attachment and a bridle to aid recovery from a vessel.
Fig. 2.

Swish float compression (a) measured in pressure tank experiments as a function of external pressure Pe (blue scatter points) and (b) derived γm.
Fig. 3.

Results from the Strait of Georgia float deployments. (a) Circular markers represent pop-up positions colored by resurfacing time scale t, the gold pentagram the deployment site. As a point of reference, gray lines represent 24 h of surface drifter trajectories passing within 2 km of the deployment site (Pawlowicz 2021). (b) A zoomed out map of the region and (c) a histogram of float resurfacing time scales t.
Fig. 4.

Results from the Gulf of Saint Lawrence float deployments. (a) A map of the deployment region where the black and gray pentagrams are the deployment sites of two deployments in October 2021 and June 2022, respectively. (c),(d) Circular markers represent pop-up positions and gray contours are bathymetry; (b),(e) histograms of float resurfacing time scales t (all are colored by resurfacing time scale t).
Fig. 5.

Mean climatological ρ (solid black lines) and temperature (red lines) profiles from (a) the Strait of Georgia and (b) the Gulf of Saint Lawrence; shading represents ±σ limits. Dashed black lines are the variation in float density ρf throughout the water column calculated from Eq. (16) for a typical float ballasted for neutral buoyancy at z = 100 m; shading represents ±2σ limits based on the variability of temperature profiles in the climatologies. Dotted black lines show the density of a water parcel with the volume of a typical float, a constant compressibility coefficient of γw = −4.4 × 10−6 dbar−1, and a variable thermal expansion coefficient calculated for the water column (αw ≈ 1.5 × 10−4 °C−1). Gray shaded regions of the profile depict depth ranges where the stability criterion [Eq. (15)] is not achieved (δρ/δz < δρf/δz); unshaded depth ranges depict where it is achieved (δρ/δz > δρf/δz).
Fig. 6.

Strait of Georgia float depth records from the June (D1; black), July (D2; blue), and September (D3; red) 2022 deployments. “Pair A” is denoted by darker red lines. Pink circles denote the initial neutral buoyancy depth of floats. (a) The entire drift depth record and (b) only the initial descent.
Fig. 7.

Lateral transport of floats. (a) Circular gray points show the float resurfacing distances. (b) Circular gray points show the separation distances of float pairs. The 2Kt is also depicted for various values of K: K = 170 m2 s−1 from the Swish floats is plotted with 95% confidence limits (gray shading); K = 88–167 m2 s−1 is the intermediate layer diffusivity estimated by Stevens et al. (2021); and K = 4000–7000 m2 s−1 is the surface layer diffusivity estimated by Pawlowicz et al. (2019), plotted for reference.
Fig. 8.

Three float frequency spectra from D3 (gray lines) in cycles per hour (CPH). The dashed line is the GM76 spectrum, the solid vertical line is f, and the dot–dashed vertical line is N.
Fig. 9.

Surface trajectories from resurfaced floats in (a) the Strait of Georgia and (c) the Gulf of Saint Lawrence; scatter points along trajectories represent the GNSS position fixes. (b) Surface separation of Strait of Georgia float pairs that resurface <3 km from one another (gray lines) and separation 2KRt using an average diffusivity for the first 24 h of KR = ∼45892 s−1 (black dashed line).
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