[15] The upper ocean observations presented here were obtained using three sensor suites deployed below the ice through hydroholes: an automated, profiling CTD, a fast response microstructure package designed to resolve the spatial scales of turbulent thermal variance dissipation, and a vertical array of turbulence sensors designed to measure flux-carrying turbulence scales. The observations are remarkable in that they resolve fine-scale vertical structure and temporal variability of the IOBL and pycnocline over an annual cycle. Data from the three systems are used to provide heat flux estimates at two vertical levels within the IOBL. The vertical array of flux sensors provides heat flux estimates within the IOBL. Thermal microstructure data are used to estimate heat fluxes at the base of the well-mixed surface layer. All of these heat flux estimates are subject to technical and/or theoretical limitations, which are detailed in the following sections. For example, as was expected for such an undertaking, there were occasional gaps in the data collection when sensors needed maintenance or the logistic infrastructure had to be adjusted to changing ice conditions. Another limitation of the observations is that during summer, when insolation complicates the vertical structure of the IOBL, it is difficult to extrapolate observational heat flux estimates to values at the ice-ocean interface. The observational heat flux estimates are thus supplemented with the SLTC numerical boundary layer model that is run with observed surface forcing and temperature and salinity structure (see section 3). Model output provides heat flux comparisons for the two observational levels as well as estimates of the interface fluxes. A common, 3-h time base is set up, over which the observations are ensemble averaged and for which an SLTC run is performed. The 3-h interval is a good compromise between achieving statistical stationarity with the turbulence estimates and resolving temporal variability of the “mean” characteristics of the IOBL.

#### 2.1. Profiling CTD

[16] The high-resolution, profiling CTD was a pumped, dual-sensor Sea-Bird 911, run topside from an automated winch and data acquisition system. The microstructure package, composed of two fast response thermistors, was mounted at the bottom of the CTD cage. The profiler cycled via the computer-controlled winch between approximately 5 and 150 m depth at a nominal speed of 0.35 m s^{−1} for a 15 min return time. The CTD data were processed using the alignment, filtering, and thermal lag correction techniques recommended by Sea-Bird. Only data from the downgoing portions of the casts are utilized here, because the fast thermistor sensors were obstructed by the CTD on the upgoing portions.

[17] A total of 12,350 downcasts were obtained during the field program. There were 21 days for which no casts were made; 9 occurred between days 447 and 455 when the development of a pressure ridge forced relocation of all the oceanographic instruments. Typically, the profiler ran for between 6 and 12 h a day; operating at this 25–50% duty cycle with a 15 min return time resulted in between 24 and 48 profiles per day. The number of casts per day increased to about 96 during the last two months of the experiment. In terms of the 3-h ensemble averaging periods, 60% had at least one downcast.

[18] The sheer volume of the CTD data set required a technique for automatically identifying profiles that were degraded by measurement problems. Raw temperature and conductivity data from the CTD sensors (recorded at 24 Hz) were averaged in 0.1 m vertical bins. A series of correlation and regression coefficients were formed between the temperature and conductivity profiles measured by the two sensor pairs for each downcast and between sequential downcasts for each of the sensor pairs. These statistics were then used to identify downcasts for which one or both sensor pairs had unacceptably large noise levels and/or offsets. Of the 12,350 downcasts recorded, 11,013 (89%) were determined to have high-quality temperature and conductivity data for at least one sensor pair. Salinity and density were calculated from temperature and conductivity using standard formulations. Individual vertical profiles of potential temperature *T*, salinity *S*, and potential density *ρ* (referenced to surface pressure) from each downcast were then ensemble averaged over the 3-h periods.

[19] Descriptive statistics derived from the CTD observations include properties that characterize the heat content of the well-mixed surface layer and the heat content and stratification of the layer just below the mixed layer where entrainment processes were active. Mixed layer values of temperature, salinity, and density, denoted by a subscript *ml*, were defined as vertical averages over the depth range 10 to 15 m. This depth range represented properties of the upper part of the typically turbulent ocean mixing layer that were sampled near the upper depth limit of the CTD system. The departure from freezing near the ice-ocean interface, *δT*_{ml} = *T*_{ml} − *T*_{fp}(*S*_{ml}) where *T*_{fp} is the freezing point as a function of salinity, was calculated from the surface values. A robust estimate of the thickness of the well-mixed surface layer, *h*_{ml}, was defined by the depth where density increased from its surface value to 20% of the difference between 100-m and surface values. This definition is effective, because there is typically a density step at the base of the mixed layer, but the magnitude of the step varied seasonally in the data set. In the remainder of the paper, the terms surface mixed layer and IOBL will be used somewhat interchangeably, recognizing that the mechanical boundary layer is typically contained within the layer we refer to as the mixed layer. An “entrainment layer” was defined as the area just below the well-mixed layer that was likely to be exposed to IOBL entrainment during strong surface forcing events. On the basis of microstructure measurements (described below), the thickness of the entrainment zone during strong forcing events is on the order of 5 m, and so the entrainment layer is taken as a 5-m-thick zone underlying the surface layer. Statistics describing the entrainment layer are denoted by a subscript *pyc*. For example, stratification was characterized as the salinity difference across the layer, Δ*S*_{pyc}, and heat content was characterized using the average departure of temperature from freezing in the layer, *δT*_{pyc}. While these criteria are subjective, the values chosen work well for the range of conditions encountered and highlight the features of interest to us here, and results are not significantly different using other, reasonable values of the criteria.

#### 2.2. Thermal Microstructure

[20] The measurement of thermal microstructure was chosen to characterize turbulence transport rates from the profiler package because of the requirement that the system run with a minimum of supervision and repairs over the yearlong duration of the program. For example, velocity microstructure measurements would have been contaminated by mechanical vibrations of the winch, and conductivity measurements would likely have been interrupted frequently by biofouling and damage to the delicate fast conductivity sensors that resolve dissipation scales.

[21] Output from two fast response, glass-coated-bead thermistors (Thermometrics FP07) was preemphasized [e.g., *Mudge and Lueck*, 1994], antialias filtered, and sampled to 16 bit resolution at 188 Hz. Upon analysis, the preemphasized data were deconvolved into the original signal and its derivative. For each downcast, temperature calibrations were obtained by regression against CTD temperature and a spectral noise model was estimated using the most quiescent sections of the cast (typically near the bottom). Casts containing high-quality data were identified with a regression/correlation coefficient analysis between sensors and casts analogous to that used to clean up the CTD data set, with an additional criterion that the variance of the noise floor model not be too large. 51% of the 3-h ensemble periods had at least three downcast profiles with high-quality data. Heat flux estimates were not attempted for ensemble periods with fewer than three downcasts.

[22] The fundamental quantity estimated from the thermal microstructure observations is the rate of dissipation of turbulent thermal variance, defined by

for one-dimensional measurements in an assumed isotropic turbulent field. Here, κ_{T} is the molecular diffusivity of heat, *dT*′/*dz* is the vertical derivative of the turbulent temperature field, and the overline notation indicates temporal averaging. The temporal measurements are translated into spatial measurements along the vertical profile using Taylor's frozen turbulence hypothesis in which sensor fall speed *u*_{drop} and the ice drift speed *V*_{ice} are included in an effective advection speed

The variance of *dT*′/*dz* was estimated spectrally, with corrections applied for the response of a glass bead–type thermistor [e.g., *Fleury and Lueck*, 1994] and sensor noise. Spectral points with frequency greater than the 1/5-power point of the of the transfer function (at about 25 Hz) were discarded. This frequency cutoff translates into a maximum resolvable wave number that decreases from *k*_{max} = 467 rad m^{−1} for motionless ice to *k*_{max} = 380 rad m^{−1} for ice moving at 0.25 m s^{−1}; unfortunately, the spatial resolution was most limited for fast moving ice (i.e., strong surface forcing).

[23] The technical difficulty of fully resolving the temperature dissipation spectrum in energetic turbulent fields with thermistors is well known [e.g., *Gregg*, 1999]. The Batchelor model of the temperature dissipation spectrum predicts an exponential roll-off at the Batchelor wave number

where *ν* is molecular kinematic viscosity, and is the dissipation rate of turbulent kinetic energy (TKE). On the basis of the maximum resolved wave number in the observed spectra and (3), we expect that the FP07 thermistors were unable to completely resolve if ε was greater than about 10^{−9} W kg^{−1}. Examples of temperature gradient spectra near the base of the mixed layer from a period of strong surface forcing (*u*_{*0} = 0.01 m s^{−1}) on yearday 431.0 (Figure 2) illustrate the resolution problem. (The term “yearday” is taken to mean fractional day of the year, beginning 1 January 1997. Yearday values extend continuously into 1998, with noon on 1 January 2008 taking yearday value 366.5.) Most of these spectra do not contain clear maxima or signs of exponential roll-off, indicating that ε in this particular instance was greater than at least 10^{−8} W kg^{−1} (by comparison of the observed spectra to the theoretical Batchelor forms plotted in the Figure 2). Because the spectral peaks occur beyond the maximum observed wave number, the spectra by themselves cannot be used to estimate the fraction of variance that went unresolved by the thermistors.

[24] In order to estimate and correct for the unresolved variance of the thermistor measurements, we have used the results of the SLTC model (section 3) to infer ε, which provides the additional information required to calculate the amount of variance beyond *k*_{max} in the observed spectra. The SLTC model is a first-order turbulence closure model, which means it does not carry an equation for TKE, but ε can be estimated from the SLTC results by assuming a local balance between TKE production and dissipation. Using the turbulent diffusivity of momentum *ν*_{T} and diagnosed horizontal velocity output from the model, the SLTC estimate of ε is

After ε^{SLTC} is converted to a Batchelor wave number using (3), the ratio *k*_{B}^{SLTC}/*k*_{max} determines the fraction of unresolved variance in any particular observed spectrum, assuming that the measured spectra follow the theoretical Batchelor form. Figure 3a illustrates that *k*_{B}^{SLTC} was several times larger than *k*_{max} during strong storm events. For ensembles with *u*_{*0} > 0.01 m s^{−1}, the average value of *k*_{B}^{SLTC} was 1347 rad m^{−1}, 3.2 times the average value of *k*_{max}, 800 rad m^{−1}. A corresponding *χ* “correction factor” (Figure 3b), which corrects for the estimated unresolved variance, has an average value of 2.6 during strong forcing conditions and it has maximal values in the range 3–7 for the largest storms encountered. In reality, some fraction (about 20% [e.g., *Osborn*, 1980]) of the TKE is lost to buoyancy production, which implies that both the estimated ε and the calculated correction factor represent upper limits of the actual values. We apply this correction factor to the spectral *χ* estimates and use the difference between the corrected and uncorrected forms as a measure of uncertainty.

[25] As noted above, the main use here for the thermal microstructure data is to estimate the heat flux across the base of the well-mixed surface layer as a quantification of the amount of heat entering the surface layer from the upper pycnocline. Heat flux is estimated from *χ* using the method of *Osborn and Cox* [1972], in which a balance is assumed to hold between the production and dissipation of turbulent temperature variance

Combining (1) and (5), the microstructure-based heat flux estimate is

where _{T} is set to a constant value of 1.4 × 10^{−7} m^{2} s^{−1}. This estimate is essentially determined by the ratio of the temperature gradient variance to the mean, or background, temperature gradient . In an episodically energetic and vertically structured environment such as the mixed layer base and upper pycnocline, it is difficult to characterize average values of these two quantities, especially with a sensor moving in the vertical direction. Extensive vertical averaging is not possible at the approximately 1-m scale required to resolve the vertical structure near the base of the mixed layer and within the entrainment layer. Also, *h*_{ml} is constantly changing because of internal wave motions and the temperature gradient inferred from a single profile at these small scales is not representative of the background profile if turbulence is active.

#### 2.3. Turbulence Instrument Clusters

[28] The vertical array of turbulence sensors consisted of sensitive mechanical current meters and nearly collocated temperature and conductivity sensors (see *McPhee* [2002] for details). Individual sets of instruments, known as Turbulence Instrument Clusters (TIC), were mounted on a rigid mast suspended below the ice to form a vertical array of between two and four clusters. During the first half of the experiment (before the forced relocation described above) four TICs were deployed at nominal depths of 4, 8, 12, and 16 m below the ice undersurface. For the second half of the experiment two TICs were deployed at nominal depths of 4 and 8 m. The TIC sensors were sampled at 6 Hz, resolving the energy-containing turbulence scales in the IOBL and allowing direct, eddy correlation estimates of turbulent fluxes of momentum and heat. Covariance estimates were calculated from fluctuations over 15-min averaging periods and the resulting fluxes were further averaged over the 3-h ensemble periods. Previous results using the system demonstrate that fluxes based on 3-h-averaging periods are highly reliable. Of the 354 days spanned by CTD operations, at least one 3-h ensemble was available from the TICs for 188, 231, 84, and 62 days, respectively with increasing cluster depth. The average number of ensembles per day with at least one ensemble was four for the shallowest sensor and five for the others. There were 108 days for which there were no ensembles available from any of the clusters. The larger number of days without TIC data (relative to profiler data) is due to a minimum flow speed requirement of the mechanical current meters. During summer, biofouling of the mechanical current meters was a problem, necessitating regular retrieval and redeployment of the TICs to allow for cleaning. Heat flux estimates from the nominal 8-m depth level, *F*_{8m}, were taken to represent heat fluxes within the IOBL.