Moored Turbulence Measurements using Pulse-Coherent Doppler Sonar

SEPTEMBER 2021 ZIPPEL ET AL. 1621 Moored Turbulence Measurements Using Pulse-Coherent Doppler Sonar SETH F. ZIPPEL,a J. THOMAS FARRAR,a CHRISTOPHER J. ZAPPA,b UNA MILLER,b LOUIS ST. LAURENT,c TAKASHI IJICHI,d ROBERT A. WELLER,a LEAH MCRAVEN,a SVEN NYLUND,e AND DEBORAH LE BELf a Woods Hole Oceanographic Institution, Woods Hole, Massachusetts b Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York c Applied Physics Laboratory, University of Washington, Seattle, Washington d Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan e Nortek Group, Rud, Norway f Gulf of Mexico Research Initiative Information and Data Cooperative, Texas A&M University–Corpus Christi, Corpus Christi, Texas (Manuscript received 12 January 2021, in final form 28 June 2021) ABSTRACT: Upper-ocean turbulence is central to the exchanges of heat, momentum, and gases across the air–sea in- terface and therefore plays a large role in weather and climate. Current understanding of upper-ocean mixing is lacking, often leading models to misrepresent mixed layer depths and sea surface temperature. In part, progress has been limited by the difficulty of measuring turbulence from fixed moorings that can simultaneously measure surface fluxes and upper-ocean stratification over long time periods. Here we introduce a direct wavenumber method for measuring turbulent kinetic energy (TKE) dissipation rates from long-enduring moorings using pulse-coherent ADCPs. We discuss optimal programming of the ADCPs, a robust mechanical design for use on a mooring to maximize data return, and data processing techniques including phase-ambiguity unwrapping, spectral analysis, and a correction for instrument re- sponse. The method was used in the Salinity Processes Upper-Ocean Regional Study (SPURS) to collect two year-long datasets. We find that the mooring-derived TKE dissipation rates compare favorably to estimates made nearby from a microstructure shear probe mounted to a glider during its two separate 2-week missions for O(1028) # # O(1025) m2 s23. Periods of disagreement between turbulence estimates from the two platforms coincide with differences in vertical temperature profiles, which may indicate that barrier layers can substantially modulate upper-ocean turbulence over horizontal scales of 1–10 km. We also find that dissipation estimates from two different moorings at 12.5 and at 7 m are in agreement with the surface buoyancy flux during periods of strong nighttime convection, consistent with classic boundary layer theory. SIGNIFICANCE STATEMENT: This study outlines a method to estimate ocean turbulence from long-enduring platforms. It is difficult to make this measurement using commonly accepted turbulence estimation methods because of ocean waves, platform motions, battery and data limitations, biofouling, and the fragility of some common turbulence instruments. We applied the method at three sites and compared the results from the new method with those from short- duration datasets that use a currently accepted method. We outline the range and limitations of the new method, based both on the instrument’s principles of operation and on the comparison with an established method. Our intention is that the new method may be applied by others in future long-enduring deployments, which will increase the number of available turbulence datasets in the upper ocean. KEYWORDS: Ocean; Turbulence; Atmosphere-ocean interaction; Boundary layer; Oceanic mixed layer; In situ oceanic observations 1. Introduction measure directly, as they depend on velocity gradients at very small scales (typically less than millimeter scale). Pope (2000) Upper-ocean turbulence modifies air–sea fluxes of momen- summarized decades of theory and laboratory studies tum, heat, and gases that are important for climate and weather (Kolmogorov 1941; von Kármán 1948; Comte-Bellot and prediction. Ocean turbulence is also important for under- Corrsin 1971; Saddoughi and Veeravalli 1994; and many standing the transport of buoyant material such as biota and others) with a form for the radial wavenumber spectrum of plastics. Of particular interest in the upper ocean are mea- turbulent velocity, surements of TKE dissipation rate , which characterizes the smallest scales of motion. Dissipation rates are challenging to E(k) 5 c2/3 k25/3 fL (kL)fh (kh), (1) where c is a constant, is the TKE dissipation rate, k is the Denotes content that is immediately available upon publica- radial wavenumber, and fL and fh are shape functions to de- tion as open access. scribe the energy containing, and dissipative scales, respectively [Pope 2000, Eq. (6.246) therein]. Here, we follow the notation Corresponding author: Seth F. Zippel, szippel@whoi.edu used in Pope (2000) such that k2 5 k21 1 k22 1 k23 , where k1, k2, DOI: 10.1175/JTECH-D-21-0005.1 Ó 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1622 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 and k3 are the wavenumbers in the along-flow, cross-flow, and Taylor’s frozen field hypothesis is not always valid. Strong vertical directions, and L represents the longest scales of tur- wave orbital motions make the frozen field assumption bulent motion that contain the majority of turbulent kinetic challenging to apply, because aliasing can occur when energy for scales kL ; 1 and smaller. Similarly, h represents the converting from a frequency spectrum to a wavenumber Kolmogorov length scale, the scale at which viscous effects turn spectrum (Lumley and Terray 1983). In the absence of kinetic energy to heat in the dissipative range (kh ; 1 waves, experimental studies have shown Taylor’s hypoth- and larger). esis to fail in free shear flows (e.g., Tong and Warhaft 1995), The most commonly accepted method, or ‘‘gold standard,’’ which can occur when turbulence intensity is large in for estimating TKE dissipation rates in the ocean is through comparison with the mean flow. microstructure shear measurements. These methods use airfoil Recently, acoustic Doppler current profilers (ADCPs) have shear probes to sense the difference in velocity fluctuations at seen use in estimating TKE dissipation rates from fixed plat- very high frequency f, which is converted to wavenumber using forms in coastal waters (Gargett 1994; Wiles et al. 2006) and the fall speed U of the probe and Taylor’s frozen field hy- near the ocean surface from moving platforms (Gemmrich pothesis, k1 5 2pf/U. These spectra are compared with a shear 2010; Thomson 2012; Sutherland and Melville 2015; Zippel spectrum, which can be derived from a universal TKE spec- et al. 2020). ADCPs yield estimates of water velocity in a dis- trum (Oakey 1982). Many different shape functions fh(kh) cretized profile, allowing for direct spatial estimates of turbu- have been proposed; however, it is standard to fit a heuristic lence that do not rely on Taylor’s frozen field hypothesis. This spectrum derived from measurements (Nasmyth 1970), which spatial method is particularly important when estimating tur- are presented in tabular form in Oakey (1982) and presented bulence in the presence of surface gravity waves, as energetic as a functional fit to the tabular data in Wolk et al. (2002, wave orbital motions can obscure turbulent velocities in similar appendix). This method is generally considered the most direct frequency ranges but tend to be more easily separated spa- method of estimating TKE dissipation rates, as it resolves tially. So far, these methods have primarily focused on using motions at or near the dissipative scales (kh ;1). This mea- second-order structure functions over short distances near the surement technique can be expensive and difficult to use on surface where dissipation rates are large . 1025 m2 s3. Here, long-duration moorings due to the sensitivity of the airfoil we discuss a wavenumber inertial subrange method intended probes to damage, and the need for a clean and constant ad- for upper-ocean dissipation rates that are much smaller than vective velocity. Although there has been some success with those seen at the surface. using shear probes on moorings (Lueck et al. 1997), it has not The inertial subrange commonly exists at scales larger than become common practice. the dissipative scales, but below the largest turbulent scales The development of the xpod (Moum and Nash 2009), (i.e., wavenumbers 1/L , k , 1/h), where the shape functions which derives turbulent statistics from measurements of tem- fL(kL) and fh(kh) are near 1 and the one-dimensional wave- perature microstructure, has allowed for the inference of TKE number spectrum is well described by the wavenumber and dissipation rates from moorings. Similar to microstructure dissipation rate only, shear, this estimate relies on Taylor’s frozen field hypothesis to convert measured frequency spectra into wavenumber spectra. E11 (k1 ) 5 C1 2/3 k25 1 /3 , (2) In addition, this method assumes the eddy diffusivity of heat Kt and density Kr are equivalent, and following the method of with C1 5 0.53 (Sreenivasan 1995), and with the relation be- Osborn (1980), uses a constant mixing efficiency parameter G tween the radial spectrum [Eq. (1)] and the 1D spectrum [Eq. and the local buoyancy frequency N2 to estimate TKE dissi- (2)] described by Pope [2000, Eq. (6.216) therein]. Here, we pation rate through Kr 5 G/N2, where mixing efficiency pa- present a wavenumber method for estimating TKE dissipation rameter is G 5 Rf/(1 2 Rf) and Rf is the flux Richardson rate using an inertial subrange technique on data from pulse- number. This relation between Kr, , and N2 stems from an coherent Doppler velocity profilers deployed on long duration assumed TKE equation: P 1 B 5 , with the flux Richardson moorings. In section 2, we overview the field programs, in- number defined as Rf 5 B/P, with P being the production of strumentation, guidance on instrument setup, the mechanical turbulence by velocity shear and B being the buoyancy flux. deployment of the instrument on moorings, and a data pro- This method has been effective in measuring turbulence from cessing workflow. Results from the method are compared with moorings (Zhang and Moum 2010; Perlin and Moum 2012; nearby microstructure data and surface fluxes in in section 3 Smyth and Moum 2013), but the assumptions used in the and discussed in section 4. A summary of the results is pre- (Osborn 1980; Osborn and Cox 1972; Oakey 1982) relation sented in section 5. make it challenging to measure non-shear-driven turbulence. For example, pure buoyancy-driven convection precludes the 2. Methods use of the (Osborn 1980) relation, since this would cause a TKE equation to become B 5 and Rf, and by association G would Nortek Aquadopp 1- and 2-MHz pulse-coherent (HR) be undefined. Further, recent studies (Scully et al. 2016; Fisher ADCPs were deployed at multiple depths on three surface et al. 2018) have suggested wave-driven fluxes in the near- moorings for approximately one year. Each Aquadopp was surface layer result from the pressure-velocity correlation in configured to sample a single beam in the horizontal plane. the turbulent transport term, which is not included in Sampling a single beam at higher sample rate was preferable to (Osborn 1980) TKE balance. Last, the assumption of multiple beams at lower sample rate for directional consistency Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1623 in the processing and analysis for each returned measurement. TABLE 1. Instrument configuration parameters, and their cal- The sampled beam was oriented away from the mooring line culated range of measured TKE dissipation rates. Instruments (upflow direction) by a directional vane. The instruments measured one burst per hour for one year each. were set to record data in 135 s bursts at the top of each hour, Parameter 2 MHz 1 MHz and then remain dormant for the remainder of the hour to a conserve battery (Table 1). This results in 1080 profiles each Pulse distance 2.22 m 3.33a m hour for the 2-MHz instrument and 540 profiles each hour for Wrapping velocity Vr 0.063 m s21 0.085 m s21 Transmit pulse length 0.036 m 0.048 m the 1-MHz instrument. Using extended instrument housings Receive gate width 0.034a m 0.044a m with lithium batteries with this configuration, the instru- User-programmed cell size 0.03a m 0.04a m ments were able to sample hourly for a full year. These Blanking distance 0.096 m 0.189 m moorings, the ninth annual deployment of the Stratus Ocean No. of bins (cells) 63 70 Reference Station mooring (hereinafter Stratus 9 mooring; Sample rate 8 Hz 4 Hz Weller 2015), the Salinity Processes Upper-Ocean Regional No. of pings per sample Np 10 13 Study 1 (SPURS-1) central mooring (Farrar et al. 2015), and Samples per burst 1080 540 SPURS-2 central mooring (Farrar and Plueddemann 2019) Burst interval 3600 s 3600 s are described briefly below. All three moorings were in 4000– Upper bound (wrapping) 1025 m2 s23 1025 m2 s23 5000 m of water, with an inverse catenary design. The Lower bound (correlation) 1028– 1028– 1029 m2 s23 1029 m2 s23 moorings all had a 2.8-m surface buoy carrying surface me- teorological instrumentation, chain in the upper few tens of a The user-programmed value of cell size and pulse distance is meters, wire rope to about 1700 m, and synthetic rope below automatically adjusted in Nortek software for a slant-beam pro- that depth. jection and varies from the physical along-beam distances. Here, The Stratus 9 mooring was deployed in the eastern cell size varies from the receive gate width by this value, and the tropical Pacific Ocean in October 2008 at 19842 0 S, 85835 0 W. reported pulse distance are shown as the along-beam distances. It was recovered in January 2010. The mooring had a The slant-beam offsets result in distances larger than the user programmed values by ;10%. surface buoy equipped to observe surface meteorological conditions and support computation of the air–sea fluxes using bulk formulas methods. Along the mooring line, conductivity–temperature (CT) sensors densely spaced in the Sea-Bird 39 and Sea-Bird 37 instruments recorded tem- upper 100 m. On this mooring, five pulse-coherent ADCPs perature and conductivity, and mean currents were ob- were placed at 7-, 21.5-, 41.5-, 61.7-, and 100-m water depth. Of served with vector-measuring current meters (VMCMs) these, the 61.7- and 100-m ADCPs failed, although limited data and an RDI ADCP. were able to be recovered from the 61.7-m instrument after The SPURS-1 mooring was deployed in the North Atlantic recovery. subtropical gyre at 248N, 388W, from late 2012 to late 2013. The methods described in this paper will be applied to all The mooring was equipped with a surface flux buoy that moorings. However, the focus is primarily on the SPURS-1 measured a suite of meteorological parameters above and at mooring data, which can be compared with microstructure- the sea surface that can be used to estimate the fluxes of heat, shear-derived estimates of TKE dissipation rate from the two momentum, and freshwater into the ocean surface (Fairall 12-day glider deployments. The Stratus 9 mooring was an in- et al. 2003; Edson et al. 2013). These measurements included tegral part of the evolution of the mechanical mount (to be air temperature, humidity, wind speed, barometric pressure, discussed in section 2c); however, the processed dissipation precipitation, solar radiation (long and short wave), sea rate data from the Stratus 9 mooring will be presented in a surface temperature, and sea surface salinity. Below the subsequent paper. mooring was a densely instrumented mooring chain with conductivity and temperature measurements every 3 m for a. Pulse-coherent ADCPs the upper 25 m, getting coarser with increasing depth (every Pulse-coherent Doppler velocity profilers measure water 5 m from 25 to 90 m, and every 20 m from 110 to 160 m). velocity at a fine scale over a range of discretized locations. The Pulse-coherent ADCPs were deployed at 12.5-, 21.5-, 41.5-, measurement technique capitalizes on the relation between 61.7-, 82-, 101.6-, and 121.6-m depths to make estimates of acoustic wave phase and the distance to the target that scatters TKE dissipation rates, as described in this study. The the transmitted pulse. The change in phase with time can then mooring data were complemented by a large number of be used to estimate local water velocity. Specifically, two nearby autonomous assets, including two 12-day deploy- acoustic pulses separated by time lag t are used to determine ments of a Slocum glider with associated temperature and the time rate of change of phase, which is related to the ve- microstructure shear data (Bogdanoff 2017; St. Laurent and locity as Merrifield 2017). 1 lf The SPURS-2 mooring was deployed at 108N, 1258W, at the V5 , (3) 2p 2 t edge of the tropical eastern Pacific fresh pool with a buoy and mooring chain equipped similarly to the SPURS-1 mooring. where V is the estimated velocity, l 5 C/F0 is the acoustic The mooring estimated surface fluxes with the Improved wavelength equivalent to the speed of sound in water divided Meteorological Packages (IMET) system, and had a chain of by the system frequency, and f is the measured phase between Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1624 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 FIG. 1. A schematic demonstrating the pulse-coherent method. The acoustic transducer transmits pressure waves (Tx) into the water, which are scattered off moving particulate. Scattered sound travels back to the transducer, which samples the reflected signal using discrete range gates (Rx) in time. Two pulses are transmitted separated by time lag t, and the change in phase between received pulses at lag t is used to estimate the water velocity through Eq. (3). The schematic on the left shows sets of particles sampled by the first pulse (solid purple circles) and the same particles after time lag t (cyan circles) that have been moved by the local water velocity. The two schematized axes on the right show a distance–time representation of the transmitted and reflected sound pulsesat the top and a representation of the amplitude time series seen by the transducer at the bottom. the pulse pairs (Zedel et al. 1996; Veron and Melville 1999). A receive window is composed of a discrete number of subsam- schematic of the pulse-pair matching is shown in Fig. 1. ples M, related to the number of processor clock cycles oc- While this technique allows for measurement of much curring during the transmit or receive window. The available smaller velocity fluctuations when compared with single- instrument bandwidth, however, is set by the duration of the pulse autocorrelation (narrow- and broadband) methods, it monochromatic transmit pulse, which is matched to the receive is limited in the range of measured velocity as the phase is window. That is, the instrument bandwidth is modified by the measured on the interval 2p # f # p. Therefore, there is a user-specified cell size, which determines the receive window limited measured velocity range set by a wrapping velocity duration. The instrument can be configured to average multi- Vr, which is related to the acoustic wavelength and the ple ping pairs in time such that the reported velocity in a given pulse lag, range cell consists of Np averaged pings, where each ping is derived from M subsamples. C The near-rectangular transmit and receive windows Vr 5 . (4) 4F0 t result in a spatial sampling filter, which can be treated as the convolution of a continuous velocity signal with two As such, these instruments are typically recommended for low ~ 5 V(x)T(LT )R(LR ), where here rectangular windows, V(x) energy environments where the range of velocities are ex- ~ V(x) is the measured velocity, V(x) is the true velocity pected to be small, and thus phase wrapping would not be an signal, x is the along-beam coordinate direction, T(L T ) issue. The Nortek software expresses the lag t in terms of pulse and R(L R ) are the transmit and receive windows, and L T distance ‘, which is determined using the speed of sound ‘ 5 and L R are the length of the transmit and receive windows. Ct/2. From the convolution theorem, the power spectral density 1) INSTRUMENT SAMPLING of measured velocities will be affected by the sampling scheme as As schematized in Fig. 1 the Nortek pulse-coherent Aquadopp uses near-rectangular transmit and receive win- ~ jFfV(x)gj2 5 G(k1 , LT , LR )jFfV(x)gj2 , (5) dows in the pulse-to-pulse sampling scheme, meaning that the amplitude of the transmitted pulse rises abruptly from zero to a where F{} represents a Fourier transform and G(k1, LT, LR) is constant amplitude, and shuts off suddenly. In practice, each the power spectrum of two rectangular windows of length LT Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1625 and LR. The Fourier transform of a single rectangular window is F{T(LT)} 5 sinc[k1Lt/(2p)], and the effect of two such win- dows (resulting in time-domain triangular/trapezoidal win- dows) results in an instrument transfer function, 2 2 k1 LT k1 L R G(k1 , LT , LR ) 5 sinc sinc . (6) 2p 2p In practice, the above instrument response function is an ap- proximation because the instrument’s transmit and receive windows are unlikely to be perfectly rectangular windows. Here, we demonstrate these sampling effects using synthetic data, and show the degree to which the sampling spectral ef- fects can be corrected by applying the inverse instrument transfer function. Multiple time series are synthesized to have a spectral shape consistent with an inertial subrange (a k25 1 /3 power-law slope). White noise is added to the original time series, which is then used to create a ‘‘subsampled’’ time series FIG. 2. Synthetic data created to have a power spectrum of the by taking a sample every 10 data points in the original time form k25/3 were sampled with a uniform subsample (orange) and series. A second ‘‘synthetically sampled’’ time series is made by with a double rectangular filter that mimics the sampling from an first taking the convolution of a trapezoidal averaging window ADCP (yellow). White noise is added during both of the synthetic (consistent with a convolution of two rectangular windows) sampling procedures (dashed black), and the power spectrum of with the original time series, and then subsampling the con- the sampled synthetic data is compared with the spectrum from the volved signal to simulate the sampling by the Aquadopp in- original synthetic time series (blue). The corrected, synthetically sampled spectrum (purple) fits the original signal over a much strument. This process is repeated, and power spectra of the larger wavenumber range. The convolution filter described in generated, uniformly subsampled, and synthetically sampled Eq. (6) is shown in dashed green, offset for clarity. signals are averaged to increase statistical stability of the spectral estimates. The averaged power spectra of the two sampled time series are then compared with the original, as where here R^ is the sample correlation coefficient and Np is shown in Fig. 2. The power spectrum from the uniformly sub- the number of averaged pings. Equation (7) differs slightly sampled time series exhibits higher energy levels than the from that presented in Shcherbina et al. (2018) due to dif- original signal with added noise, as subsampling (alone) raises ferences between the Aquadopp and the Signature1000 in- the high-frequency end of the original spectrum due to aliasing. struments. For the Aquadopp, the instrument bandwidth is The simulation of Aquadopp sampling due to the effective limited by the transmit pulse length LT, which is matched to spatial smoothing that acts to reduce energy in the tail below the receive length LR (or cell size), such that larger cells will both the original signal and the uniformly subsampled case. A contain more subsamples (or clock cycles), but these sub- corrected spectrum is also shown in the figure, where the power samples themselves do not directly relate to more averaging. spectrum of the synthetically sampled data is divided by the In contrast, the Signature1000 bandwidth is fixed and unre- theoretical transfer function [Eq. (6)]. The corrected spectrum lated to the cell size such that larger cell sizes directly relate to matches the spectrum made from the original signal to higher more spatial averaging (i.e., the subsamples are indepen- wavenumber than the uncorrected, and uniform subsample dent). We note that the Aquadopp instrument returns cor- spectra. Because the sinc functions become small at high relation as a percentage, which differs from R^ by a factor of wavenumber and the synthetically sampled time series has 100. We also note the resemblance of Eq. (7) to the equation some amount of increased variance due to aliasing from for standard deviation of phase factor estimates presented in downsampling, the corrected spectrum becomes artificially Bendat and Piersol [2011, Eq. (9.91) therein]. This variance large near the Nyquist wavenumber. estimate assumes a sufficient number of independent samples 2) NOISE ESTIMATION are used (Np $10), because it relies on the central moment expansion in its derivation and simplification (Shcherbina The probability density function of pulse-pair estimates has et al. 2018). Instruments used in this study had Np 5 10 and 13 been explored in the literature for radar methods (Miller and (Table 1) such that this estimate of noise variance is expected Rochwarger 1972), applied for the Doppler sonar case for re- to apply, but caution is taken in imposing this estimate of lating sample correlations to velocity variance theoretically noise on the results. (Dillon et al. 2012), and tested with data (Shcherbina et al. 2018). These studies have shown that the variance of a velocity b. Spectral signal-to-noise estimates to guide instrument estimated from pulse-pair methods can be approximated as configuration 2 2 ^22 Pulse-coherent instruments can be configured to mini- 1 Vr Vr R 2 1 var(V) 5 var(f) ’ , (7) mize phase wrapping along the measurement profile while Np p p 2Np maintaining a signal-to-noise ratio (SNR) necessary to estimate Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1626 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 the power in the inertial subrange [Eq. (2)]. Here, we define a instrument setup, and local environmental factors, such as the spectral SNR based on the estimates presented in Eq. (7) and the number of scatterers in the water, platform motion and cross- expected inertial subrange: beam flow (Zedel et al. 1996), and the turbulence itself (Shcherbina et al. 2018). For example, one may be tempted to C1 2/3 k125/3 increase the pulse lag and instrument range in an attempt to SNR 5 , (8) var(V)/kN measure smaller turbulence levels. However, these choices may result in decreased sample correlations (and therefore where the instrument noise is assumed to have a uniform increased noise) effectively giving poorer resolution. Still, we spectral response such that var(V)/kN 5 s2N (k), and kN is find Eq. (11) useful to consider during deployment planning, the Nyquist wavenumber. The inertial subrange is by its even if intuition with regard to the expected R^ remains an art. nature a red spectrum, with increasing spectral density at We further hope that the configurations and noise levels re- smaller wavenumbers (larger eddy scales). In contrast, the ported in this study can serve as a guidepost for future, similar noise is assumed to be white (spectrally uniform). This re- deployments. sults in an SNR that is a function of wavenumber, with For this study, the instrument configuration parameters higher SNR at the low wavenumbers and low SNR at high shown in Table 1 resulted in a sufficient number of moderate wavenumbers. and larger sample correlations R^ . 0:6, which we applied to A second constraint can be placed on the instrument during Eqs. (8) and (9) to estimate typical measurement ranges of 1 3 setup to minimize the effects of phase wrapping. It is preferable 1028 , , 1 3 1025 m2 s23 for the 2-MHz instrument. At high that no velocity wraps are expected along the profile. This will correlation returns, this noise floor may be significantly lower, greatly aid in interpretation and processing of the data, de- and measurements of may be possible 1–2 orders of mag- scribed further in section 2d(1), as no attempt is made to cor- nitude lower. The range of wavenumbers and energy levels rect for low-mode nonturbulent velocities. Here, we pose the expected to be resolved by this method are shown with problem such that the standard deviation of the expected tur- theoretical spectra in Fig. 3. The lower bounds for each box bulent velocities sy along the beam is small when compared show the white noise estimated from Eq. (7) using correla- with the wrapping velocity. We arbitrarily use 4 standard de- tions of 0.6 and 0.95, respectively. The horizontal extent of viations, such that if the velocities are assumed to be Gaussian the box shows the range of wavenumbers resolved due to the distributed, roughly 99.99% of velocities would not be ex- instrument bin size and profile length, which is dependent on pected to wrap because of turbulence. Using the inertial sub- the instrument setup and frequency. The upper bound is range to estimate the standard deviation of velocity gives the limited by the unwrapping constraint [Eq. (9)], and spectral constraint, energies above this limit would be expected to cause wrap- ð !1/2 ping and are not trusted. Theoretical spectra are shown at k0 4 C1 2/3 k25 1 /3 dk # Vr , (9) three dissipation rates to highlight the resolved portion of kN the energy spectrum. where the bounds of integration kN and k0 5 2p‘21 are de- c. ADCP mounting and mechanical deployment termined by the bin size and the profile length. Note that the In the first deployment (Stratus 9 mooring), pairs of ADCPs profile length is itself constrained by the pulse-to-pulse time were mounted to a 1-in.-diameter titanium alloy rod, with pad lag, and thus is directly related to Vr. Here, we assume the eye–like attachment points welded to the rod on top and on profile length and pulse distance are equivalent. Combining bottom to allow shackles to tie into the mooring. A fin and Eqs. (8) and (9), we can show how instrument setup relates to swivel system allowed the ADCPs to pivot into the current. On the expected range of TKE dissipation rates. Specifically, recovery, the 1-in. (2.54 cm) titanium alloy rod fractured where 1/2 it was welded to the pad eye at the bottom of the 8.4-m ADCP 3 1/2 4 C 2/3 (k22 0 /3 2 k22 N ) /3 # Vr and (10) pair, and the mooring line and all instruments deeper than 2 1 8.4 m fell to the sea floor. As a result, the deeper ADCP pairs p2 Np (C1 2/3 k25 1 /3 )kN imploded, and their data were lost. Vr2 . (11) ^ SNR(R 2 1) 22 In the subsequent two mooring deployments, ADCP’s were mounted to the mooring using Delrin clamps attached to a Noting here that the maximum profile length that sets k0 is vertical, weldless titanium alloy flat stock (Fig. 4). The titanium limited by the same pulse distance that limits Vr. The first bar is therefore free of welds that created a weak point in the condition essentially sets the upper bounds of that can mooring system and led to the catastrophic failure of Stratus 9. reasonably be measured before phase wrapping starts to The updated mount can attach to the main mooring line di- modify the along-beam velocity variances. The second rectly via shackles at the bar end points. Two Delrin cups screw represents the ability to resolve an inertial subrange above onto the titanium bar as an attachment point for the Delrin instrument noise. ADCP clamps. Two Delrin figure-8 shaped clamps hold the A significant caveat to Eq. (11) is that the sample correlation ADCP’s cylindrical body and the Delrin cups attached to the R^ is a diagnostic parameter, and cannot be fully predicted prior titanium bar. The Delrin cup/Delrin clamp connection is slip- to instrument deployment. The returned sample correlations pery, allowing the clamps to rotate in response to local flow depend on a number of factors specific to the deployment, conditions. An orientation fin attaches to the two Delrin Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1627 FIG. 3. Example one-sided turbulence spectra for dissipation rates 5 1029, 1028, 1027, and 1026 m2 s23 for the Pope model spectrum (black). The overlaid dashed boxes show the range of wavenumbers sampled, the maximum spectral estimates due to phase wrapping [Eq. (9)] and the range of white-noise levels predicted by Eq. (7) bounded by the minimum mean along-beam correlations allowed in quality control [see section 2d(2)], and the (roughly) highest returned correlation level (R^ 5 0:6 and R^ 5 0:95; shaded boxes). We note that these noise levels are not guaranteed and that it is possible that a mix of different instrument configurations and environmental variables could result in uniformly lower correlations (and thus noise levels). The values here are representative of observed noise levels across multiple mooring deployments used in this study. The color of the dashed boxes differentiates the 1-MHz (green) and 2-MHz (purple) instruments. Based on this parameter space, we expect to resolve the inertial subrange for ; 1028–1025.5 m2 s23, with measurement of dissipation rate ; 1029–1028 m2 s23 possible with high correlation returns. clamps opposite the ADCP cylinder, keeping the ADCP body mean flow because the mean flow along the beam has no oriented toward the local flow direction. The ADCP is roughly effect on our estimate of the wavenumber spectrum and the 30 cm from the titanium bar centerline. dissipation rate. We note that Shcherbina et al. (2018) as- sessed the value of multiple existing unwrapping methods d. Data processing toward the pulse-coherent acoustic velocimetry problem Data processing consists of four primary steps: phase specifically with respect to the Nortek Signature instrument, unwrapping, quality control, spectral analysis, and fitting. and the multicorrelation pulse-coherent processing method. There are a number of user specific choices during each of Here, we describe a different method developed parallel to these steps, which create a large user parameter space. those outlined in Shcherbina et al. (2018). Here, phase These choices can significantly modify the resulting esti- wrapping is caused primarily by mean velocities that are mates of TKE dissipation rate; however, the decision space much greater than along-beam velocity gradients. The is too large to explore fully. Instead, we will highlight the methods in Shcherbina et al. (2018) should arrive at similar effect of many of these choices and discuss how they might solutions to the method outlined here below but were also compound. Last, we put forward our best advice for pro- developed for phase unwrapping under larger velocity cessing moving forward. gradients. The approach to unwrapping is to find the minimum 1) PHASE UNWRAPPING variance solution along the beam that is consistent with The pulse-coherent instruments were programmed such ~ 6 n(x)Va , where n(x) is an integer. Note Vunwrap (x) 5 V(x) that phase wrapping due to turbulence is not expected here that Vr is the maximum unambiguous velocity ampli- across the spatial extent of the measurement [via Eq. (9)]. tude, and the wraps range from 2Vr to 1Vr and vice versa, Mean flow, wave orbital motions, and platform motions can such that the velocity ambiguity is Va 5 2Vr. We process easily create flow across the instrument’s sampling volume each realization in time independently, using only the spa- to induce phase wraps from the mean. We seek to estimate tial structure of the measurements, and proceed as follows. along-beam variance, and do not attempt to estimate the Each measured profile of length Mp is multiplied by nVa, Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1628 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 FIG. 4. (a) A side-on view of the Aquadopp mount showing the no-weld titanium bar, Delrin clamps, and orientation fin. (b) The Delrin swivel that attaches the ADCP clamp to the titanium bar. (c) The configured mount on deck before deployment as part of the SPURS-2 mooring. The Aquadopp is equipped with the current-meter transducer head, with the active beam oriented in the horizontal plane pointing upflow from the directional fin. where n 5 [1, 2, 3, 4, 5]. A histogram is generated for the range cells. This flow distortion would manifest as low- length 5 3 Mp values. If the shear over the ADCP range is wavenumber energy in wavenumber spectra that would artifi- less than Vr, the histogram is expected to show groupings of cially increase dissipation rate estimates if not dealt with counts consistent with bands of unwrapped solutions, with appropriately. means offset by Vr. We identify one such grouping through The flow distortion shape is qualitatively consistent with a separation of peaks in the histogram using null, or zero- theoretical model for potential flow around a cylinder, count bins between each grouping. Since the mean velocity which yields a radial velocity along the flow centerline of will be removed in subsequent spectral analysis, any three of the form the five expected groupings will provide the solution of in- terest. An example demonstrating this procedure is shown V R2 in Fig. 5. If the along-beam velocity gradient is large and no 5 12 2 , (12) V‘ r groupings of histogram counts can be identified, the profile is rejected from further analysis. where V ‘ is the free stream velocity, R is the cylinder ra- dius, and r is the distance from the center of the cylinder. 2) QUALITY CONTROL Figure 6 shows a subset of measured velocities in com- Strong head-on flows can create a region of high pressure at parison with the mean-removed potential flow model to the leading edge of the instrument, leading to flow stagnation. demonstrate this effect. Here, the cylinder radius is esti- This results in a velocity profile that decreases toward zero mated as the distance from the mooring line to the ADCP, velocity as flow approaches the instrument. In a mean-removed roughly 30 cm. Although instrument mount is clearly non- profile, the flow distortion results in large positive velocities at cylindrical (Fig. 4), we note that perturbation solutions for low range, with weak negative velocities at farther ranges. This more complex geometries typically have Eq. (12) as the trend is visible in the example unwrapped burst shown in Fig. 5 first-order solution, and therefore, it remains a somewhat as a band of positive velocities (colored yellow) in the low reasonable approximation. Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1629 FIG. 5. An example of the unwrapping procedure for an arbitrary burst (SPURS-2; 41.5-m depth). (a) An ex- ample of a wrapped profile that has been multiplied by 2nVr. The unwrapped profile is shown with the black circles. (b) The histogram used to find the groupings of unwrapped data. (c) The mean-removed unwrapped velocities for the entire burst, consisting of 1080 profiles. (d) The mean-removed wrapped data, shown for comparison. Red triangles mark the specific profile shown in (a) and (b). To circumvent the introduction of low-wavenumber en- ping pairs together, fast instrument rotations blur the di- ergy by flow distortion, we choose to remove a subset of the rection of the returned averaged values. As a quality control near-sensor data, only allowing distances for which the metric, we remove measurements with fast heading rate of distorted flow is 90% of the free stream velocity, y/y ‘ . 0.9, changes to limit the directional blurring. We arbitrarily set a which is roughly equivalent to 95 cm from the mooring max du/dt 5 4 rad s21. We note dissipation rates were centerline, or the first 18 velocity bins for the 2 MHz in- not significantly modified by changing this cutoff, but the strument. This is an effective extension of the instrument somewhat loose metric set here resulted in reduced vari- blanking distance to avoid including the spatial signal of ance of the dissipation rate estimates, likely due to allow- flow distortion around the mooring line and instrument ance of more profiles in averaging. In part, the effects of mount. The remaining data are linearly detrended, which rotation are lumped in with data removed due to low cor- accounts for the low-slope tail of the flow distortion. The relations. Cross-beam motion (transverse relative velocity) linear trend removal also reduces the energy in the lowest can also degrade the signal, as scatterers in the first acoustic wavenumber of the spectrum, which is not used in subse- ping are moved out of the sample volume during the sub- quent fitting (more on this later). sequent ping. This is directly reflected through lower ping- The Aquadopps were mounted such that they were free to pair correlations, for example (Zedel et al. 1996, Fig. 8 rotate into the flow direction, which is needed to ensure the therein) saw correlations lower to C 5 0.6 at cross-beam instrument is looking away from the trailing wake. A more flows of 1 m s21 (although the actual decorrelation likely thorough discussion of self-wake contamination by wave depends on pulse lag and range). orbital motions is presented in the appendix, and here we Profiles and points with low correlations are removed discuss the effects of platform rotation due to the orbital from analysis, following previous studies (Rusello 2009; motions. Thomson 2012). Two distinct correlation criteria were used The rotational motions are primarily orthogonal to the in this study, the mean along-profile correlations and the beam direction, so the velocity estimates themselves are not correlations associated with measurements at each velocity expected to be biased directly. However, rotational motions bin. Profiles with mean along-beam correlations lower than can still degrade the velocity measurement in a number of 0.6 are removed from analysis. Of the remaining profiles, ways. Since the instrument is set up to average a number of individual data points are removed if their correlation is Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1630 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 4) SPECTRAL SLOPE ESTIMATION (REGRESSION) Computed power spectra are then used to estimate TKE dissipation rate and instrument noise using least squares regression to a model spectrum. Rather than ignoring the presence of noise or imposing a model of the instrument noise in estimating the velocity wavenumber spectrum, we instead choose to estimate both the inertial subrange spec- tral level and the instrument noise. In this case where we seek estimates of both the signal and the noise, it can be useful to have SNR , 1 at the high wavenumbers such that the noise floor can be estimated from the measurements without need for imposing the Shcherbina et al. (2018) noise model, which will itself have associated error. In this sense, we are effectively viewing both the signal (the inertial sub- range spectrum) and the instrument noise as signals to be estimated, because of their different spectral slopes and the fact that we will be fitting to the spectrum over a range of FIG. 6. Example velocity profiles shown in distance from moor- wavenumbers. ing line (thin colors). The potential flow solution for flow around a The full measured spectrum is expected to have the form cylinder with radius of 0.3 m and V‘ 5 0.1 is shown in black. The vertical blue line shows the location of the Aquadopp head, 30 cm kL 2 kL 2 P~11 (k1 ) 5 sinc 1 T sinc 1 R (C1 2/3 k125/3 1 N) , (13) from the mooring line (equivalent to the estimated cylinder ra- dius), and a vertical red line shows the range where the potential 2p 2p flow is 90% of the free stream velocity, nearly 1 m from the mooring line, and 63 cm from the Aquadopp head. The measured from combining a theoretical inertial subrange [Eq. (2)], velocity profiles have ambiguous absolute velocity values but are instrument response [Eq. (6)], and Doppler noise N. A least shown here offset by the assumed V‘ value. squares solution is found using MATLAB’s ‘‘mldivide’’ function, which solves the matrix equation Ax 5 b, with the first column of A defined as GC1 k125/3 , the second column of lower than 0.4, and they are replaced via linear interpola- A defined as G, where G is the instrument transfer function, tion. Profiles with more than two adjacent removed values and b 5 P~11 (k1 ). The two returned elements of x are then the are not considered for further analysis, as interpolating least squares estimates for 2/3 and N. A subset of the mea- across multiple removed points can alias variance into the sured wavenumbers are used for the fitting. The lowest lower wavenumber bands. wavenumber is removed because its variance is affected by Previous studies have also removed data associated with low the linear detrend operation applied during spectral pro- backscatter, as a low concentration of scatterers can make cessing. Similarly, the four largest wavenumbers are ex- acoustic velocimetry difficult and be a source of error. Here, we cluded because of the overly large compensation from the did not observe periods when backscatter was low enough to transfer function that can cause the variance at those cause velocimetry to fail, and we will focus on correlation for wavenumbers to be artificially large (Fig. 2). Inflated vari- the main quality control metric. However, attempts to extend ance at high wavenumbers would cause increased estimates the methods presented in this paper to low scattering envi- of noise N that would then decrease the value of the esti- ronments (such as polar regions) may need to include back- mated TKE dissipation rates. scatter in data quality assessments. e. Example spectral fit 3) SPECTRAL ANALYSIS An example power spectral estimate along with the best fit Quality controlled data are used to estimate the wave- spectrum are shown in Fig. 7. The spectrum is well fit by the number spectrum of velocities as follows. Following stan- model over most wavenumbers. The recurve due to the spatial dard spectral analysis techniques, the linear trend of each sampling filter can be seen around k1/(2p) ; 5 cpm as the profile is removed, and each profile is tapered with a measured spectrum decreases at the highest wavenumbers, Hamming window. A power spectrum is estimated for each rather than approaching a flat-sloped white-noise offset. When profile in the burst, multiplied by a compensation factor to corrected for transfer function (as was done in Fig. 2), the correct for the reduction of variance by the taper (1.59 for a rolloff to white noise is clearer. Hamming window), and then averaged to yield a wave- number spectral estimator. This process is similar to using Welch’s method on a time series, with each spatial profile of 3. Results velocity analogous to a segment from Welch’s method. The a. Comparison to microstructure data resulting spectral estimators should then have roughly 2N degrees of freedom, where N is the number of profiles that Here, we compare the estimated TKE dissipation rates passed quality control. with estimates made from a nearby Slocum glider that Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1631 FIG. 7. An example of a spectral fit. (a) The fit includes the sampling filter [e.g., Fig. 2 and Eq. (6)], resulting in the high-wavenumber rolloff despite the existence of white noise. (b) The measured spectrum and fit are corrected for the effect of the sampling filter and are shown with the components of the best fit model, where the estimated white-noise level is shown with the dashed red line and the estimated inertial subrange level is shown with the dashed purple line. The sum of the dashed lines is equal to the solid black best fit determined through regression. carried a Rockland Scientific Microrider (St. Laurent and during a second period for 12 days in March–April 2013. Merrifield 2017; Bogdanoff 2017). Glider measurements More details on the glider measurements can be found in were taken over the course of 12 days in September– St. Laurent and Merrifield (2017) and Bogdanoff (2017). October 2012 within 3–5 km of the mooring location and Figure 8 shows a comparison of TKE dissipation estimates FIG. 8. Depth–time plots of temperature from (a) the glider and (b) the mooring are shown with the TKE dissipation rates at (c) 12.5 and (e) 21.5 m. The largest disagreements between microstructure-derived (glider) and ADCP-derived (mooring) dissipation rates (boxes D.1, C.2, D.2, C.3, and D.3) coincide with differences in temperature profiles, suggesting spatial variability can explain some of the dis- agreement in dissipation rate estimates. The glider tended to see more temperature stratification (box A.3 compared with box B.3) and lower subsurface dissipation rates during nighttime convection, whereas the mooring temperature profiles showed less stratification, with dissipation rate estimates that were more similar to the surface buoyancy flux B0. Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1632 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 from the mooring and the glider at 12.5 and 21.5 m along with contour plots of temperature for the 2012 glider de- ployments. Measurements from glider and mooring are also available at 41.5- and 61.5-m depths but are not compared here. For the duration of the glider deployments, the mixed layer depth varied between 30 and 50 m. Small changes in mixed layer depth over the 2–5-km separation between the measurements would be expected to have a large effect on local TKE dissipation rates, making the comparison difficult. The turbulence instruments on the mooring and glider have different time–space sampling properties that need to be taken into account to compare the two. The mooring dissipation rate estimates are derived from an average of spectra computed from O(20) 1-m profiles of velocity (col- lected over 135 s). The glider dissipation rate estimates are made by breaking each vertical profile of the glider into 8-s bins, which translates to roughly 2.5 m of water. These bins are then processed spectrally to form dissipation rate esti- FIG. 9. Direct comparison of time-smoothed microstructure mates for each bin. Because dissipation rates are approxi- dissipation rates and mooring-derived dissipation rates for both mately log-normally distributed, linear averaging of more 12.5- and 21.5 m depths. Boxed regions in Fig. 8 have been ex- estimates or sampling a larger volume will tend to produce cluded. Black diamonds represent log-mean bin averages, with higher dissipation rates. The amount of linear averaging is associated vertical bars showing the 95% confidence interval of the log mean (1.96 times the standard error). Bin averages with related to the length of time or equivalent volume of water less than 10 values are excluded, and bins were arbitrarily used to estimate velocity or shear spectra, such that longer- chosen as 40 evenly log-spaced bins on the interval from 10210 to duration estimates are likely to estimate larger TKE dissipation 1026 m2 s23. The dashed black line shows the 1:1 agreement rates (closer to the linear expected value of the lognormal level. Mooring- and glider-derived dissipation rates agree well distribution). Therefore, the amount of averaging needs to be above of ;1028 m2 s23, below which the mooring-derived es- commensurate for comparing the estimates from the moor- timates appear to be biased. Confidence in the mean is roughly a ing and the glider. Dissipation rates from the glider are factor of 2 (gray dashed lines), similar to previous studies smoothed here using an eight-point moving average in time (Moum et al. 1995). along each depth bin for the comparison to better reflect the volume of water over which dissipation rates are estimated in the mooring-derived estimates (i.e., 80 s and ;20 m for the glider data above 5 1028 m2 s23 is good. Mooring-derived glider estimates, as compared with 135 s and ;20 m for the estimates are biased positively (high) below 5 1028 m2 s23, mooring estimates). The moving average used here is in- which is consistent with where ADCP noise variance becomes tended to make the two dissipation estimates more com- a large fraction of the total measured spectral variance for the mensurate; however, we acknowledge that there are further minimum allowed mean correlation returns (C 5 65; Fig. 3). subtleties involved in the comparison of turbulence estimates With low dissipation rates and high noise floor, the ADCP- that are beyond the scope of this paper and are not explored derived estimates become sensitive to the estimate of the white further here. noise in the spectral fitting. An alternative explanation to TKE dissipation rates estimated from the mooring com- the disagreement at 5 1028 m2 s23 is discussed further in pare favorably to the smoothed microstructure-derived esti- section 4b. mates from the glider much of the time, as seen in Fig. 8. A time series of dissipation rates from the 2013 glider However, at times the two estimates disagree up to two orders deployment is shown in Fig. 10. As in Fig. 8, the glider data of magnitude (Fig. 8; labeled boxes). Often these disagree- have been smoothed to better represent averaging inter- ments align with differences in the temperature profiles vals for the estimates. Here, the glider was set to dive deeper measured at the two sites and may relate to horizontal vari- than in the 2012 deployment, and therefore, comparisons ability in the vertical stratification of the upper ocean. For are shown to 122 m. All depths show some agreement be- example, when the temperature profile indicates near-surface tween the two estimates, with the best agreement at stratification during nighttime convection at the glider sites, the shallow depth instruments. Agreement is particularly the less-stratified mooring-derived dissipation rates are sim- strong during the last three glider deployment days (3– ilar to the surface buoyancy flux as predicted by Monin– 5 April), with both methods showing similar trends over Obukhov (MO) theory (Fig. 8; boxes C.3, C.4, and D.4). The roughly four orders of magnitude of TKE dissipation rate. horizontal variability of stratification and the related differ- Similar to Fig. 9, a direct comparison for the second de- ences in TKE dissipation rates are discussed further in ployment (Fig. 11) shows good agreement on average section 4a. above 5 10 28 m 2 s 23 , with the mooring biased positively A direct comparison of the TKE dissipation rates is shown in (high) relative to the glider estimates of below 5 Fig. 9, excluding times boxed in Fig. 8. General agreement for 1028 m 2 s 23 . Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1633 FIG. 10. Comparison of time-smoothed glider-derived microstructure dissipation rates and mooring-derived dissipation rates for all depths during the second glider deployment in March and April 2013. Measurements at depths of 12.5, 21.5, 41.5, 82, and 122 m were made by 2-MHz instruments, with measurements at 61.7 m made by a 1-MHz instrument. Agreement between the glider and mooring mea- surements is best during 3–6 Apr. b. Comparison with surface buoyancy flux primarily limits B0 . 1028 m2 s23, coinciding with the range of values over which mooring-derived dissipation estimates were The comparisons of the new method for estimating TKE unbiased when compared with shear-microstructure estimates dissipation rates with microstructure shown in Figs. 8 and 9 are (Figs. 9 and 11). limited in scope, only covering 12 days of the multiple years of data available using the new method. As a further check c. Long duration time series on the validity of the new estimates, we compare mooring- derived dissipation rates with measurements of surface Contours of the TKE dissipation rate for the duration of the fluxes from the same mooring. Under MO theory, the upper- SPURS-1 mooring are shown in Fig. 13. The TKE dissipation ocean dissipation rate should equal the surface buoyancy rates are generally larger near the surface, and larger above a flux B0 under strong convection defined with the MO simi- mixed layer depth estimated from temperature (defined as the larity parameter z/L (Wyngaard and Coté 1971), with depth at which temperature is 0.058C different from the surface L 5 u3* /(cvk B0 ), where u* is the friction velocity and cvk is value). The , 1028 m2 s23 contour, near the range of values von Kármán’s constant. Here, we compare surface buoy- often used to define a turbucline (Clayson et al. 2019) or a ancy fluxes and TKE dissipation rates from the measure- mixing layer depth (Sutherland et al. 2014) is consistently near ment nearest the surface (12.5 m for SPURS-1; 7 m for the mixed layer depth, particularly when the mixed layer is SPURS-2). We limit the comparison to periods for which deepening. This is qualitatively consistent with previous stud- we expected 5 B0, which we set as z/L , 25, and z/MLD , ies that show the mixed layer depth and the depth of active 0.75. Comparisons are shown in Fig. 12. mixing are often similar, but not always the same (Brainerd TKE dissipation rates agree with surface buoyancy fluxes in and Gregg 1995). This can be seen on seasonal scales (Fig. 13a), the mean for near-surface depths for both SPURS-1 and as the mixed layer depth deepens from October to December SPURS-2 deployments. In both cases, choosing z/L , 25 2012 and then shallows again over the spring/summer of 2013. Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1634 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 study have many similarities to Moum et al. (1995). TKE dis- sipation rates differ at times by several factors of 10 (Fig. 8; boxes), but there is agreement in the mean above ’ 1028 m2 s23 with 95% confidence bars suggesting mean bias roughly a factor of 2. Following Moum et al. (1995), we conducted a two-sample x 2 test finding that at most depths (with the exception of the 21-m comparison) the mooring and glider estimates of TKE dissipation rates are unlikely to be de- rived from different distributions at a 95% significance level (here, the test was restricted to values above ’ 1028 m 2 s 23 ). Next, we will discuss potential explanations for the occasional discrepancies between the glider- and mooring-based observations. a. Horizontal variability of surface stratification and TKE dissipation rates in SPURS-1 In contrast to the Moum et al. (1995) study, times of largest FIG. 11. Direct comparison of time-smoothed microstructure disagreement between the two estimates seem to be associ- dissipation rates and mooring-derived dissipation rates for all ated with differences in the vertical structure of temperature depths (12.5, 21.5, 41.5, 61.7, 82, and 122 m) during the second between the two sites. These differences cause either the glider deployment in March and April 2013. The vertical bars glider estimates to be larger in comparison with the mooring show the 95% confidence interval of the log mean (1.96 times estimates (Fig. 8; box C.2), or vice versa (Fig. 8; boxes C.3, the standard error). Bin averages with less than 10 values are C.4, C.5, D.1, D.3, D.4, and D.5). That the differences are excluded, and bins were arbitrarily chosen as 40 evenly log- seen in both directions (e.g., mooring estimates could be spaced bins on the interval from 10 210 to 10 26 . The dashed black line shows the 1:1 agreement level. As in Fig. 9, agree- larger or smaller than glider estimates) provides further ment between the two dissipation rate estimates is good above support for natural variability. However, we do note that 5 10 28 m 2 s 23 . these differences occur more frequently as mooring estimates larger than glider estimates, which could reflect the limita- tions of the mooring estimates to capture small dissipation The qualitative agreement between dissipation contours and rates, or a sampling bias (rather than instrument bias) be- mixed layer depths can also be seen over diurnal cycles tween the two estimates due to mesoscale flow features over (Fig. 13b), as exemplified by classic pattern of nighttime con- the 2 weeks of sampling. vection and daytime stratification in May 2013. TKE dissipa- Regardless, disagreement between the mooring dissipation tion rates below the mixed layer are generally less than rates and the glider dissipation rates do seem to occur with 1028 m2 s23, which is close to the noise floor of our estimates differences in glider and mooring temperature profiles (boxes, (as indicated in Fig. 9). Fig. 8). These temperature differences are indicative of dif- ferences in vertical stratification that modify the local TKE dissipation rates, and their relation to the local surface fluxes. 4. Discussion As shown in Fig. 14, satellite-derived SST products [VIIRS The agreement between glider-derived and mooring- NPP; NOAA Office of Satellite and Product Operations derived TKE dissipation rates in this study is similar to the (OSPO); NOAA OSPO 2019] confirmed temperature dif- results from Moum et al. (1995), which compared estimates of ferences on 2-km scales similar to the glider–mooring dif- TKE dissipation rates from independent shear probes located ferences (DT of 0.18–0.28C), which gives further reason to between 1 and 11 km apart, with little upper-ocean differences believe these temperature differences are real, and not between the two sites. In their study, Moum et al. (1995) found simply instrument error. the two sets of TKE dissipation rate measurements showed Boxes B.2, A.3, and A.5 in Fig. 8 all show temperature significant variability at short time scales, with individual data inversions that are indicative of the existence of barrier pairs differing by 1–2 orders of magnitude. However, they also layers. Associated with these temperature inversions are found that hourly averages showed significant correlation, and dissipation rates that are smaller than the nearby measure- histograms of the two datasets at some, but not all depths, were ment with weaker or nonexistent temperature inversions. statistically likely to be derived from the same distribution, That is, mooring dissipation rates in box C.2 are smaller than determined through a two-sample x 2 test. Moum et al. (1995) the glider estimates, and the mooring sees a larger temper- attributed the variability between estimates at the two sites to ature inversion (box B.2) than in the glider data (box A.2). be related to natural variability of turbulence and suggested Similarly, glider dissipation rates are smaller than the that the systematic bias of the dissipation rate estimates was mooring estimates in boxes C.3, D.3, C.5, D.5, where tem- roughly a factor of 2. perature inversions exist in the glider data (boxes A.3 and The comparison between the mooring-derived TKE dissi- A.5) but not the mooring data (boxes B.3 and B.5). During pation rates and glider-derived TKE dissipation rates in this these periods when nighttime convection was strong, the Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1635 FIG. 12. Upper (a) SPURS-1 and (b) SPURS-2 dissipation rate estimates in comparison with surface buoy es- timates of surface buoyancy flux (COARE) during strong convective conditions z/L , 25 and above the mixed layer depth z/MLD , 0.75. Data arbitrarily binned with 35 even intervals in log space between 1029 and 1026 are shown as solid black diamonds, with vertical bars showing 1 standard deviation within the bin. Bin averages are only shown if they contain more than 10 data points. mooring TKE dissipation rates were similar to the surface (2018)], newer ADCPs likely can measure a larger dynamic buoyancy flux as expected from boundary layer theory. range of . Differences in mooring and glider dissipation rates in boxes An alternate hypothesis is that the assumption of an iso- C.4, D.4 correspond with the existence of a warm near-surface tropic inertial subrange breaks down where stratification layer in the glider data (box A.4) not seen in the mooring data limits low-wavenumber energy, and the imposed turbulence (box B.4). Here, the mooring dissipation rates follow the ex- model is no longer valid. In other words, the application of pected boundary layer theory for strong nighttime convection Eq. (2) cannot be made, since the shape function fL(kL) is and are similar to the surface buoyancy flux. The existence of no longer close to 1. Under stratified turbulence, the the near-surface temperature stratification in the glider data Ozmidov scale Loz 5 1/2/N3/2, where N is the buoyancy may indicate the importance of horizontal gradients and/or frequency, is often used to describe the largest vertical eddy advection. scale. Using stratification and dissipation rates from the glider, Differences seen in boxes A.1, B.1, and D.1 seem to be as- Ozmidov scales were in the range 1021 # Loz # 102 m, as sociated with deviations of the size and arrival time and depth compared with the ;1.5-m pathlength used by the mooring- of temperature stratification seen in both glider and mooring mounted ADCPs. Because of the small range of stratification data. Differences in TKE dissipation rates at the 12.5-m depth measured during the glider deployment, the Loz ; 1 m limit are minimal during this period. corresponds to ; 1028 m2 s23, similar to the estimate of the ADCP noise floor. The glider-derived dissipation rates are b. Noise floor or anisotropy? made closer to the Kolmogorov scale and would be less sen- The mooring-derived TKE dissipation rates agree with sitive to the Ozmidov scale rolloffs. In contrast, the mooring- the glider-derived TKE dissipation rates down to 5 derived estimates rely on the slightly longer, more energetic 10 28 m 2 s 23 for both glider deployments, as shown in Figs. 9 scales that are more quickly affected by limiting buoyancy. and 11. Given the noise levels suggested from Eq. (7) The exact cause of the disagreement between the two dis- (Shcherbina et al. 2018), as presented graphically in Fig. 3 sipation estimates is somewhat ambiguous, as both anisotropy (shaded boxes), it is likely that this energy level is simply and the ADCP noise levels that start to affect the results occur too close to the noise floor of the ADCP. Given the ad- at glider-measured ; 1028 m2 s23. Future work to improve vances of newer signal processing software to improve ve- ADCP-derived estimates of turbulence would benefit from locity wrapping range and to increase instrument bandwidth both lower spectral noise, and the possibility of including local [e.g., Nortek Signature1000 as discussed in Shcherbina et al. estimates of stratification in the theoretical spectrum, which Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1636 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 FIG. 13. Contour plots of TKE dissipation rate estimates for SPURS-1, with the depth of the estimates shown with gray circles to the left. Hourly estimates of mixed layer depth are shown above the contours (estimated as the depth at which temperature is 0.058C different from the surface value), with (a) 24-h moving mean for clarity. The full duration results in (a) generally show that dissipation rates are larger above the temperature-estimated mixed layer depth. (b) Diurnal variability in TKE dissipation rates are seen to be consistent with the variability in the mixed layer depth. Missing values have been interpolated in (a) and (b). will help to push confidence in the measurement below ; may indicate the importance of small-scale horizontal pro- 1028 m2 s23. cesses in setting upper-ocean turbulence. Upper-ocean TKE dissipation rate estimates and the locally measured surface buoyancy flux agreed in the mean during 5. Summary periods of strong convection when the instruments were above We present a method for estimating TKE dissipation rates from pulse-coherent ADCPs on deep-ocean moorings. We overview practices for programming the ADCP to ensure a range of measurable TKE dissipation rates and present a mount for minimizing the chance of mooring failure, and self-wake contamination. We also overview data quality control, spectral methods, flow contamination, and an estimate of the instru- ment’s spectral response function needed to apply inertial sub- range fits to mooring-measured velocity wavenumber spectra. We find TKE dissipation rates estimated with the method outlined in this paper compare favorably to measurements made with a microstructure shear probe on a nearby glider for ; 1028 m2 s23 and larger. The comparison between nearby TKE dissipation rate estimates in this study are similar to those between two microstructure shear probes in past studies, which have suggested natural variability often causes hourly averages FIG. 14. Satellite-derived SST taken at 0330:02 UTC 30 Sep 2012 is shown with positions of the SPURS-1 central mooring and the of to differ by several factors of 10, but with systematic bias glider track during the September–October sampling period (i.e., less than a factor of 2 (Moum et al. 1995). In this study, the data shown in Fig. 8). SST variability on the order of 0.28C periods of disagreement between the glider-derived dissi- exists over small scales, suggesting that some of the differences in pation rates and the mooring-derived dissipation rates are local water properties and turbulent statistics seen between the associated with differences in the vertical temperature mooring and glider datasets are physical rather than manifestations profiles at both locations (horizontal scales of 2–5 km). This of sensor or methodological errors. Unauthenticated | Downloaded 12/20/23 09:48 PM UTC SEPTEMBER 2021 ZIPPEL ET AL. 1637 FIG. A1. Four phases of a simulated wake with monochromatic waves and a constant off-wave angled mean velocity. (a)–(d) Snapshots of the 3D view of the wake at four unique phases. (e)–(h) A top-down 2D view during the same phases as in (a)–(d). The red line shows the upflow direction mimicking the expected orientation of the ADCP. The yellow-to-blue circles show a simulated wake, with locations determined through the advection of the previous instrument locations. The simulated wake’s color scale indicates timing of wake cre- ating. The vertical line in (a)–(d) shows a reference mooring line. Here, simulated 8-s-period 2-m-in-height monochromatic waves propagate in the positive x direction, with a small mean cross flow (Uy/Uorb 5 0.075, Uy 5 0.03 m s21) in the positive y direction. At no part of the wave period does the simulated ADCP beam intersect the wake. mixed layer depths, consistent with boundary layer theories. Data availability statement. Data from the SPURS moorings Vertical gradients in TKE dissipation rates were qualitatively including the processed dissipation rates are available through consistent with mixed layer depths, showing large decreases in NASA’s PO.DAAC (https://podaac.jpl.nasa.gov/; https://doi.org/ dissipation rates below the mixed layer depths on both sea- 10.5067/SPUR1-MOOR1 for SPURS-1, https://doi.org/10.5067/ sonal and diurnal time scales. SPUR2-MOOR1 for SPURS-2) and through WHOI’s UOP website (http://uop.whoi.edu/projects/SPURS/spurs.html). Code Acknowledgments. This work was funded by NASA as part used to process TKE dissipation rates and generate the of the Salinity Processes in the Upper Ocean Regional Study figures is available on github (https://github.com/zippelsf/ (SPURS), supporting field work for SPURS-1 (NASA Grant MooredTurbulenceMeasurements). Intermediate data prod- NNX11AE84G), for SPURS-2 (NASA Grant NNX15AG20G), ucts used in making figures are available on Zenodo (https:// and for analysis (NASA Grant 80NSSC18K1494). Funding for doi.org/10.5281/zenodo.5032511). early iterations of this project associated with the VOCALS project and Stratus 9 mooring was provided by NSF (Awards APPENDIX 0745508 and 0745442). Additional funding was provided by ONR Grant N000141812431 and NSF Award 1756839. The Stratus Wave Orbital Motions and Self-Wake Contamination Ocean Reference Station is funded by the Global Ocean Monitoring and Observing Program of the National Oceanic and Large wave orbital motions have the ability to bring the Atmospheric Administration (CPO FundRef Number 100007298), turbulent wake of the mooring back in front of the sample through the Cooperative Institute for the North Atlantic Region volume of the ADCP, potentially contaminating and artifi- (CINAR) under Cooperative Agreement NA14OAR4320158. cially increasing the turbulence estimate from the ambient Microstructure measurements made from the glider were supported value. Even for vaned instruments that look into the flow, flow by NSF (Award 1129646). We also thank Andrey Shcherbina, Jim reversal due to large local orbital velocities can cause the in- Edson, and Carol Anne Clayson for helpful discussions on Nortek strument to reverse directions and point toward the mean instruments, spectral analysis, and boundary layer turbulence. downstream direction. A rough estimate of the impact of wave Unauthenticated | Downloaded 12/20/23 09:48 PM UTC 1638 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 38 orbital motions on advection at the ADCP location is the local Clayson, C. A., J. B. Edson, A. Paget, R. Graham, and ratio of mean velocity to rms wave orbital velocity. Here, we B. Greenwood, 2019: Effects of rainfall on the atmosphere estimate RMS wave orbital velocity from the surface elevation and the ocean during SPURS-2. Oceanography, 32 (2), 86– power spectral density, E(v), provided by the wave package on 97, https://doi.org/10.5670/oceanog.2019.216. the surface mooring. Assuming deep water waves and linear Comte-Bellot, G., and S. Corrsin, 1971: Simple Eulerian time correlation of full-and narrow-band velocity signals in grid- dispersion, the wave orbital variance is generated, ‘isotropic’ turbulence. J. Fluid Mech., 48, 273–337, ð 1/2 https://doi.org/10.1017/S0022112071001599. orb Urms 5 v2 E(v) exp(2zv2 /g) dv . (A1) Dillon, J., L. Zedel, and A. E. Hay, 2012: On the distribution of velocity measurements from pulse-to-pulse coherent Doppler Using this definition, we find the ratio of mean advection to rms sonar. IEEE J. Oceanic Eng., 37, 613–625, https://doi.org/ wave orbitals, U/Urmsorb , to be primarily between 0.1 and 1 for the 10.1109/JOE.2012.2204839. near-surface locations (less than 20-m depth) and primarily Edson, J. B., and Coauthors, 2013: On the exchange of momentum over the open ocean. J. Phys. Oceanogr., 43, 1589–1610, between 1 and 10 for deeper locations. The surface locations, https://doi.org/10.1175/JPO-D-12-0173.1. therefore, are most suspect because of having U/Urms orb , 1. Fairall, C., E. Bradley, J. Hare, A. Grachev, and J. Edson, 2003: Bulk However, U/Urms orb , 1 does not mean all observations from parameterization of air–sea fluxes: Updates and verification for these locations must be thrown out. The 3D nature of the wake, the COARE algorithm. J. Climate, 16, 571–591, https://doi.org/ and the highly directional wave orbital motions, can make self- 10.1175/1520-0442(2003)016,0571:BPOASF.2.0.CO;2. wake contamination unlikely, even when U/Urms orb , 1. Farrar, J. T., and A. J. Plueddemann, 2019: On the factors driving To demonstrate the challenge of self-wake contamination upper-ocean salinity variability. Oceanography, 32 (2), 30–39, with a small cross flow, we pose a simplified model below. https://doi.org/10.5670/oceanog.2019.209. 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