Flippin’ χSOLO, an Upper-Ocean Autonomous Turbulence-Profiling Float
1. Introduction
Neutrally buoyant floats have been used for ocean observation since at least as early as the 1950s (Swallow 1955). Over the next few decades, float observations focused on following subsurface currents using acoustic tracking (Rossby and Webb 1970). Acoustic tracking required the support of either moorings or ships, limiting its usefulness to regions where that support was practical. The addition of buoyancy adjustment permitted periodic surfacing of the autonomous float Autonomous Lagrangian Circulation Explorer (ALACE) which then used the Argos satellite system for surface position (Davis et al. 1992). Sensors to measure temperature and salinity yielded vertical profiles (Davis et al. 2001), leading to a float called the Sounding Oceanographic Lagrangian Observer (SOLO) and then to the Argo array (Roemmich et al. 2009). A comprehensive history of the progression of float technology leading to Argo can be found in Gould (2005). Promising new directions for the Argo program, including the potential inclusion of turbulence (mixing) measurements (ArgoMix), are discussed by Roemmich et al. (2019).
Our primary objective in developing an upper-ocean autonomous turbulence profiling capability was to make clean, acceptably low-noise profiling measurements of turbulence. As a metric to define acceptable noise levels, the temperature variance dissipation rate χ and the turbulence kinetic energy dissipation rate ϵ were to be no greater than those measured by the OSU Ocean Mixing profiler, Chameleon (Moum et al. 1995). To accomplish this requires undisturbed fluid ahead of the vehicle, and minimization of vehicle vibrations that contribute accelerations sensed by turbulence shear probes and of radiated digital switching noise that can contaminate both shear probes and fast thermistors.
Another important objective is to make continuous rapid profiles through the sea surface. Reliable profiling measurements of the upper 10 m are impossible with downward profilers launched from ship (Moum et al. 1995) due to the significant disturbance presented by the vessel. We considered that an important role for vessel-free autonomous profilers is measurement through the sea surface under all conditions and particularly including times when extreme surface forcing prevents vessels from operating in the area (such as during tropical cyclones). Flippin’ χSOLO (FχS) is designed to do this for a period of 60 days at the maximum profiling rate. It can profile for longer periods by profiling less frequently and saving energy spent on changing and shifting ballast. Various missions are envisioned, including deployment and then parking FχS at depth, surfacing periodically for mission updates, to await strong forcing events at which point rapid profiling would be initiated.
In addition, and in keeping with the Argo program philosophy, the autonomous turbulence profiler should be considered expendable. This requires a robust scheme to reduce the data that must be transmitted by satellite (presently Iridium) from remote locations. For FχS, this is treated separately by Hughes et al. (2023).
In the past decade, we have begun to see development of several autonomous turbulence measurements. The ASIP profiler of Ward et al. (2014) also targets the near surface of the ocean although it must be tended from ship. The inclusion of fast thermistors on EM-APEX floats by Lien et al. (2016) is a valuable addition to the float’s electromagnetic velocity profiling capability. Recent glider enhancements that include microstructure packages (Fer et al. 2014; Rainville et al. 2017; St. Laurent and Merrifield 2017) are providing new and relatively long term turbulence measurements of the upper ocean. FχS supplements these existing measurement platforms with a truly autonomous vertical profiler that includes both fast thermistors and shear probes.
In the following, we describe the essential modifications to the SOLO float that were necessary to accommodate the turbulence measurements (section 2), its basic profiling characteristics (section 3), processing of the turbulence signals (section 4) and provide an evaluation of the turbulence measurements (section 5) from a 3.5 day field experiment that included deployment of two autonomous turbulence profilers nearby a shipboard turbulence profiler (Chameleon) operated from the Research Vessel Oceanus. A summary follows (section 6). A separate appendix defines the computation of surface wave height spectra from accelerometers in FχS while surfaced and compares significant wave heights estimated from two FχS units to those from a nearby wave buoy.
2. FχS
a. The flip
On most profiling floats, the antenna must be the highest point on the float for clear transmission while surfaced. Thus, regardless of which end the sensors are deployed, they are in the lee of wake eddies shed by the antenna while profiling upward. To measure the small, centimeter-scale fluctuations of temperature and velocity created by ocean turbulence requires that the flow ahead of the sensors remain undisturbed by the presence of the measurement platform. FχS solves this problem by defining a clear “leading edge,” or nose, and “trailing edge,” or tail with sensors at the nose and antenna at the tail of the float. Following upward profile through the surface, the float flips to be tail up in order to communicate, as seen in Fig. 1. This 180° flip is accomplished by moving ballast, as is done in underwater gliders (Sherman et al. 2001; Rudnick et al. 2004). In so doing, the leading edge always leads, providing clean flow to the sensors during both ascent and descent.
Flippin’ χSolo completing a flip to expose communication antenna at the tail following a profile through undisturbed fluid at the sea surface. The turbulence sensors at the nose are pointed nearly downward in the photo as FχS prepares for a downward profile.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
b. Modifications to SOLO-II
The SOLO-II profiling float is a second generation of the original SOLO. SOLO-II increased the buoyancy change from 240 to 680 cc by replacing the one-stroke piston pump with a robust reciprocating pump, which allows greater payload capacity across all ocean environments, and switched from Argos to Iridium communications, leading to significant power savings. Like most profiling floats, SOLO-II is ballasted to maintain a vertical orientation, with the antenna at the highest point to allow communication while on the surface. When temperature sensors were first added to ALACE, they were put on the top cap for two reasons: 1) to profile up to and through the surface, and 2) for the operational reason that all electronics were already in the top cap.
FχS is an extension of proven SOLO-II float technology, explicitly designed to carry turbulence sensors in a separate pressure case, or turbulence pod. FχS includes the SOLO-II buoyancy engine that also supplies power to the turbulence pod, and communicates with it to allow synchronization of sampling with the dive cycles, and to allow FχS to send diagnostic data to shore.
FχS (Fig. 2) was designed with an objective of 60 day missions at maximum profiling rates—mission lengths are prolonged by reducing the profiling rate via parking FχS at depth for a specified duration. Profiling speeds are 0.1–0.3 m s−1, and FχS yields profiles roughly every 20 min to 100 m at maximum profiling rates. With a pressure rating corresponding to 240 m, deeper profiles are possible with correspondingly longer intervals between profiles.
Schematic of Flippin’ χSolo. Note that the right-hand view has been rotated 180° about the horizontal axis and 90° about the vertical axis, thus exposing the SBE conductivity sensor in the left-hand view and the SBE thermistor in the right-hand view.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
This float design can accommodate any sensor that has a separate pressure case in the volume available on the nose of the float and meets ballasting requirements (has near-neutral buoyancy).
The following basic modifications to SOLO-II were made in the design and constructions of FχS:
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Addition of the turbulence pod situated at the nose/leading edge.
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Use of the stand-alone Seabird Electronics Glider Payload CTD (SBE GP-CTD) next to the turbulence pod, but far enough away to allow clean flow.
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Repositioning of the antenna to the opposite end of the pressure case, enabling (i) clean flow around the turbulence sensors, and (ii) extra height out of the water for the antenna since the sensors do not also have to be lifted out of the water. A stability disk is retained to enhance surface following for communications in wavy conditions.
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Inclusion of movable ballast (battery packs + lead) on the internal chassis to permit flipping. This is accomplished (at perigee) by a lead screw that drives the movable battery pack toward the tail, flipping the float nose-up. The operation is reversed at the sea surface.
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Total float dry mass was increased from 19.5 to 28 kg. A new and larger battery pack provides 2000 W h with 20% allocated to the turbulence pod.
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Thinner pressure case wall given the shallower target depth from the original SOLO of 2000 m.
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Modification of hydraulics to allow pumping in either orientation.
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Addition of a reinforced tail bail for deployment and recovery, and a lead drop weight in the event of hydraulics failure.
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Addition of Bluetooth for ease of communication on deck.
The mass of FχS is 28 kg, with total length (sensor tips to antenna tip) of 1.95 m. The lead screw moves 8 kg of payload (batteries and lead) up to 23 cm, which leads to a change in righting moment from +3 cm (ascent) to −3 cm (descent, surface communication). The buoyancy of the float with a full/empty bladder is approximately ±215 g. A hollow nose shell allows clean flow to the nose sensors. The nose cone is 35.5 cm long, including a 17 cm tapered section that accommodates the SBE GP-CTD, its pump, and the turbulence pod (7.6 cm diameter, 38.8 cm sensor tips to aft bulkhead).
c. Turbulence pod and sensors
We refer to the pressure case housing the turbulence sensors as the turbulence pod. The turbulence pod (Fig. 3) includes sensors to measure small-scale fluctuations in temperature using two FP07 thermistors (Lueck et al. 1977; Nash et al. 1999), velocity (pitot tube), and velocity gradient (two shear probes, as described by Moum et al. 1995). The temperature variance dissipation rate χ is derived from the spectrum of temperature gradient measured by the thermistors (Osborn and Cox 1972). The turbulent kinetic energy dissipation rate ϵ is derived from the velocity shear spectrum measured by the shear probes (Osborn 1974). Though not presently implemented in firmware, the pitot tube offers a measurement of flow speed as well as estimates of turbulence kinetic energy and covariance heat flux (w′T′) as shown by Moum (1996, 2015). Both fast thermistors and shear probes are somewhat fragile. We include two of each sensor for both redundancy and as a consistency check on our computations of ϵ and χ. These sensors are all manufactured, tested and calibrated by the Ocean Mixing Group at OSU. Explicit forms for χ and ϵ are found in Zhang and Moum (2010) and Moum et al. (1995), for example. The specific details of Chameleon processing are provided by Moum et al. (1995). The specific details of FχS processing are provided by Hughes et al. (2023). All processing software is available at github.com/OceanMixingGroup. A summary of the processing used for the analysis in this paper is in section 4.
Turbulence sensors at leading edge of Flippin’ χSolo.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
In addition to the turbulence sensors, there is a pressure sensor (0–300 psi Measurement Specialties 86 Compensated) and a three-axis linear accelerometer (Analog Devices ADXL335). The latter provides (i) a measure of vehicle vibrations and any physical contact made with FχS (sharks, for example) that would contaminate the measurement and (ii) at low frequencies, deviations in gravitational accelerations caused by instrument tilts. Also, they provide a measurement of surface wave height spectra that leads to significant wave height while FχS is at the sea surface (appendix). In addition, for these tests, vehicle attitude was measured with a Honeywell HMC6343 three-axis linear accelerometer and compass that provides a 4 Hz serial data stream that we multiplex with internally sampled data. We interpret low-frequency (<1 Hz) accelerations as gravitational from which changes in vehicle attitude are derived. The HMC6343 is unique from and duplicates the ADXL335 sampled at 100 Hz to detect vehicle vibrations but which also detects tilts at low frequencies. The HMC6343 was included for these tests as it includes a compass heading measurement used in an unsuccessful attempt to compute directional surface wave spectra (see appendix, section c) and will not be included in future versions of FχS.
The turbulence pod houses analog and digital electronics to process and sample sensor voltages. Data are sampled at 100 Hz per channel (eight channels). All data are stored on a single 32 GB micro SD card. The turbulence pod receives commands from the SOLO-II module and sends reduced data back to be included in Iridium transmissions. Using the complete datasets from these tests, a data reduction scheme has been developed and will be implemented in future deployments. In this completed scheme, voltage spectra of shear and differentiated thermistor signals are calculated and fit in a specific manner over a fixed frequency band of 1–5 Hz. From these fit values, together with other voltage quantities from the thermistors and pressure sensor, ϵ and χ are calculated in postprocessing. Overall, data are reduced for transmission by a factor of 240–3 kB per 100 m of profile at a nominal 1 m resolution (Hughes et al. 2023).
3. Profiling characteristics
The sensitive axis of one accelerometer is aligned with the longitudinal axis of FχS so that it reads +1 g when oriented with turbulence pod sensors pointed upward. This sensor yields a cosine response to small angle tilts of the longitudinal axis from vertical. The sensitive axes of the other two accelerometers are oriented so that they read 0 g with turbulence pod sensors pointed upward and downward. These provide a sine response to small angle tilts of the longitudinal axis from vertical. We refer to the signal from the first sensor as pitch (which defines the vertical orientation of the instrument) and that from the other two sensors as roll (which might also be referred to as tilt), displaying only one component in Fig. 4 due to axial symmetry. Pitch and roll are referenced in units of angular degrees in Figs. 4c and 4d.
Roughly 1 h time sequence from FχS showing two descents and two ascents indicated by (a) depth changes, (b) vehicle rise rate w (w < 0 are descents and w > 0 are ascents; here w is filtered at 0.2 Hz), (c) vehicle pitch angle (pitch = +90°, turbulence sensors point up), and (d) vehicle roll is the small angle deviation from vertical.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
A short time series from one FχS unit shows the basic profiling sequence (Fig. 4). Following descent with terminal speed w ≃ −0.2 m s−1 (the ascent/descent rate, w = dz/dt, is computed as the time rate of change of depth derived from the pressure signal) and upon a command from the SOLO-II controller, the turbulence pod ceases sampling to write data files and perform computations—hence the record gaps. Upon another SOLO-II command to indicate FχS has flipped and reballasted, the turbulence pod restarts sampling. FχS ascends reaching a terminal speed w ≃ 0.3 m s−1. The influence of surface waves are clear in w, pitch, and roll as FχS nears the sea surface. Having breached the sea surface, FχS again flips to expose antennas and transmit data before repeating the cycle. Below the influence of surface waves (below about 20 m), roll amplitudes are about 1.5° with a 7–8 s period. Nearer the surface, amplitudes are larger and periods are set by the surface wave field.
4. Processing of turbulence signals
For the purpose of this analysis of measurements from initial at-sea profiling tests of FχS, we followed the procedures to compute ϵ and χ described in this section. As FχS is ultimately expendable, we have also devised a scheme to significantly reduce the data for transmission from remote ocean sites. This method is fully described and tested by Hughes et al. (2023). Future processing will follow the Hughes et al. (2023) algorithms.
a. ϵ
The 100 Hz shear probe voltage data were calibrated into units of velocity gradient uz following Moum et al. (1995). Spectra computed from this signal were partially corrected for the limited wavenumber response of our shear probes using the form defined by Ninnis (1984) which was measured for probes of nearly identical physical dimension to our present probes. Spectra were further corrected for the four-pole Butterworth antialiasing filter (cutoff frequency 40 Hz). While vibrational corrections (Goodman et al. 2006) are clever and useful, they are not used for these energetic upper-ocean measurements based on initial spectral evaluations that show minimal contamination in the data bands (section 5b).
Note that the lower limit for integration of Chameleon spectra is set to 2 cpm (Moum et al. 1995). The slower speed of FχS prompted the change to 4 cpm for FχS analysis, thus moving spectra away from the dominant surface wave bands.
The Nasmyth spectrum is based on measurements in a very high Reynolds number turbulent tidal channel flow (Nasmyth 1970) with a useful analytical form by Lueck (2013).
b. χ
5. Evaluation of turbulence measurements
An example upward FχS turbulence profile (Fig. 5) shows several aspects of the measurement. The signals shown include temperature (T; Fig. 5a) as measured by fast thermistor as well as temperature microstructure gradients (
FχS profile upward through the sea surface. (a) Temperature from one of the fast thermistors; (b) profiles of
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
The T profile shows a near-surface thermocline at 10 m depth and a deeper one at 48 m. Between these depths, the profile is continuously stratified. Above 10 m, the profile is unstratified.
a. Field tests
It is impossible to evaluate platforms built to measure turbulence at sea from laboratory measurements alone. In the laboratory, we can attempt to minimize self-generated internal radiated noise, but we cannot replicate the physical forcing induced by profiling through the fluid that in turn creates vibrations contributing to a signal sensed by the shear probes, which is not environmental and which largely defines the noise floor of the measurement (Moum and Lueck 1985).
In situ measurements provide the best way to evaluate their integrity. Such exercises have proven invaluable in confirming measurements from different platforms (Moum et al. 1995) and indeed from very different methods on different platforms (Perlin and Moum 2012). A field experiment designed to evaluate FχS noise levels and provide a platform-to-platform comparison to proven measurements using Chameleon was conducted off Oregon in May 2019. Two FχS units (FCS1, FCS2) were deployed within a few hundred meters of each other for a period of roughly 3.5 days. For these tests, both units were deployed to depths ranging from 100 to 175 m as we tested profiling configurations (adjustments are made remotely via satellite communication). During this time, R/V Oceanus remained in the area while profiling with Chameleon. The ship track and FχS surface trajectories are indicated in Fig. 6. The floats remained within a 5 km radius of their initial deployments while tracing inertial trajectories. The floats were recovered 6 km to the NE separated by 2.5 km.
Positions of two FχS profiling floats and R/V Oceanus during a 3.5-day field experiment off Oregon in May 2019. Ordinate is distance north and abscissa distance east from the geographical coordinate (45°00′N, 125°29.7′W). Profiles were conducted nearly continuously from the ship while tracking the float positions. Separations between the two floats ranged from 470 m to 1.75 km. Separations between ship and floats ranged from 65 m to 5.2 km.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Both FχS units were programmed to run the SBE CTD on the downward profiles. This requires mechanical pumping of water through the conductivity cell, a potential vibrational contaminant to the shear probe measurement on the turbulence pod. The SBE CTD was shut down for all upward profiles to provide a baseline comparison.
Evaluation of the turbulence measurements is based on 1-m-averaged values of χ and ϵ. Chameleon estimates of ϵ are as described by Moum et al. (1995). FχS estimates are derived from 512-point segments (Hughes et al. 2023), roughly 1 m at 0.2 m s−1 profiling speed. The data were then gridded to precisely 1 m intervals.
Time series of the vertical structure of χ and ϵ from the three platforms are shown in Figs. 7 and 8 with the number of profiles (including both upward and downward profiles) noted in the lower-left box. Chameleon profiles downward at roughly 1 m s−1 compared to FχS profiling rates of 0.2 m s−1, contributing to the greater number of Chameleon profiles per unit time. As a result, Figs. 7a, 7b, 8a, and 8b look relatively grainy at this scale compared to Figs. 7c and 8c. FCS1 operated continuously throughout the period. FCS2 was recovered on 15 May to replace a faulty sensor and redeployed. Data are flagged due to defective sensors or data glitches and missing when Chameleon profiling was suspended to attend to other shipboard tasks. Data glitches due to impacts by zooplankton on FχS shear probes are despiked (Hughes et al. 2023) following the procedure of Lueck et al. (2018). For Chameleon, plankton glitches are removed automatically in software, as in Moum et al. (1995): when the estimate of ϵ from one probe exceeds the other by a factor ≥ 10, the lower estimate is used. Otherwise, the average value of the two ϵ estimates is used. The qualification, of course, is that the probes are generally in working order.
Time–depth series of χ as measured by (a),(b) two FχS profilers and (c) Chameleon over 3.5 days in May 2019. The several hour gap in FχS2 and Chameleon data on 15 May was due to a recovery and redeployment of FχS2 for probe replacement. The upper 9 m of the Chameleon profiles are flagged to remove potential influences of vessel flow disturbance.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Time-depth series of ϵ as described in Fig. 7.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Figures 7a, 7b, 8a, and 8b show alternating white bands near the surface indicating alternating upward/downward FχS profiles. The downward FχS profiles provide no useful data above 2 m while the upward profiles penetrate the sea surface. In contrast, the presence of the vessel precludes near-surface values from Chameleon profiles executed from the fantail. Here, the upper 9 m is conservatively flagged. There is no obvious banding in the FχS image plots that would indicate significant differences in noise level between upward and downward profiles, such as might be due to the CTD pumping on downward profiles.
The distinctive near-surface structures of χ and ϵ are clear in Figs. 7a, 7b, 8a, and 8b. The vertical structure of χ emphasizes the variable depth thermocline in the upper 15 m and tends to 0 in the mixed layer above. The presence of active turbulence is indicated by the vertical structure of ϵ, which tends to continuously increase toward the sea surface as discussed further in section 5d.
b. Shear spectra
Example spectra from Chameleon and from each of the two FχS units on both ascents and descents indicate a few distinctions (Fig. 9). Ten spectra were randomly selected from each unit’s data record and each value of ϵ with the condition that the value of ϵ be within 50% of the nominal values shown in Fig. 9. Median values of the spectra represent central tendencies (thick lines). On FχS descents/ascents, the CTD was turned on/off. The spectral signature of the CTD pump is a peak at 16 Hz. Vibrations introduced by the pump appear in the descent spectra (Figs. 9b,d) and not on the ascent spectra (Figs. 9c,e). Unit FCS2 appeared to be more adversely affected, with the spectra exhibiting harmonics and subharmonics of the 16 Hz pump signal.
Sets of 10 randomly selected frequency spectra of shear
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
The frequency spectra in Fig. 9 were converted to wavenumber spectra in Fig. 10 so as to compare to the empirical (and apparently universal) redimensionalized forms of Nasmyth (1970). The wavenumber ranges of fits to the Nasmyth spectra are smaller than those affected by the CTD pump vibrations. The reduced range of fits for Chameleon spectra in Fig. 10a avoid additional vibrational peaks present in Chameleon but absent in FχS. This is emphasized in Fig. 11 that shows spectra from low values of ϵ together with vibrational spectra in the form ϕacc/W from accelerometers on Chameleon (e.g., Moum and Lueck 1985), with W the flow speed past the sensors and “acc” a generic reference to the acceleration component (all three components are shown in Fig. 11). The broad vibrational peak at 20–25 Hz in the lateral (x, y) accelerations are clear in Chameleon shear spectra, albeit with different amplitude as the ϕacc/W analogy is incomplete in terms of vibrations excited in the simply supported bimorph piezoceramic beam embedded in the shear probe. By comparison, FχS shear spectra from ascents are relatively clean of vibrational contamination. Note that FχS accelerations were not sufficiently resolved at high frequencies and are not shown here.
Shear spectra from Fig. 9 shown as functions of wavenumber, k = f/w, where wavenumber k is related to frequency f via the flow speed past the sensor w. Dashed lines are Nasmyth spectra with values of ϵ equal to ±50% of the three nominal values. Thick lines represent the wavenumber ranges over which measured spectra are fitted to the Nasmyth form following Moum et al. (1995).
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Near-noise level shear spectra. Each spectrum shown is the median of 10 individual spectra. Each of these 10 spectra is derived from a 512-point segment in which ϵ was 5 × 10−10 W kg−1 ±50%. Spectra of A/W were similarly computed and represent vehicular vibrations in comparable units.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
The vibrational accelerations are in proportion to the ratio of the hydrodynamic force (Fh) on the body to the mass (m) of the body, i.e., a = Fh/m. The value of Fh is proportional to the product of the body’s cross-sectional area and its squared speed, Fh ∝ r2w2, with r the radius of the body. Given the properties in Table 1 and assuming FχS and Chameleon have the same empirical drag coefficients, accordingly the ratio of expected vibrational accelerations is
Chameleon and FχS mass, radius, and speed.
c. Statistics of χ and ϵ
Experiment-averaged vertical profiles of χ (5 m mean values are shown in Fig. 12) indicate general agreement within 95% confidence limits at all depths other than the uppermost Chameleon value at 12.5 m. The reason for this low value is not clear and mean values of ϵ from all three profilers are consistent at that depth (Fig. 13). The averaged FχS profiles show the enhanced values of χ at the shallow thermocline above 15 m and the deeper thermocline at about 40 m depth. The mixed layer null in χ above a maximum in the shallow thermocline that is clear in Figs. 5 and 7 is obscured in the averaged profile by the vertical variability of the thermocline.
Averaged profiles of χ from Chameleon and two FχS profilers during 3.5-day field trials. Shown are 5 m vertical averages for clarity. Bootstrapped 95% confidence intervals are indicated by shading.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Averaged profiles of ϵ from Chameleon and two FχS profilers during 3.5-day field trials. Bootstrapped 95% confidence intervals are indicated by shading.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Mean vertical profiles of ϵ from the three platforms (Fig. 13) also show general agreement at the 95% confidence level at almost all depths. The tendency for ϵ to increase toward the sea surface is made clear from the upward FχS profiles; as shown here, the uppermost value is 2.5 m depth.
Histograms of the 1-m-averaged values of χ over the depth range 20–50 m are shown in Fig. 14. The spread of the data, indicated by bars showing 75% and 90% data ranges, overlap but are not identical. Median values of χ from FCS1 are shifted to slightly lower values as it seems that noise levels are somewhat smaller. Mean values differ within 95% bootstrapped confidence limits but by less than a factor of 2 (by comparison to the bar at center bottom). Interplatform measurement comparisons by Moum et al. (1995) and Perlin and Moum (2012) have shown factor of 2 agreement between independent averaged estimates. One suggestion has been that natural geophysical variability of the turbulence may make it difficult for estimates to converge any better than this on time scales shorter than weeks to months.
Histograms (normalized such that the sum of the bar heights = 1) of χ from Chameleon and the two FχS profilers using all 1 m (nominal depth interval) averaged data between 20 and 50 m depth. The thick bars denote 75% data range and thin bars denote 90% data range. Circles indicate median values. Diamonds represent mean values of each distribution with bootstrapped 95% confidence intervals shown by the horizontal bars. For reference, the logarithmic range of a factor of 2 is shown at bottom center.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Greater variability is seen in the comparative histograms of ϵ in Fig. 15. In this case the noise levels differ considerably. And the range of the data and medians reflect this. However, mean values do not differ significantly within 95% confidence limits and we expect that the turbulence that matters, that is the largest values of ϵ that dominate the means in these high kurtosis distributions, has been adequately sampled.
Normalized histograms of ϵ with format as specified in Fig. 14.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
d. Near-surface measurements
FχS introduces a new measurement capability to obtain continued clean measurements of turbulence through the sea surface, a notoriously difficult environment, particularly in the presence of strong atmospheric forcing, which is when these measurements are most critical. Profiling through the sea surface in a similar manner has been accomplished (awkwardly) by releasing weights from a buoyant tethered profiler which then profiles upward (Dillon et al. 1981; Anis and Moum 1995), requiring the presence of a ship and hence to a limited range of atmospheric forcing. Ward et al. (2014) developed an autonomous turbulence profiler that was buoyant and driven downward by thrusters prior to profiling upward. Power requirements limited the number of profiles (60 profiles from 100 m depth) and recovery was required to download data. This has also been accomplished with a bottom mounted profiler in shallow water by Prandke and Stips (1998) and Stevens and Smith (2004), albeit the latter study with thermistors only. Here we provide a closer look at the structure of ϵ(z) near the sea surface from our FχS field tests.
Averaged vertical profiles from the two FχS profilers indicate general agreement in magnitude and vertical structure (Fig. 16a). It has long been known that, beneath the ocean’s free surface, ϵ exceeds predictions that are based on flows adjacent to solid boundaries (Agrawal et al. 1992; Anis and Moum 1992). In the latter scaling ϵ robustly follows
Averaged vertical profiles of ϵ through the sea surface derived from two FχS profilers: (a) ϵ; (b) ϵ normalized by log-layer scaling; (c) ϵ normalized by wave parameters. Depth is scaled by significant wave height Hs. All ordinates are logarithmic.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
A particularly novel aspect of these measurements is the interpretation of the accelerometer signals to determine properties of the surface wave field while FχS is surfaced and reporting data. In the appendix we demonstrate the computation of significant wave height, Hs, and wave height spectra from the two FχS units (independently) in comparison to that computed from measurements at a nearby National Data Buoy Center wave buoy. From the wave height spectra are computed ωm and cm [see Sutherland and Melville (2015) for example definitions]. We use these parameters to scale the near-surface measurements as shown in Fig. 16c. Sutherland and Melville (2015) showed general agreement of a range of measurements with this wave-based scaling of ϵ for z > 0.1Hs, as seen in Fig. 16c. However, they noted turbulence enhanced above this level at z < 0.1Hs, a range not included in our data. Planned new deployments of many FχS profiling floats in more energetic wave environments will yield greater values of Hs and smaller values of
6. Summary
We have adapted a SOLO-II float to make continued profiles of turbulence for periods of up to 60 days at the rate of roughly 3 profiles per hour from 100 m through the sea surface, including time to transmit data at the surface and to flip at top and bottom of profiles. This time is extended by reducing profiling rates which is achievable by parking FχS at fixed depth with electronics in sleep mode.
Inclusion of both shear probes and fast thermistors on FχS permits dual concurrent estimates of turbulence diffusivities (Osborn and Cox 1972; Osborn 1980; for thermistors and shear probes, respectively), allowing quantitative consistency checks and perhaps reassessments of mixing efficiency estimates (Oakey 1982; Gregg et al. 2018; Smyth 2020). This sensor combination also yields an estimate of turbulence in the absence of microstructure in regimes such as the surface mixed layer, the primary target of FχS.
Our primary objective in developing an upper-ocean autonomous turbulence profiling capability with acceptably low-noise profiling measurements of turbulence has been met. Our metric, that noise levels of χ and ϵ are no greater than those measured by Chameleon are demonstrated in Figs. 14 and 15. Together with the accompanying development of a robust data reduction scheme (Hughes et al. 2023), FχS provides a significant step toward ArgoMix as defined by Roemmich et al. (2019).
FχS is intended as a tool to quantify air–sea couplings. In particular, continuous profiles through the upper ocean and sea surface over periods of months lead to detailed vertical profiles of heat and momentum fluxes (Moum 2021) over a range of forcing conditions. Assessment of the flux divergences define their contributions to changes in upper-ocean temperature and velocity distributions. While this is not yet part of the Argo mission, experience gained from these and future deployments contribute to understanding challenges to ArgoMix (Roemmich et al. 2019). Deployments of eight FχS floats in 2023 and 2024 in the western Pacific as part of ONR’s ARCTERX program will help to define survival rates of sensors over several tens of thousands of upper-ocean profiles. A principal concern is the tendency of fish to aggregate and cause mechanical breakage. These deployments will also contribute to defining best practice sampling strategies. By subsampling of nonstop profiles, we ought to be able to determine profiling rates that optimize the conflicting requirements of temporal resolution and power consumption. In addition, we can begin to assess rationales for optimal spacings between profilers.
Acknowledgments.
This work was funded by the Office of Naval Research under Grant N00014-17-1-2700 (OSU) and N00014-17-1-2762 (SIO) and continued as part of the Island Arc Turbulent Eddy Regional Exchange (ARCTERX) program under Grants N00014-21-1-2878 (OSU) and N00014-21-1-2762 (SIO). The comments of two anonymous reviewers helped to improve the clarity of the text.
Data availability statement.
Our MATLAB implementation of the processing code is available from github.com/OceanMixingGroup/flippin-chi-solo. Raw and processed data for the 2019 experiment are available at doi.org/10.5281/zenodo.5719505. Data from buoy 46050 are available from the National Data Buoy Center at ndbc.noaa.gov.
APPENDIX
Significant Wave Height from Surface Measurements of Vehicle Acceleration
Between ascents and descents, FχS spends ∼5 min at the surface to transmit data. The acceleration signals from these periods are converted to a sea surface height spectrum from which are computed quantities such as significant wave height.
a. Acceleration components
When at the surface, FχS remains approximately vertical on average, but pitches and rolls by 10°–20°. Therefore, all three components of acceleration factor into our calculation of the wave state. This differs from our experience with a surface-following platform in which only the vertical component is needed (Hughes et al. 2020).
b. Comparison to wave buoy
To confirm that the FχS-derived wave states are reasonable, we compare them to a nearby buoy maintained by the National Data Buoy Center. Specifically, we used buoy 46050, which is situated ∼80 km southeast of where our 2019 field experiment took place.
Agreement between the wave state measured by the two FχS units against that from a nearby buoy in terms of (b) significant wave height and (c)–(e) wave height spectra.
Citation: Journal of Atmospheric and Oceanic Technology 40, 5; 10.1175/JTECH-D-22-0067.1
Without the correction for pitch and roll, the significant wave height derived from the FχS units is often too large by a factor of 2 (not shown).
c. Failure to compute directional wave spectra
We attempted to infer the direction of the dominant surface waves from the direction of FχS tilts while at the sea surface. To determine this, we plotted the two roll components against each other at each surfacing. We were looking for a preferred direction of alignment dictated by the wave direction. But these plots were quite noisy and did not convincingly show a preferred direction. FχS is an axially symmetric body. Perhaps an axially asymmetric platform would tilt with the waves in a more convincing manner.
REFERENCES
Agrawal, Y. C., E. A. Terray, M. A. Donelan, P. A. Hwang, A. J. Williams III, W. M. Drennan, K. K. Kahma, and S. A. Kitaigorodskii, 1992: Enhanced dissipation of kinetic energy beneath surface waves. Nature, 359, 219–220, https://doi.org/10.1038/359219a0.
Anis, A., and J. N. Moum, 1992: The superadiabatic surface layer of the ocean during convection. J. Phys. Oceanogr., 22, 1221–1227, https://doi.org/10.1175/1520-0485(1992)022<1221:TSSLOT>2.0.CO;2.
Anis, A., and J. N. Moum, 1995: Surface wave–turbulence interactions: Scaling ϵ(z) near the sea surface. J. Phys. Oceanogr., 25, 2025–2045, https://doi.org/10.1175/1520-0485(1995)025<2025:SWISNT>2.0.CO;2.
Davis, R. E., L. A. Regier, J. Dufour, and D. C. Webb, 1992: The Autonomous Lagrangian Circulation Explorer (ALACE). J. Atmos. Oceanic Technol., 9, 264–285, https://doi.org/10.1175/1520-0426(1992)009<0264:TALCE>2.0.CO;2.
Davis, R. E., J. T. Sherman, and J. Dufour, 2001: Profiling ALACEs and other advances in autonomous subsurface floats. J. Atmos. Oceanic Technol., 18, 982–993, https://doi.org/10.1175/1520-0426(2001)018<0982:PAAOAI>2.0.CO;2.
Dillon, T. M., J. G. Richman, C. G. Hansen, and M. D. Pearson, 1981: Near-surface turbulence measurements in a lake. Nature, 290, 390–392, https://doi.org/10.1038/290390a0.
Edson, J. B., and Coauthors, 2013: On the exchange of momentum over the open ocean. J. Phys. Oceanogr., 43, 1589–1610, https://doi.org/10.1175/JPO-D-12-0173.1.
Fer, I., A. K. Peterson, and J. E. Ullgren, 2014: Microstructure measurements from an underwater glider in the turbulent Faroe Bank Channel overflow. J. Atmos. Oceanic Technol., 31, 1128–1150, https://doi.org/10.1175/JTECH-D-13-00221.1.
Goodman, L., E. R. Levine, and R. G. Lueck, 2006: On measuring the terms of the turbulent kinetic energy budget from an AUV. J. Atmos. Oceanic Technol., 23, 977–990, https://doi.org/10.1175/JTECH1889.1.
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.
Gregg, M. C., E. A. D’Asaro, J. J. Riley, and E. Kunze, 2018: Mixing efficiency in the ocean. Annu. Rev. Mar. Sci., 10, 443–447, https://doi.org/10.1146/annurev-marine-121916-063643.
Hughes, K. G., J. N. Moum, and E. L. Shroyer, 2020: Evolution of the velocity structure in the diurnal warm layer. J. Phys. Oceanogr., 50, 615–631, https://doi.org/10.1175/JPO-D-19-0207.1.
Hughes, K. G., J. N. Moum, and D. L. Rudnick, 2023: A turbulence data reduction scheme for autonomous and expendable profiling floats. Ocean Sci., 19, 193–207, https://doi.org/10.5194/os-19-193-2023.
Kraichnan, R. H., 1968: Small-scale structure of a scalar field convected by turbulence. Phys. Fluids, 11, 945–953, https://doi.org/10.1063/1.1692063.
Lien, R.-C., T. B. Sanford, J. A. Carlson, and J. H. Dunlap, 2016: Autonomous microstructure EM-APEX floats. Methods Oceanogr., 17, 282–295, https://doi.org/10.1016/j.mio.2016.09.003.
Lueck, R., 2013: Calculating the rate of dissipation of turbulent kinetic energy. RSI Tech. Rep. 28, 19 pp., https://rocklandscientific.com/wp-content/uploads/2021/12/TN-028-Calculating-the-Rate-of-Dissipation-of-Turbulent-Kinetic-Energy.pdf.
Lueck, R., O. Hertzman, and T. R. Osborn, 1977: The spectral response of thermistors. Deep-Sea Res., 24, 951–970, https://doi.org/10.1016/0146-6291(77)90565-3.
Lueck, R., E. Murowinski, and J. McMillan, 2018: A guide to data processing: ODAS MATLAB library v4.3. RSI Tech. Rep. 39, 41 pp., https://rocklandscientific.com/support/knowledge-base/technical-notes/.
Marusic, I., J. P. Monty, M. Hultmark, and A. J. Smits, 2013: On the logarithmic region in wall turbulence. J. Fluid Mech., 716, R3, https://doi.org/10.1017/jfm.2012.511.
Moum, J. N., 1996: Energy-containing scales of turbulence in the ocean thermocline. J. Geophys. Res., 101, 14 095–14 109, https://doi.org/10.1029/96JC00507.
Moum, J. N., 2015: Ocean speed and turbulence measurements using pitot-static tubes on moorings. J. Atmos. Oceanic Technol., 32, 1400–1413, https://doi.org/10.1175/JTECH-D-14-00158.1.
Moum, J. N., 2021: Variations in ocean mixing from seconds to years. Annu. Rev. Mar. Sci., 13, 201–226, https://doi.org/10.1146/annurev-marine-031920-122846.
Moum, J. N., and R. G. Lueck, 1985: Causes and implications of noise in oceanic dissipation measurements. Deep-Sea Res., 32A, 379–390, https://doi.org/10.1016/0198-0149(85)90086-X.
Moum, J. N., M. C. Gregg, R. C. Lien, and M. E. Carr, 1995: Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers. J. Atmos. Oceanic Technol., 12, 346–366, https://doi.org/10.1175/1520-0426(1995)012<0346:COTKED>2.0.CO;2.
Nash, J. D., D. R. Caldwell, M. J. Zelman, and J. N. Moum, 1999: A thermocouple probe for high-speed temperature measurement in the ocean. J. Atmos. Oceanic Technol., 16, 1474–1482, https://doi.org/10.1175/1520-0426(1999)016<1474:ATPFHS>2.0.CO;2.
Nasmyth, P. W., 1970: Oceanic turbulence. Ph.D. thesis, University of British Columbia, 106 pp., https://doi.org/10.14288/1.0302459.
Ninnis, R., 1984: The effects of spatial averaging on airfoil probe measurements of oceanic velocity microstructure. Ph.D. thesis, University of British Columbia, 119 pp., https://doi.org/10.14288/1.0053131.
Oakey, N. S., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr., 12, 256–271, https://doi.org/10.1175/1520-0485(1982)012<0256:DOTROD>2.0.CO;2.
Osborn, T. R., 1974: Vertical profiling of velocity microstructure. J. Phys. Oceanogr., 4, 109–115, https://doi.org/10.1175/1520-0485(1974)004<0109:VPOVM>2.0.CO;2.
Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 83–89, https://doi.org/10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;2.
Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn., 3, 321–345, https://doi.org/10.1080/03091927208236085.
Perlin, A., and J. N. Moum, 2012: Comparison of thermal variance dissipation rates from moored and profiling instruments at the equator. J. Atmos. Oceanic Technol., 29, 1347–1362, https://doi.org/10.1175/JTECH-D-12-00019.1.
Perlin, A., J. N. Moum, J. M. Klymak, M. D. Levine, T. Boyd, and P. M. Kosro, 2005: A modified law-of-the-wall applied to oceanic bottom boundary layers. J. Geophys. Res., 110, C10S10, https://doi.org/10.1029/2004JC002310.
Prandke, H., and A. Stips, 1998: Test measurements with an operational microstructure-turbulence profiler: Detection limit of dissipation rates. Aquat. Sci., 60, 191–209, https://doi.org/10.1007/s000270050036.
Rainville, L., J. I. Gobat, C. M. Lee, and G. B. Shilling, 2017: Multi-month dissipation estimates using microstructure from autonomous underwater gliders. Oceanography, 30 (2), 49–50, https://doi.org/10.5670/oceanog.2017.219.
Roemmich, D., and Coauthors, 2009: The Argo program: Observing the global ocean with profiling floats. Oceanography, 22 (2), 34–43, https://doi.org/10.5670/oceanog.2009.36.
Roemmich, D., and Coauthors, 2019: On the future of Argo: A global, full-depth, multi-disciplinary array. Front. Mar. Sci., 6, 439, https://doi.org/10.3389/fmars.2019.00439.
Rossby, T., and D. Webb, 1970: Observing abyssal motions by tracking swallow floats in the SOFAR channel. Deep-Sea Res. Oceanogr. Abstr., 17, 359–365, https://doi.org/10.1016/0011-7471(70)90027-6.
Rudnick, D. L., R. E. Davis, C. C. Eriksen, D. M. Fratantoni, and M. J. Perry, 2004: Underwater gliders for ocean research. Mar. Technol. Soc. J., 38, 73–84, https://doi.org/10.4031/002533204787522703.
Sherman, J., R. E. Davis, W. B. Owens, and J. Valdes, 2001: The autonomous underwater glider “Spray.” IEEE J. Oceanic Eng., 26, 437–446, https://doi.org/10.1109/48.972076.
Smyth, W. D., 2020: Marginal instability and the efficiency of ocean mixing. J. Phys. Oceanogr., 50, 2141–2150, https://doi.org/10.1175/JPO-D-20-0083.1.
St. Laurent, L., and S. Merrifield, 2017: Measurements of near-surface turbulence and mixing from autonomous ocean gliders. Oceanography, 30 (2), 116–125, https://doi.org/10.5670/oceanog.2017.231.
Stevens, C. L., and M. J. Smith, 2004: Temperature microstructure beneath surface gravity waves. J. Atmos. Oceanic Technol., 21, 1747–1757, https://doi.org/10.1175/JTECH1659.1.
Sutherland, P., and W. K. Melville, 2015: Measuring turbulent kinetic energy dissipation at a wavy sea surface. J. Atmos. Oceanic Technol., 32, 1498–1514, https://doi.org/10.1175/JTECH-D-14-00227.1.
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.
Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. MIT Press, 300 pp.
Terray, E. A., M. A. Donelan, Y. C. Agrawal, W. M. Drennan, K. K. Kahma, A. J. Williams, P. A. Hwang, and S. A. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26, 792–807, https://doi.org/10.1175/1520-0485(1996)026<0792:EOKEDU>2.0.CO;2.
Ward, B., T. Fristedt, A. H. Callaghan, G. Sutherland, X. Sanchez, J. Vialard, and A. ten Doeschate, 2014: The Air–Sea Interaction Profiler (ASIP): An autonomous upwardly rising profiler for microstructure measurements in the upper ocean. J. Atmos. Oceanic Technol., 31, 2246–2267, https://doi.org/10.1175/JTECH-D-14-00010.1.
Zhang, Y., and J. N. Moum, 2010: Inertial-convective subrange estimates of thermal variance dissipation rate from moored temperature measurements. J. Atmos. Oceanic Technol., 27, 1950–1959, https://doi.org/10.1175/2010JTECHO746.1.
