Autonomous and expendable profiling-float arrays such as those deployed in the Argo Program require the transmission of reliable data from remote sites. However, existing satellite data transfer rates preclude complete transmission of rapidly sampled turbulence measurements. It is therefore necessary to reduce turbulence data on board. Here we propose a scheme for onboard data reduction and test it with existing turbulence data obtained with a modified SOLO-II profiling float. First, voltage spectra are derived from shear probe and fast-thermistor signals. Then, we focus on a fixed-frequency band that we know to be unaffected by vibrations and that approximately corresponds to a wavenumber band of 5–25 cpm. Over the fixed-frequency band, we make simple power law fits that – after calibration and correction in post-processing – yield values for the turbulent kinetic energy dissipation rate
Measurements of oceanic turbulence have been made since the 1950s using platforms and sensors of various shapes and sizes
One approach to reducing turbulence data is given by
Our scheme is for profiling instruments that contain shear probes and, optionally, fast thermistors (Sect.
We intend our data reduction scheme to be sufficiently general so as to be portable to all vertical turbulence profilers that contain shear probes. It can also be used with gliders if a measure of flow speed past the sensors is available
FCS is a descendant of the SOLO-II profiling float
To reverse profiling direction, FCS adjusts buoyancy and flips via internal shifting of the battery pack. This causes the turbulence sensors to always point into undisturbed fluid. Flipping therefore permits profiling on both descent and ascent, including sampling of the upper 5 m on the ascent.
As a prototype, a standard (non-flipping) SOLO float with a modified
Two FCS units were vetted over 4 days in May 2019 off the Oregon coast. During this period, each unit profiled from the surface to
The core of our data reduction scheme uses power law fits of voltage spectra that are calculated on board and subsequently converted to meaningful turbulence quantities in post-processing. Additional voltage quantities are also recorded to determine temperature, pressure, and profiling speed.
All quantities measured by FCS that are discussed in this paper are sampled at 100 Hz. All voltage spectra are frequency spectra and are denoted by Physical spectra of shear and temperature gradient are wavenumber spectra and are denoted by Wavenumber The Kraichnan model spectrum A pair of angle brackets, To calculate spectra for a given 512-element voltage segment, we first remove the linear trend, then we use three half-overlapping, Hamming-windowed, 256-element subsegments (i.e.,
In general, the values of
We do not pursue the possibility of using accelerometers to decontaminate spectra
The voltage reported by the shear probe
Two voltage signals are recorded for each fast thermistor.
The gradient of the temperature calibration is
Rewriting Eq. (
Pressure has a linear calibration:
The flow speed past the sensors, denoted
No smoothing is necessary before calculating
Wave orbitals can introduce variability when
In this paper, we immediately discard all segments in which
In this section, we are ultimately going to fit measured spectra to an inertial subrange model that does not necessarily apply at the relevant frequencies or wavenumbers. We will elaborate as we go, but we want to emphasize in advance that measured spectra do not need to conform to an inertial subrange model for us to obtain accurate values of
Shear measurements ideally capture both the inertial and viscous subranges and hence use a wide band of the measured spectrum to derive values for
Here we develop a new and simpler two-stage approach to fitting shear spectra to
In the inertial subrange, shear spectra are proportional to
Our choice of
Our inertial subrange assumption is often false. Indeed, “assumption” is perhaps a misnomer, as we do not expect it to be true; we know that viscous roll off will often occur at frequencies lower than 5 Hz (25 cpm for a nominal value of
The full Nasmyth spectrum and its inertial range approximation are as follows
Let
Consider two contrasting examples of low and high turbulence with
Calculation of the correction function
Nasmyth spectra can be flattened to unity over the inertial subrange with the normalization
With
The correction function
To simplify calculations in the upcoming section, we make one final change to Eq. (
Since
Measured shear spectra are often quality controlled either by manual visual inspection or, more objectively, by quantifying the level of mismatch between them and their associated model. Possible mismatch quantities include the mean absolute deviation or the variance of the ratio
To retain at least some information about the shape of each voltage spectrum, we will split the 1–5 Hz range and compute two fits rather than one. Doing so allows for a first-order check that the spectrum over the 1–5 Hz range approximately follows the expected shape.
A visual demonstration of how the
Examples of measured shear spectra exhibiting a range of
Mathematically, there is nothing special about our choice
When
To test the accuracy of the shear reduction scheme described in the previous section, we apply it retrospectively to the dataset from the 2019 test cruise (Sect.
A profile-by-profile comparison of the two schemes is shown in Fig.
Testing the proposed data reduction scheme for shear measurements against the standard processing approach. One upward and one downward profile from each of the two FCS units were arbitrarily chosen for this comparison.
Statistical test of the proposed data reduction scheme for
To demonstrate the ability of the
As the
The scheme to reduce fast-thermistor data to enable measurement of
Here we take the Kraichnan spectrum
A fit against Eq. (
The derivation of
Like we did for
The approach to quality controlling the fast-thermistor data is the same as that for shear (Sect.
We do not apply a low
Profiles of
Testing the proposed data reduction scheme for fast-thermistor measurements. The profiles used are the same as those chosen in Fig.
Statistical test of the proposed data reduction scheme for
Compared to shear spectra, non-dimensionalized temperature gradient spectra have lower fit scores. Especially for the lowest fit scores, the measured temperature gradient spectra tend to be too high at lower frequencies and too low at frequencies near
Same as for Fig.
There are three reasons for the poorer fits to temperature gradient spectra compared to that for shear. First, shapes of temperature gradient spectra are often more variable; the best choice for the non-dimensional spectral model can be debated
Our scheme requires a few user-defined parameters: Choose Ensure that there are no known issues such as vibrations that are likely to adversely affect spectral coefficients within the Define Use more than two fitting bands if desired. We use only two bands (1–3 and 3–5 Hz) so as to minimize the file size to be transmitted, but there is nothing preventing there being three or more bands (e.g., adding a 5–7 Hz band). Indeed, this would enable improved estimates of the fit scores (Eqs. Choose Reasonable choices for
One step that cannot be automated is the heuristic evaluation of the reduced turbulence data after they have been converted from voltage quantities to physical ones. For this evaluation, we recommend looking into multiple quantities. First consider the fit scores (Eqs. turbulent features in successive profiles.
The last point is most applicable for a vertical profiler cycling rapidly – for example, twice per hour for FCS. In this case, the profiler is nominally sampling the same vertical fragment of the ocean on a timescale comparable to that over which turbulence evolves. In our experience, many turbulent patches extend over 5–10 profiles.
Recall, also, that all uncertainty in
We have developed a data reduction scheme applicable to vertical profiling of turbulence variables in which each
Summary of the data reduction scheme. Each 512-element segment of data is ultimately compressed down to the 12 highlighted quantities that are then transmitted. These are calibrated and/or converted into turbulence quantities in post-processing.
This reduction compresses the output data file size for each dive from megabytes to kilobytes. For example, the total amount of data per dive (two profiles) can be estimated assuming our nominal dive depth and profiling velocity of 120 m and 0.2 m s
One luxury we lose is the ability to inspect the raw signals. Typically this would help to (i) cultivate faith in the data, (ii) flag which segments to discard, and (iii) inform work-arounds such as filtering out potential narrowband vibrations in shear spectra. Our scheme accounts for this constraint in two ways. First, we fit spectra over relatively low frequencies (1–5 Hz) that are unlikely to be affected by noise or vibration. Second, we reduce the data in a way that uses as little arithmetic as possible. Obviously, we cannot reverse-engineer the raw signals, but by making the onboard calculations simple, we give ourselves the best chance to later fix or identify any unforeseen issues.
Although the onboard reduction eliminates possibilities in how we process turbulence data, it opens up possibilities in how we obtain turbulence data. By visualizing how turbulence evolves over successive dives in near-real time, we can concentrate on regions of interest by adapting the dive schedule to profile more frequently or to different depths. If instead we encounter quiescent periods, we might consider profiling less frequently, thereby conserving battery life. Our ultimate objective is to treat FCS floats as expendable.
Voltage signals from shear probes and thermistors are a smoothed representation of the true environmental signal. If the smoothing is a spatial effect, it is described by a transfer function
Shear probes built and calibrated by the Ocean Mixing Group are very close in dimension to those examined by
Temporal averaging of temperature at high frequencies due to the thermal response of the fast thermistor is modeled using a double-pole filter:
Raw shear and thermistor voltage signals are both subject to two filters. First, an analog anti-aliasing filter (two-pole Butterworth) with an
After the analog signal is anti-aliased, it is digitized at 400 Hz. Before subsampling to the final 100 Hz output, the signal is digitally filtered. For the 2019 FCS cruise, the signal was convolved with a symmetric 29-element kernel in which the first 15 elements were
Early in our processing routine, we partition the raw voltage signals into 512-element segments. In order to discard the segments in which FCS was not profiling, we need robust (yet simple) criteria that demarcate the start and end of a profile. For the start, we search for the first three consecutive segments in which
A drawback of this approach is the appearance of a quantity in physical units (0.05 m s
At least for the initial implementation of our scheme, we do not include an algorithm to detect the surface to within centimeters. Doing so would let us work backward to put our uppermost depth bin as close to the surface as possible. However, we expect that this could be a fragile part of the scheme. Further, FCS lacks a micro-conductivity sensor, which is likely the sensor best suited for identifying the air–sea interface
Without surface detection, the depths of the uppermost bins will be realized randomly. In the worst cases, we would discard the top
In this paper, we use power law fits to derive turbulence quantities:
Assume we are fitting the vector
We had originally intended to find
The standard processing of FCS turbulence data differs from the reduced scheme in three ways. First, raw data are despiked differently (Appendix E). Second, the 100 Hz raw voltage signals are calibrated into physical quantities right away. Hence, means and spectra are calculated in physical units and not in voltage units. Third, the integration of spectra occurs over a variable wavenumber band, which is found iteratively.
When integrating shear spectra (after correction; see Appendix A) to find
A similar but non-iterative approach is used for integrating
To properly despike the raw output of a shear probe requires several steps.
In our standard processing of FCS data, we use the
Our MATLAB implementation of the processing code is available from
Raw and processed data for the 2019 experiment are available at
KGH designed the reduction scheme and led the writing of the paper. All authors contributed to the final version. JNM and DLR lead the development of the FCS profiler on which much of the paper is based.
The contact author has declared that none of the authors has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was funded by the Office of Naval Research under grant nos. N00014-17-1-2700 (OSU) and N00014-17-1-2762 (SIO) and continued as part of the ARCTERX (Island Arc Turbulent Eddy Regional Exchange) program under grant nos. N00014-21-1-2878 (OSU), N00014-21-1-2762, and N00014-21-1-2747 (SIO). Engineers who contributed to the design and construction of FCS and its sensors are Craig Van Appledorn, Kerry Latham, Pavan Vutukur, and Mark Borgerson (all from OSU) and Ben Reineman, Kyle Grindley, and Jeff Sherman from SIO. Aurélie Moulin executed initial turbulence processing, and Emily Shroyer provided many helpful comments on early drafts. Thanks to the reviewers, including Cynthia Bluteau and Toshiyuki Hibiya.
This research has been supported by the Office of Naval Research (grant nos. N00014-17-1-2700, N00014-17-1-2762, N00014-21-1-2878, N00014-21-1-2762, N00014-21-1-2747).
This paper was edited by Katsuro Katsumata and reviewed by Toshiyuki Hibiya and Cynthia Bluteau Toshiyuki Hibiya and one anonymous referee.