## 1. Motivation

The need for extended observations of mixing is highlighted by the potentially prominent role played by mixing in changing equatorial SST on interannual (El Niño) time scales. Coincident with the passage of a downwelling Kelvin wave observed prior to the 1991–93 El Niño, reduced mixing observed by Lien et al. (1995) may have provided positive feedback toward increasing SST in the central Pacific. At the other extreme, enhanced subsurface mixing is a prime (but unproven) candidate for the 8°C surface cooling (in 1 month) at 0 125°W to abruptly conclude the strong 1997–98 El Niño (McPhaden 1999; Wang and McPhaden 2001). This enhanced mixing, inferred from bulk estimates, must also be highly intermittent (characteristic of naturally occurring turbulence) and not amenable to observation from shipboard campaigns, which are infrequent, of necessarily short duration, and must be planned years in advance. This is exemplified by three experiments to examine the nature of turbulent mixing in the central equatorial Pacific: in 1984, TROPIC HEAT (Moum and Caldwell 1989); in 1987, TROPIC HEAT 2 (Moum et al. 1992a); and in 1991, the Tropical Instability Wave Experiment (TIWE; Lien et al. 1995). All of these experiments focused on the site at 0°, 140°W, largely because of the presence of long-term moored observations predating the full implementation of the Tropical Ocean and Global Atmosphere–Tropical Atmosphere Ocean (TOGA–TAO) equatorial array of moorings (McPhaden 1993). The sum duration of these intensive profiling observations was about 100 days over a period of 7 yr, with none since 1991. Moreover, mixing parameterizations based on these experiments have not been particularly successful (Zaron and Moum 2008, manuscript submitted to *J. Phys. Oceanogr.*). Reliably establishing the role of mixing in interannual climate phenomena such as El Niño is impossible without longer-term records.

To progress toward the goal of establishing extended observations of mixing and internal gravity waves, we have developed, tested, and deployed a string of moored temperature microstructure recorders (*χ*pods; Fig. 1) at the 0°, 140°W TAO mooring site. The initial deployment yielded a highly resolved, 4-month time series of temperature *T*, the rate of dissipation of temperature gradient fluctuations *χ _{T}*, the turbulent kinetic energy dissipation rate

*ε*, and the turbulence diffusion coefficient

*K*at three depths over the range 30–90 m. We have since attempted to maintain a presence at 0°, 140°W and have deployed

_{T}*χ*pods at three to six depths continually since September 2005.

Our objective is to provide a simple, reliable, and affordable device that can be readily integrated into existing moorings or autonomous vehicles. We expect these measurements will provide a meaningful beginning toward the objectives of dynamically linking the mixing to the larger spatial scales and longer time scales at this and other locations.

In this paper, we describe the basic configuration and philosophy behind *χ*pod, some of the lessons we have learned from our first deployment, and some preliminary results. We begin with a set of definitions and our procedure for estimating *χ _{T}* (section 2), followed by a summary of design considerations (section 3). The configuration of

*χ*pod is discussed in section 4. We then present some basic results, including measurements of the cable motion (section 5). The effect of cable motion is critical to our estimate of

*χ*and is discussed in section 6. This is followed by a comparison to historical data (section 7) and, finally, a summary and conclusions (section 8).

_{T}## 2. Definitions and procedures

### a. *χ*_{T}, *ε*, and *K*_{T}

_{T}

_{T}

The ultimate objective of these mixing measurements is the computation of *χ _{T}*,

*ε*,

*K*, the turbulent heat and buoyancy fluxes

_{T}*K*and

_{T}dT/dz*N*

^{2}

*K*, and their vertical divergences. Here,

_{T}*N*

^{2}= −

*g*/

*ρ*·

*dρ*/

*dz*is the squared buoyancy frequency,

*g*is the acceleration due to gravity, and

*ρ*is density.

*T*in the diffusive subrange of turbulence, the dissipation rate of temperature variance can be computed as which for isotropic turbulence becomes where

*dT*/

*dx*is the alongpath (not necessarily horizontal at all wavenumbers) component of temperature gradient,

*D*the thermal diffusivity, and Ψ

_{T}*(*

_{Tx}*k*) the wavenumber spectrum of

*dT*/

*dx*. The brackets ideally refer to an ensemble average; in this particular case, they refer to a time average. We do not measure

*dT*/

*dx*directly; rather, we infer it from the measured time derivative

*dT*/

*dt*via Taylor’s frozen flow hypothesis where

*u*represents the flow speed past the thermistor. Following Osborn and Cox (1972), the eddy diffusivity is defined through the turbulent temperature variance equation, assuming isotropic turbulence acts on a background state with the only mean gradient in the vertical coordinate direction,

*dT*/

*dz*. From this, the eddy diffusivity for heat is The wavenumber extent of Ψ

*depends on*

_{Tx}*ε*through the Batchelor wavenumber

*k*= [

_{b}*ε*/(

*νD*

_{T}^{2})]

^{1/4}. Because thermistors typically capture a small fraction of temperature gradient variance (Lueck et al. 1977; Nash et al. 1999),

*k*must be estimated to determine

_{b}*χ*from partially resolved spectra. In the absence of direct measurement of the microscale velocity shear, we make the assumption that

_{T}*K*=

_{ρ}*K*to determine

_{T}*ε*and hence

*k*(i.e., Alford and Pinkel 2000). Here, is defined assuming a steady-state balance between shear production, turbulence energy dissipation, and buoyancy production

_{b}*J*, with a constant mixing efficiency Γ setting the ratio between

_{b}*ε*and

*J*(Osborn 1980). Assuming the equality of Eqs. (4) and (5), where

_{b}*ε*denotes

_{χ}*ε*computed from

*χ*.

_{T}### b. Estimating *χ*_{T}

_{T}

Because flow speeds are typically large (and variable) and computations are made over short time intervals (for reasons discussed in section 6), gradient spectra contain only a small fraction of the diffusive subrange at moderate dissipation rates, with the highest wavenumbers almost always attenuated because of sensor response. As a result, individual spectra seldom look like the canonical Batchelor (1959) form, so curve-fitting procedures (e.g., Luketina and Imberger 2000) fail to be robust. In contrast, the procedure we use is insensitive to the shape of the temperature gradient spectrum and in no way requires that the diffusive roll-off be resolved. Our procedure does require Γ; however, the dependence on it is weak (see appendix).

*χ*when the spectrum is incompletely resolved requires fitting observed spectra over limited bandwidth to an accepted universal form. In practice, we determine

_{T}*χ*by integrating Ψ

_{T}*(*

_{Tx}*k*) over a subrange

*k*

_{min}<

*k*<

*k*

_{max}that is resolved by the thermistor. Because the frequency-response transfer functions we determine for each thermistor (see section 4) are neither perfect nor do they extend to

*k*for high

_{b}*ε*and

*u*, we account for variance not resolved by the probe by assuming a universal form for the scalar spectrum at unresolved wavenumbers. The variance between the measured [Ψ

*(*

_{Tx}*k*)]

_{obs}and theoretical [Ψ

*(*

_{Tx}*k*)]

_{theory}spectra at resolved wavenumbers is assumed to be equal: Then

*χ*is computed from the full integral of the theoretical spectrum. Theoretical forms for the scalar spectra have been proposed by Batchelor (1959) and Kraichnan (1968). It has been found that Kraichnan’s universal form more closely matches both field observations (Nash and Moum 2002) and fully resolved turbulence simulations (Smyth 1999). We use the Kraichnan form here but note that this choice has little quantitative effect on our results.

_{T}The wavenumber extent of the theoretical scalar gradient spectrum depends on the value of the universal constant *q* and the Batchelor wavenumber, which we estimate through Eq. (6) as *k _{b}* = [

*ε*/(

_{χ}*νD*

_{T}^{2})]

^{1/4}. We use an iterative procedure to determine

*χ*and

_{T}*ε*that is consistent with Eqs. (2), (6), and (7) for nominal values of Γ(0.2) and

_{χ}*q*(7), initial values of

*k*

_{min}and

*k*

_{max}, and measured values of

*N*

^{2},

*dT*/

*dz*, and Ψ

*. The procedure is as follows: First we estimate*

_{Tx}*χ*based on an initial guess of

_{T}*k*We set

_{b}.*k*

_{max}=

*k*/2 or to a wavenumber equivalent to

_{b}*f*= 40 Hz [i.e.,

*k*

_{max}= 2

*π*(40)/

*u*], whichever is smaller. We then use Eq. (6) to refine our estimate of

*k*and recompute

_{b}*χ*using Eqs. (2) and (7). This sequence is repeated and converges after two or three iterations. Estimates of

_{T}*χ*from this iterative procedure are equivalent to the explicit formulation of Alford and Pinkel (2000), except that we use the Kraichnan form of the spectrum. Biases associated with this procedure are explored in the appendix.

_{T}### c. Flow speed past the thermistor

*u*past a sensor is the vector sum of the fluid speed

*U*and the speed at which the instrument package (or the cable to which it is attached) moves because of surface-induced pumping. In the case that the sensor is aligned with the fluid flow in the

*x*coordinate direction (as in Fig. 2), the flow speed past the sensor is The cable velocities

_{c}*u*,

_{c}*υ*, and

_{c}*w*can be deduced from measurements using motion sensors. Measured accelerations in orthogonal coordinates (

_{c}*x*,

_{c}*y*, and

_{c}*z*, where

_{c}*z*> 0 is upward) are where the overdot denotes the time derivative, and the approximation for the vertical component holds for small angles. The accelerations [Eq. (9)] include a gravitational component (tilting) and an inertial component. The tilts

_{c}*α*and

_{c}*θ*are typically referred to as pitch and roll. A full motion package, including linear accelerometers and angular rate sensors, would allow unambiguous distinction between tilting and inertial accelerations, as well as evaluation of angular velocities at the thermistor tip. Because of power and data storage constraints, our package included only orthogonally mounted linear accelerometers. Although our estimates of

_{c}*w*are unambiguous, there exists ambiguity in our estimate of

_{c}*u*and therefore, uncertainty in

_{c}*u.*The effect of this on our estimate of

*χ*is addressed in section 6.

_{T}## 3. Design considerations

We anticipated three major problems in making a successful measurement of mixing from a mooring:

- ensuring that the sensors are exposed to undisturbed flow;
- contamination of the measurement by cable motion; and
- biological fouling of the sensors through either mechanical destruction by large creatures or biological growth, including the buildup of a bacterial film on the thermistor glass, which we imagined could slow the heat transfer between water and sensor, thereby reducing the sensor’s frequency response.

Consideration of these issues helped dictate the final design of *χ*pod—complicating the design but ultimately making the measurement successful. We discuss each problem in turn, our design solutions, and the overall construction of *χ*pod.

### a. Exposure of sensors to undisturbed flow

Measurements of small-scale microstructure fluctuations of temperature, conductivity, or velocity on profilers (Moum et al. 1995) or towed bodies (Moum et al. 2002) are possible in part because sensors are located at the leading edge of an instrument package that moves relative to the fluid, either by freely falling or by being towed through undisturbed fluid. On a mooring, sensors must be clamped to the mooring cable and mean currents relied upon to refresh the sampled fluid. To sense undisturbed fluid, they must either be made to swivel to the upstream side of the cable or multiple sensors must be deployed so that at least one is upstream of the cable. We chose to orient *χ*pod using a vane diametrically opposed to the sensors (Figs. 1 and 2). This follows a design similar to that used on the TAO moorings to reduce contamination in Doppler current measurements (Freitag et al. 2003). Rather than use a separate mechanical swivel, measurements of the torsional rigidity of the cable (1.27-cm diameter jacketed steel Nilspin) indicated that a vane of width 15 cm and length 75 cm (similar to that shown) would provide enough hydrodynamic torque to the package at speeds greater than about 0.1 m s^{−1} even if adjacent units were clamped in opposition to each other at 1-m intervals (the worst-case scenario for deployment at sea). This was confirmed by numerous tests of multiple units on cabled moorings in Yaquina Bay, in which currents change direction on tidal periods and range from 0 to 1.5 m s^{−1}.

To monitor the relative directions of ambient currents and the *χ*pod vane, a compass was installed. In the event that the vane did not provide sufficient steerage to expose sensors to the upstream side of the cable, data were flagged.

### b. Cable motion

Microstructure measurements from profilers and towed bodies also require the instrument package to be sufficiently quiet (in a hydrodynamic sense) that package motions do not contaminate the measurement.^{1} In preparation for the proposal that funded this development, we first sought high-frequency (0.1–100 Hz) accelerometer data from moorings that might provide us guidance on broadband cable motion. Finding none, we performed simulations in which we sampled a two-dimensional field of synthetically generated temperature microstructure that obeyed a Batchelor wavenumber form along the path induced by mooring motion at a range of frequencies and amplitudes of current speed–induced cable oscillations. These indicated that spectral contaminations would be acceptable if peak-to-peak cable oscillations in the data band remained below about two cable diameters.

### c. Biological fouling

For use in other instrumentation, we typically manufacture our sensor stings (which house the thermistor beads) from stainless steel. For these long *χ*pod deployments, the stings were constructed from copper, a known biological poison, as a means of discouraging growth on the thermistors. Upon recovery from our first 4-month deployment in fall 2005 there was growth on the acetal pressure case but none on the copper stings. Nor was there any indication of a reduction in the frequency response of the sensors.

For this first deployment, we decided to fully expose sensors, hoping that the cable clamps and cable would provide enough protection from mechanical breakage due to marine life or fishing line. As it turned out (section 5a), this was not sufficient to prevent breakage, so we have since added small probe protectors (shown in Fig. 1c); these have contributed to uninterrupted records over a subsequent 8-month deployment at four depths.

## 4. Instrument configuration

Our final design included two FP07 thermistors separated by 0.9 m (for redundancy and, with both working, to obtain a local estimate of heat flux divergence). These were calibrated in our laboratory as a function of temperature. For typical oceanic values of *ε*, FP07 thermistors are not fast enough to completely resolve the temperature variance at moderate flow speeds (i.e., *u* > 0.2 m s^{−1}). The frequency response of microbead thermistors is unique to individual thermistors (Nash and Moum 1999). For each thermistor, a frequency transfer function was determined from measurements in Yaquina Bay while mounted on our turbulence profiler *Chameleon* beside a thermocouple with much faster response (Nash et al. 1999). This, as well as a frequency transfer function to correct for antialiasing filters, was applied to restore lost variance to temperature gradient spectra prior to integration to compute *χ _{T}* (section 2). Error and bias associated with the response corrections are discussed in the appendix.

The thermistors were mounted on both end caps of a 0.75-m-long, 0.1-m outside diameter pressure case constructed of acetal with wall thickness 0.0095 m. These were sampled at 10 Hz and their differentiated signals (*dT*/*dt*) at 120 Hz (Table 1). Three orthogonally oriented 0–2-g linear accelerometers were sampled at 120 Hz. A compass was sampled at 1 Hz.^{2} A pressure sensor ported through the lower end cap was sampled at 10 Hz. Data were sampled as 24-bit words and the most significant bits stored as 16-bit words. The total data rate of 631 16-bit words s^{−1} required storage on an internal IDE hard disk drive.^{3}

To enable long deployments, the current load for both analog and digital electronics was minimized. The final design draws 24 mA average current over a 24-h cycle. For a 6-month deployment, this requires 20 lithium D-cell batteries. The pressure case is primarily a battery pack.

## 5. Results from the first deployment

Three *χ*pods were deployed by National Oceanic and Atmospheric Administration (NOAA) personnel aboard the R/V *Ka’imimoana* on the TAO mooring at 0°, 140°W on 22 September 2005 and recovered on 16 January 2006. The TAO mooring configuration is discussed on NOAA’s TAO Project Web site (http://tao.noaa.gov/). For this deployment, we purposely positioned *χ*pods at 29, 49, and 84 m to be close to TAO temperature sensors at 28, 48, and 80 m and TAO current meters (Sontek Argonauts) at 25, 45, and 80 m. The TAO temperature sensors were sampled at 10-min intervals. The current data were sampled at 1 Hz and averaged to 10 min before storage. A nearby subsurface ADCP mooring provided hourly averaged currents from 3-s samples.

In this section, we discuss the temperature measurements and survivability of the thermistors, as well as the basic engineering measurements used to understand the behavior of *χ*pod.

### a. Thermistor survivability

Measurements of temperature from the dual thermistors on each of three *χ*pods are compared to nearby TAO Sea-Bird Electronics MicroCat recorder (SBE37) measurements on the mooring cable (Fig. 3). The upper thermistor at 49 m was destroyed upon deployment. The lower thermistor at 49 m shifted voltage rapidly after 3 weeks but steadied and continued to track fluctuations in the TAO temperature measurement. The upper thermistor at 84 m drifted slowly by 1 V after 2 weeks and remained there for the remainder of the deployment. The lower thermistor at 84 m lasted the entire deployment and was destroyed on recovery. The remaining thermistors were apparently mechanically broken while on the mooring; the signal was lost (open circuit voltage) between successive 10-Hz samples. The upper thermistor at 29 m broke in mid-November and the remaining two sensors (at 29 and 49 m) broke within 5 min of each other on 25 November. There was no evidence of fishing line entangled in any of the mooring gear recovered in January 2006. We suspect that schooling fish caused the breakage. Subsequent designs incorporate a protective copper housing to help prevent mechanical breakage of the tip (Fig. 2c). These have contributed to 80% data recovery in the August 2006–May 2007 deployment. With this configuration, and the dimensions noted in Fig. 2c, we do not expect there to be any contamination when the flow remains aligned within ±45° of head-on.

The temperature measurements shown were derived from our laboratory calibrations of thermistors. Aside from the drift at 49 m (Fig. 3c) that we cannot account for because the sensor was later broken, our calibrations agree to within 0.1°C of the TAO temperature measurements. The temperature difference (*δT* = *T _{χ}*

_{pod}−

*T*

_{TAO}) and its variability can be attributed to the local temperature gradient and its temporal variations. Both the magnitude and variability in

*δT*are largest at 84 m for two reasons. First, the separation between sensors is largest there: 4-m separation at 84 m compared to 1-m separation at 29 and 49 m. Second, both

*dT*/

*dz*and its variability is largest at 84 m. We note that

*δT*is well described by

*δz*(

*dT*/

*dz*), where

*δz*is the spacing between sensors and

*dT*/

*dz*is estimated locally from

*T*

_{χ}_{pod}using the cable motion as described in section 5c.

### b. Steering and tilts

Current speed and direction at 25-m depth are shown in gray in Figs. 4a,b. The direction of the vane is represented by the black trace in Fig. 4b. Unfortunately, our compass failed in mid-November. (In fact, all three compasses failed during the deployment; hence the switch to a new manufacturer.) Even at relatively slow current speeds (below 0.1 m s^{−1}) the vane was aligned with the currents to within 20°. At least on a mean basis, the package maintains a relatively constant heading, and the thermistors were steered into the flow to our satisfaction.

Mean body tilts were defined from the 75-min averages of linear accelerations, via Eq. (9), with the assumption that inertial accelerations do not contribute over long time scales. Tilts were speed dependent but limited to maxima of 13°. These were not entirely related to the current speeds at 25 m because there is strong veering of the currents in addition to direct atmospheric forcing on the surface float; both factors influence the shape of the cable.

### c. Cable motion

The details of the motion of a point on the cable are considerably more complex than can be discerned from averaged data (Fig. 4). Without angular rate sensors, it is impossible to reconstruct the details of the motion because of the ambiguity in relative contributions of gravitational and inertial accelerations represented by Eq. (9); that is, we cannot tell the difference between tilting and cable accelerations. Because knowledge of the instantaneous speed of the fluid past the sensor is critical to our estimate of *χ _{T}*, both through Eq. (3) and in converting frequency to wavenumber for spectral comparison to a theoretical standard, we first consider the ranges of motions and later evaluate the consequences of uncertainties in it (section 6).

Typical acceleration spectra (Fig. 5) show the influence of surface gravity waves (at 0.1–1 Hz) and of vortex-induced vibrations (at 5–20 Hz) in all components and at all *χ*pod depths; the source of the 40-Hz signal is not clear. The effect of surface waves is largest in the vertical component (Fig. 5c), where it is equal in magnitude at all *χ*pod depths. Wave signatures in the two horizontal components (Figs. 5a,b) differ although their magnitudes decay with increasing depth. Strouhal frequencies ( *f _{d}* =

*U*/5

*d*) associated with the mean flow (

*U*; noted in the caption) past the cable (diameter

*d*) are 16 Hz at 25 m, 9 Hz at 45 m, and 8 Hz at 80 m. There is presumably broadband excitation associated with both the range of current speeds over the upper 100 m and the numerous other mooring components deployed along the cable. Cable displacements at high frequencies are found to be relatively small in the

*x*and

_{c}*y*directions; rms < 2 mm over 1–45 Hz and rms < 0.1 mm over 5–20 Hz.

_{c}For small tilts, the gravitational contribution to the vertical acceleration is negligible, so that the vertical speed is determined from _{c} = *a _{c}*

^{z}+

*g*[Eq. (9)]. This is confirmed in Fig. 6a, which shows vertical cable velocity spectra coincident with spectra of the time derivative of depth (as sensed by

*χ*pod’s pressure sensor) over the band of surface wave-induced motion; these two signals are coherent and in phase at all depths. Vertical excursions of ±1 m and vertical speeds of ±0.5 m s

^{−1}at surface wave frequencies are common and of equal magnitude at all

*χ*pod depths. We conclude that the vertical cable speed

*w*and displacement

_{c}*z*are reliably determined from

_{c}*a*

_{c}^{z}.

Because there is significant vertical motion in the wind wave band that can be reliably estimated from our accelerometer measurements, we test how well these cable motions correspond to surface winds. Wind speeds measured from the surface buoy of the mooring were compared to rms values of *w _{c}* determined by integrating velocity spectra over 0.1 <

*f*< 1 Hz. This frequency band includes both wind waves and swell (Fig. 6a), although the vertical speed is dominated by frequencies in the wind wave range (Fig. 6b). Surface winds and rms vertical cable speeds are highly correlated (Fig. 7; rms values of

*w*and mean values of

_{c}*U*

_{wind}were computed over 75-min periods for the entire 116-day record). This suggests that implementation of inexpensive and simple high-frequency motion packages on TAO moorings may be useful for determination of significant wave height.

One benefit of the large vertical excursions of *χ*pod is that we can use these to derive a robust local estimate of *dT*/*dz.* We do this by fitting *T* to *z* over a time period that includes at least several wave periods (in the analysis to follow, we use 1 min).

#### 1) The spectrum of *dT*/*dt*

One adverse consequence of the cable motion is that the measured *dT*/*dt* can be dominated by vertical pumping of the sensor through a background vertical temperature gradient *dT*/*dz* when *w _{c}* is large (Fig. 8). In the swell data band (near 0.1 Hz), the example 5-h spectrum of

*dT*/

*dt*corresponds identically with that of

*w*/

_{c}dT*dz*at both 49 and 84 m, where

*dT*/

*dz*is also large at this point in time. At 29 m,

*dT*/

*dz*is smaller, and surface wave contamination is barely apparent over the band 0.1 <

*f*< 1 Hz. Significantly, it is also evident from Fig. 8 that this band of contamination is distinct from the dissipation subrange used to compute

*χ*(>2 Hz) and the internal gravity wave range

_{T}*f*< 0.1 Hz. Note that these spectra only roughly resemble theoretical forms in the turbulence subrange because the tremendous range in both

*χ*and

_{T}*ε*over the 5-h period represented by Fig. 8 distorts the spectral shape.

### d. Examples of high-frequency data

A short record of calibrated temperature and its fluctuations (Fig. 9) shows a few features. During this period, current speeds were 0.35–0.4 m s^{−1} at the *χ*pod depth of 29 m. Presumably the dominant signal in Fig. 9 is the advection of fine structure and microstructure past the mooring by the mean flow. From analysis of TAO temperature sensors at 1, 5, 10, 13, 20, 25, and 28 m, the mixed layer deepened from about 5 m at 0200 UTC to about 25 m at 1000 UTC, part of the nighttime mixing cycle (the mixed layer depth is shown in another context in Fig. 15b). The sequence of sample records at increasing temporal resolution in Fig. 9 indicates the complexity of the temperature structure and how much of that complexity is not sampled at typical 10-min TAO temperature sample rates (gray dots in the figures). Although it cannot be seen on the scales shown in Fig. 9, the noise level of the temperature measurement is <1 mK. The precision of the measurement can be enhanced, if necessary, by incorporating the temperature gradient signal (Mudge and Lueck 1994).

## 6. Effects of cable motion

*u*. The horizontal components of velocity cannot be unambiguously determined from linear accelerations alone; that is,

*a*

_{c}^{x}can arise from inertial acceleration, tilt, or a combination of the two. However, we find

*υ*to be small compared to

_{c}*w*so we ignore its contribution to

_{c}*u*. We then use

*a*

_{c}^{x}to set bounds on

*u*If

_{c}.*a*

_{c}^{x}is due solely to inertial acceleration, then where

*u*is computed as ∫

_{c}*a*

_{c}^{x}

*dt*. Because there is undoubtedly some unknown contribution of tilt to

*a*

_{c}^{x}, we consider Eq. (10) a bound on

*u*. At the other extreme, we suppose that our measurement of

*a*

_{c}^{x}is solely due to tilting, in which case Because

*u*can add or subtract from

_{c}*U*, its effect is to broaden the distribution of

*u*estimates according to Eq. (10) relative to those deduced from Eq. (11). The bias is clearly seen in Fig. 10, as is the positive skewness resulting from the fact that

*U*is always >0, whereas

*u*is nearly equally <0 and >0. Consequences are addressed in this section.

_{c}Three complications arise because of the induced cable motions. First, vortex-induced vibrations cause flow speed variations with many cycles over a 1-s spectrum (Fig. 5). Second, surface wave–induced cable motion results in flow speed variations over a fraction of a cycle in a 1-s spectrum (Fig. 6). Finally, the ambiguity associated with Eq. (9) means that there is uncertainty in the correct value of *u* that applies to a given sample.

Flow speed variations due to cable motion cause the sensor to follow a contorted three-dimensional path through the turbulent flow field. This complicates our use of Eq. (3) (used to infer spatial gradients from temporal gradients) because *u* (the advecting flow speed past the sensor) is not constant over the 1-s period during which we compute a spectrum. It also leads to a distortion of the wavenumber inferred from the alternate form of Taylor’s frozen-flow hypothesis, *k* = *f* /*u*.

We have addressed the first two complications using sensitivity studies on simulated turbulent flow fields in which we resampled temperature gradients along the contorted path and at the speed prescribed by either vortex-induced oscillations or by measured surface wave–induced flow speed variations.^{4} In the first case, we determined that the spectral distortion resulting from cable oscillations larger than two cable diameters *d* was insufficient to cause more than a 20% bias in *χ _{T}*. Because we also calculated the maximum observed cable oscillations [from double integration of Eq. (9)] to be rms < 0.15

*d*over 1–45 Hz and rms < 0.005

*d*over 5–20 Hz, we conclude that this factor does not cause a serious bias in our estimate of

*χ*.

_{T}Because wave-induced speed variations contaminate *dT*/*dt* between 0.1–1 Hz, we compute *χ _{T}* from windowed and detrended 1-s segments. The use of such a short record minimizes both the variability of

*u*over individual spectra and the contributions from

*w*/

_{c}dT*dz*to

*dT*/

*dx.*Although this period is shorter than we might have preferred, it is no different from what we typically choose when computing spectra over 1-m intervals from our turbulence profiler while profiling at 1 m s

^{−1}.

Sensitivity studies on the consequences of flow speed variations from surface waves over a 1-s spectral estimate suggest that these can at worst introduce a 15% spread in the distribution of possible values of *χ _{T}* in a turbulence field characterized by a factor of 2 spread in

*χ*due solely to natural intermittency. We conclude that flow speed variations caused by surface wave–induced cable motion (sub-1-s time scales) do not significantly affect our estimates of

_{T}*χ*.

_{T}The more significant problem is associated with our uncertainty in the correct value of *u* in a 1-s average. This is tested using the potential range of *u* suggested by our measurements of currents and *χ*pod accelerations applied to computing *χ _{T}* from measurements of

*dT*/

*dt.*In the following we use a 48-h record from 28–29 September 2005 to estimate the effect of uncertainty in

*u*on

*χ*

_{T}.The uncertainty in *u* is represented by the differences in the two estimates computed through Eqs. (10) and (11) and is likely solely due to ambiguity in *u _{c}.* It seems that

*w*is well defined (see Fig. 6) and that

_{c}*υ*is small relative to

_{c}*w*. For these sampling tests, we suppose that Eq. (11) defines the true value of

_{c}*χ*and that uncertainty is introduced by the addition of

_{T}*u*= ∫

_{c}*a*

_{c}^{x}

*dt*, as in Eq. (10).

Examples of 1-s spectral estimates that have been corrected for the dynamic response of individual thermistors and for antialiasing filters are shown in relation to a Kraichnan spectrum in Figs. 11a–c. These were selected over a finite range of *χ _{T}*,

*ε*, and

*u*and then averaged in logarithmically spaced frequency bins. In each case, noise is apparent at high wavenumbers. At higher speeds (Figs. 11a,b), the spectra are flatter than the Kraichnan form, presumably because of frequency to wavenumber distortion when

*u*changes appreciably over independent 1-s spectral estimates.

We suppose that the time scales for changes in *χ _{T}* are long relative to that for speed changes. That is, a stationary turbulence field is sampled many times at both low and high values of

*u*, extrema of which occur at ∼10-s intervals. We then compare distributions of

*χ*obtained using all of the data (black line, Fig. 12) and compare these to distributions of

_{T}*χ*obtained at high speeds (

_{T}*u*> 1.1 m s

^{−1}; red line) and at low speeds (

*u*< 0.9 m s

^{−1}; blue line). These indicate a clear but relatively small bias represented by the medians of 1-s

*χ*estimates (the bias is ≃25% low at high speeds and negligibly larger at low speeds).

_{T}We now use 1-s spectral estimates of *χ _{T}* from the same 48-h period to determine, on a point-to-point basis, the uncertainty in

*χ*associated solely with our presumed uncertainty in

_{T}*u.*The result (Fig. 13) indicates the uncertainty to be less than a factor of 3 95% of the time on 1-s estimates; it is roughly predicted by the curve (

*U*

^{2}+

*w*

_{c}^{2})/[(

*U*+

*u*)

_{c}^{2}+

*w*

_{c}^{2}], which is how the estimate of

*χ*is affected through Eq. (3).

_{T}Uncertainty is reduced considerably over a 60-s average (Fig. 14). This is due to the fact that the largest unresolved speed fluctuations (both positive and negative) are on periods significantly less than 60 s, so these are averaged. Presumably, the remaining (small) positive bias in *χ _{T}* results from the asymmetric curve in Fig. 13a. For further analysis of long time series, 60-s averages represent the base dataset.

It is very likely that short time scale variations cause local velocity fluctuations that are unresolved in the TAO velocity measurements. These may be due to phenomena such as narrow band internal gravity waves, for example, that are thought to play an important role in equatorial mixing (Moum et al. 1992b). It is unlikely, however, that the velocity signals of these are as large as the cable speeds induced by surface waves.

Other sources of uncertainty in our estimates of *χ _{T}* arise independently from uncertainties in the precise form of the theoretical spectrum, the magnitude of the mixing efficiency required to evaluate Eqs. (5) and (6), and the cutoff frequency determined to represent the dynamic response of individual thermistors. These are discussed separately in the appendix.

## 7. Time series of *χ*_{T}, *ε*, and *K*_{T} and comparison to historical data

_{T}

_{T}

The purpose of this measurement is to obtain long, uninterrupted time series of equatorial mixing. In examining the entire record of this and following deployments, there appear to be many different mixing states; this is a focus of ongoing scientific analysis. For the purpose here of developing confidence in this new measurement, we consider a short, 4-day record (Fig. 15) that shows strong variability on a daily time scale. Here, the TAO buoy measurement of shortwave radiation distinguishes between night and day (Fig. 15a). Local temperature maxima (≃l0.1°C) at 29-m depth occur after sunset and are accompanied by high frequency-fluctuations (these are narrowband and near *N*; not shown here). The daily cycle is echoed in *χ _{T}* (Fig. 15e),

*ε*(Fig. 15f), and

*K*(Fig. 15g). In each case, day–night differences are about three to four orders of magnitude.

_{T}The daily cycle in turbulence has been previously documented at the equator (Moum and Caldwell 1985; Gregg et al. 1985; Moum et al. 1989) and associated with high-frequency (near-*N*), short wavelength (a few hundreds of m) internal gravity waves (Moum et al. 1992b). In particular, sample data from a 3 1/2-day time series in November 1991 (Moum et al. 1995) include intensive turbulence profiling with shear probes from which *ε* is directly estimated. *Chameleon* estimates of *χ _{T}* and

*ε*are shown as red dots in Figs. 15e,f. The hours of day of the 1991 data are correct; the dates have been adjusted for comparision. Although these two sets of observations were made at the same location, they are separated in time by 14 yr and are derived from fundamentally different observations. Background currents and stratification also differ; how these differences affect mixing is an important scientific issue and a matter of a separate study that includes not only these measurements but also profiling measurements from 1984 and

*χ*pod measurements from 2006. Our purpose here is to identify a few similar characteristics. First, the ranges of magnitudes of

*χ*and

_{T}*ε*, although not identical, are not very different. This is more easily seen in Fig. 16, which shows perhaps a lower noise level in

*χ*from the 1991 profiler measurements and a tendency to larger values of

_{T}*ε*, which may be due to differing oceanographic forcing of turbulence between the two measurement periods. Second, the daytime suppression of

*χ*and

_{T}*ε*is in phase between the two datasets, although both the timing and magnitude of nighttime excitation differ. And finally, the total day/night variability is nearly the same (three to four orders of magnitude in both

*χ*and

_{T}*ε*).

As a final sampling test on the uncertainty in *χ _{T}* caused by uncertainty in

*u*, we reconsider the

*χ*pod data represented by Figs. 15 and 16. The entire 4-day record was recomputed using both Eqs. (10) and (11) and the results were summarized in Fig. 17. The result is that 95% of the values of 60-s estimates of

*χ*are within a factor of 2 of each other.

_{T}## 8. Summary and conclusions

At the design stage, we had full confidence that we could reduce power consumption and increase data storage sufficiently to execute long and continuous deployments that included not only the basic measurement of temperature and its high wavenumber gradients but also a measure of the instrument package motion. We were more concerned that bare thermistors would not survive long deployments, that they would not be reliably exposed to undisturbed flow, or that vortex-induced vibrations might contaminate the measurement. Fortunately, none of these factors have been limiting. Although mechanical breakage of sensors on the first deployment led to shortened records, our subsequent addition of protective rings to the sensors has resulted in much higher data recoveries.

The use of a vane to steer the *χ*pods has been a successful means of keeping the sensors exposed to undisturbed fluid, at least at the range of current speeds observed to date. Although vortex-induced vibrations of the moored cable are clearly evident (Fig. 5), their amplitudes are sufficiently small (no more than 0.15 cable diameters rms across all potentially excited frequencies) that their effect on the measurement of *χ _{T}* is imperceptible.

A potentially more critical problem has been the large surface wave–induced cable motions that cause vertical displacements of ±1 m and vertical cable speeds of ±0.5 m s^{−1} in the surface wave frequency band (2–10 s). One of two unanticipated benefits has been that *χ*pod acts as a vertical profiler (at least over limited range), yielding a robust local measure of *dT*/*dz.* Also, because the spectral energy of *w _{c}* is dominated by frequencies in the wind wave band (Fig. 6), there exists a close correlation to the surface wind speed (Fig. 7).

The vertical motion appears in the temperature gradient spectrum Ψ* _{Tx}* as

*w*/

_{c}dT*dz*, which clearly defines the band of frequencies contaminated by surface wave pumping (Fig. 8). At lower frequencies, we expect internal gravity waves to dominate. At higher frequencies, the turbulence subrange is apparently unaffected, thus permitting our estimation of

*χ*. In fact, Ψ

_{T}*(Fig. 8) looks very much like isopycnal slope spectra measured from the towed body*

_{Tx}*Marlin*(Klymak and Moum 2007), with the exception of the surface wave contamination in the moored spectra. Inasmuch as fluid is advected by the fixed sensors by the currents, the reference frame is similar and we might consider the moored measurements in the same framework, with the important caveat that the finite vertical extent of features propagating or advected through the highly sheared equatorial flow will complicate the interpretation in wavenumber/frequency space at a fixed point.

Because the cable speeds are of the same order as (and frequently much larger than) the advecting current speed, they represent a significant component of the flow speed past the thermistors. This motion must be included in our computations of *χ _{T}* through our use of Taylor’s frozen flow hypothesis, both via Eq. (3) and in the frequency to wavenumber conversion

*k*=

*f*/

*u*. Because the dominant motion is in the surface wave band (2–10 s), and we apply a constant value of

*u*to evaluate both of these for spectral fitting [Eq. (7)], we minimize the change in

*u*over a spectral estimate by choosing 1 s as the basis for estimating

*χ*. However, the relative contributions of gravitational and inertial accelerations to measured horizontal components of acceleration is unknown [Eq. (9)], and hence our estimate of flow speed past the sensor has some uncertainty.

_{T}To reconcile our estimates of *χ _{T}* with this uncertainty in

*u*, we conducted sampling experiments using both simulated spatial series of temperature gradients in a turbulent field as well as resampled

*χ*pod measurements with known bounds on

*u*. The result is that although the uncertainty of individual 1-s estimates of

*χ*is less than a factor of 3, 95% of the time, averaging nonetheless helps. On 60-s averages (about 10 cycles of the dominant contaminant motion), the uncertainty is less than a factor of 2, 95% of the time.

_{T}Although it has turned out that the expected bias to our estimate of *χ _{T}* is acceptably small, we have implemented angular rate sensors on a subset of

*χ*pods to be deployed at the equator in spring 2008. The measurements from these rate sensors, together with those from linear accelerometers, will provide an unambiguous description of the high-frequency motions experienced by the

*χ*pods.

Despite the adverse conditions under which these measurements were made, there are good reasons to have confidence in the estimates of *χ _{T}*,

*ε*, and

_{χ}*K*derived from them. Probably the biggest factor is quantitative comparison with historical data (Figs. 15 and 16). These indicate (from a selected sample) that magnitudes of

_{T}*χ*and

_{T}*ε*and their variability, as well as their relative phase over several daily cycles, are not tremendously different from what was observed at a similar time of year in 1991.

The initial deployment discussed here has been followed by three others at the same site and at least one more is planned. Upon recovery of the first deployment of three *χ*pods in January 2006, four *χ*pods were deployed (29, 49, 59, and 84 m). The surface buoy broke free in May 2006 and has not been recovered. Those *χ*pods are either still dangling beneath the buoy or on the seafloor. Five *χ*pods were deployed in September 2006 (29, 39, 49, 59, and 84 m) and recovered in May 2007. This resulted in continuous records over the entire 8-month deployment at the upper four depths; the *χ*pod at 84-m depth was damaged prior to deployment and recorded no data. Upon recovery an additional six *χ*pods were deployed at 29, 39, 49, 59, 69, and 84 m. Ten *χ*pods will be deployed on the TAO mooring at 0°, 140°W in spring 2008 and an additional ten on an ancillary adjacent mooring (R-C. Lien and M. Gregg, University of Washington) in fall 2008. During this latter deployment, we will execute an 18-day profiling station using *Chameleon*, acoustic Doppler current measurements, and high-frequency acoustic flow imaging echo sounder.

In addition, *χ*pods have been deployed on a coastal mooring off Oregon (M. Levine, Oregon State University) and on drifters in the South China Sea (L. Centurioni and P. Niiler, Scripps Institution of Oceanography) and have been flown on gliders across both western and eastern continental shelves (K. Shearmann, Oregon State University; S. Glenn, Rutgers University). These have all been successful and have contributed additional and valuable learning experiences to our group as we continue to improve the basic *χ*pod design.

This work was funded by the National Science Foundation (0424133). Ray Kreth and Mike Neeley-Brown (with help from Mark Borgerson, Oceanographic Embedded Designs) constructed the *χ*pods. Alexander Perlin helped in organizing data. Numerous NOAA personnel have aided this effort with their professional handling of our instruments on deployment and recovery. The TAO mooring group at PMEL in Seattle were most helpful in sharing their expertise at the design and testing stage, in particular Paul Freitag, Andy Shepherd, and Chris Meinig. We are especially grateful to Mike McPhaden for his encouragement and support of this effort, and the TAO Project Office for continued support. Comments by Alexander Perlin, Emily Shroyer, and Yanwei Zhang on an early draft are appreciated. Insightful and constructive comments by three anonymous reviewers helped to sharpen several aspects of this paper.

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# APPENDIX

## Uncertainties in χT due to q, Γ, and fc

Our method of computing *χ _{T}* involves extrapolation of partially resolved spectra using a theoretical form to compute the total variance of

*dT*/

*dx*[Eq. (7)]. This procedure depends on three key parameters:

*q*, the “universal” constant in the Kraichnan form of the theoretical spectrum;- Γ, the mixing efficiency; and
*f*, the cutoff frequency for thermistor corrections._{c}

We have assumed each of these to be constant. While our choices are not arbitrary, to a certain extent their values are loosely constrained. Our objective here is to assess their contribution to the uncertainty in *χ _{T}* due to reasonable bounds on each. In addition, the uncertainty will depend on

*ε*and

*u*because these control the amount of variance resolved by a thermistor (i.e., the fraction of variance resolved increases for both low

*ε*and low

*u*). In the following, independent 1-s estimates of

*χ*were computed while systematically varying

_{T}*q*, Γ, and

*f*to determine the relative effect of potential uncertainties in each on our estimate of

_{c}*χ*(Fig. A1). We assume

_{T}*q*= 7 and Γ = 0.2 as a baseline to compute

*χ*, (these values are used for all of the computations made in this paper);

_{T}*χ*′ represents that computed with perturbed

*q*, Γ, and

*f*.

_{c}For fixed *k _{b}*, the wavenumber extent of Ψ

*depends on*

_{Tx}*q*. As a result, increasing

*q*reduces the total variance for a given spectral level in the viscous-convective subrange. Hence, an overestimation in

*q*will cause a reduction in

*χ*′. Following Smyth (1999), 5 >

*q*> 10 represents an extreme range (for the Kraichnan form), with

*q*= 7 being a likely value.

Note that Γ is required to estimate *ε _{χ}* through Eq. (6), so that

*k*scales with Γ

_{b}^{−1/4}. Although it is typically assumed that Γ = 0.2 (as we have done here), 0.1 > Γ > 0.35 represents possible oceanographic bounds (Moum 1996; Smyth et al. 2001).

*f*, which enters into Ψ

_{c}*through the single pole transfer function used for spectral corrections: where*

_{Tx}*f*≈ 20 Hz is typical for our thermistors. Although we measure

_{c}*f*prior to deployment (and use a different

_{c}*f*for each thermistor), biological buildup could alter sensor response time. Our sensitivity test consisted of varying

_{c}*f*according to

_{c}*f*

_{c}^{test}=

*βf*for

_{c}*β*spanning from 0.75 to 1.3. For

*β*< 1, too much response correction is applied, leading to increased

*χ*′.

We also examined the effect of estimating *dT*/*dz* using different time intervals for averaging but found no associated bias.

The sensitivities, summarized as mean values of *χ*′/*χ _{T}*, are shown in Fig. A1. These are consistent with the above expectations. In all cases, biases increase with increasing

*ε*and increasing

*u*because these require the most spectral corrections. Only for the highest

*ε*and

*u*does the bias approach 1.5 for the most extreme values of

*q*, Γ, and

*β*. We thus conclude that biases associated with spectral extrapolation using improper parameters have a smaller effect on estimates of

*χ*than potential bias caused by uncertainty in

_{T}*u*(section 6).

*χ*pod sensors.

^{1}

These requirements are less stringent for temperature or conductivity than they are for velocity (Lueck et al. 2002).

^{2}

We have since switched from a Precision Navigation, Inc. model V2Xe compass to a more reliable and higher-resolution Honeywell HMC6352.

^{3}

We expect that continued expanded capacity of flash cards and reduction in our data sampling will enable storage on compact flash.

^{4}

We refrain from reporting the details of these computations here because we also find neither of these problems to be serious.