Shear-based and/or strain-based fine-scale parameterizations of turbulent dissipation rates in the deep ocean become erroneous near topographic features where internal wave spectra deviate from Garrett-Munk (GM). Although the Gregg-Henyey-Polzin (GHP) parameterization incorporates this spectral deviation, the applicability remains uncertain. We evaluate “α” and “β” representing the local internal wave energy in the high frequency (2f < ω < N) and low frequency (f < ω < 2f) bands, respectively, scaled by their corresponding values in GM using fine-scale vertical shear and strain simultaneously measured near mixing hotspots. The local internal wave spectra are biased toward higher frequencies (α/β ≫ 1) over rough bathymetry where high frequency internal waves are generated, whereas they are biased toward lower frequencies (α/β≪ 1) at latitudes where high vertical wavenumber, near-inertial shears are created byparametric subharmonic instabilities. Compared with the shear-based and/or strain-based parameterizations, GHP more accurately estimates turbulent dissipation rates by compensating for deviations from GM.
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 The return flow of the global thermohaline circulation consists of upwelling in the Indian Ocean and the North Pacific. This upwelling is enabled by downward mixing of heat across the thermocline, reducing the density of the cold deep water and decreasing the amount of energy required for upwelling. The downward mixing is not uniform throughout the ocean, but focused in patches of localized high mixing in a background of low mixing. Considering that the global thermohaline circulation is a major transporter of heat in the climate system and has a major influence on Earth's climate, mapping the intensity of turbulent mixing throughout the deep ocean is indispensable for accurate climate change prediction.
 The energy available for deep ocean mixing is thought to originate from tides and winds and shift across the local internal wave spectrum down to small dissipation scales. Results from dynamical models such as McComas and Müller  and Henyey et al.  indicate that the turbulent dissipation rate ε increases as the energy level of the local internal wave field E increases such that the empirical relationship ε ∼ N2E2 holds, where Nis the local buoyancy frequency. So, instead of time-consuming microstructure measurements, fine-scale parameterizations based on this empirical relationship are frequently used to quantify turbulent dissipation rates.
 Relevant fine-scale parameterizations include Gregg's empirical formula [Gregg, 1989, hereinafter G89] and Wijesekera's empirical formula [Wijesekera et al., 1993, hereinafter W93], both of which assume that the local internal wave field maintains the same spectral shape as the Garrett-Munk [Garrett and Munk, 1972, 1975, hereinafter GM; Cairns and Williams, 1976] wave field while varying its energy level. Based on this assumption, G89 evaluates the energy level of the local internal wave field in terms of the ratio of the vertical shear level to the corresponding value in the GM wave field, whereas W93 evaluates the energy level of the local internal wave field in terms of the ratio of the vertical strain to the corresponding value in the GM wave field. If the local internal wave field has the spectral shape close to the GMprescription, both of these empirical formulae yield, of course, the same estimates of turbulent dissipation rates. If the internal wave spectrum is biased toward lower (or higher) frequency portion which is more occupied by kinetic (or potential) energy than the other portion of the spectrum, however, the shear-based Gregg's empirical formula overestimates (or underestimates) the energy level of the local internal wave field and hence the turbulent dissipation rates, whereas the strain-based Wijesekera's empirical formula underestimates (or overestimates) the energy level of the local internal wave field and hence the turbulent dissipation rates.
 Taking into account the possible distortion of the internal wave spectrum, Polzin et al. applied a frequency-based correction to the dynamical model ofHenyey et al.  to propose a modified version of G89, namely, the Gregg-Henyey-Polzin parameterization (hereafter GHP). More specifically,Polzin et al.  introduced a new parameter Rω, the ratio of fine-scale vertical shear to fine-scale vertical strain of the local internal wave field to make a correction toG89.
 In this study, using the fine-scale vertical shear measured by expendable current profiler (XCP) and fine-scale vertical strain measured by conductivity-temperature-depth profiler (CTD), we examine the possible distortion of the internal wave spectrum near the mixing hotspots in the real interior ocean more directly by calculating “α” and “β” which are the ratios of the local internal wave energy in the high frequency (2f < ω < N; f is the inertial frequency) and low frequency (f < ω < 2f) bands, respectively, to the corresponding value in the GM spectrum. At the same time, we estimate the turbulent dissipation rates at each depth and location using G89, W93, and GHP, respectively, and then compare these values with the turbulent dissipation rates directly measured using microstructure profiler VMP-5500 to assess the efficacy of each fine-scale parameterization.
2. Field Observations and Data Analysis
 Field observations were carried out at several locations near the representative topographic features in the North Pacific, namely, the Aleutian Ridge, the Emperor Seamounts, and the Izu-Ogasawara Ridge (Figure 1) on cruises of the training vessel Oshoro-Maru of Hokkaido University (June and November in 2008). At each location, we deployed the un-tethered free-fall microstructure profiler VMP-5500 (manufactured by Rockland Scientific Inc.) equipped with a Seabird CTD sensor which measured micro-scale velocity shear at a rate of 512 Hz together with fine-scale potential temperature structure while descending at a speed of ∼0.6 ms−1. At a few tens of meters above the ocean floor, VMP-5500 released ballast and started floating back to the sea surface again at a speed of ∼0.6 ms−1. Coincident with each microstructure measurement, we deployed XCPs to obtain the fine-scale velocity structure from the sea surface to ∼1600 m depth at each location.
 The obtained vertical profiles of fine-scale potential temperature and horizontal velocity were divided into 75%-overlapping 200 m depth bins and smoothed using a 1-m wide triangular window applied every 0.4 m. For each depth bin, the vertical wavenumber power spectrum of horizontal velocity and that of potential temperature divided by the mean temperature gradient were calculated and multiplied by the squared vertical wavenumber. Sample spectra are shown inFigure 2, where the vertical wavenumber at which the spectrum starts to roll off decreases as the fine-scale shear and/or strain spectral level increases fromFigure 2a to Figure 2c, consistent with the results from previous field observations [Gregg et al., 1993] and numerical experiments [Hibiya et al., 1996, 1998]. These spectra are integrated up to a vertical wavenumber of 0.04 cpm to obtain fine-scale shear variance 〈VzOBS 2〉 and fine-scale strain variance 〈ξzOBS 2〉, respectively. It should be noted that an odd peak often appears in the shear spectrum at vertical wavenumbers of 0.05–0.06 cpm which is likely due to the fluctuations in the XCP's fall speed [Sanford et al., 1993] (Figure 2c) so that this spectral range is excluded from the integration.
 The micro-scale velocity shear profile, on the other hand, was high-pass filtered to eliminate shear components with frequency less than 0.5 Hz and then divided into consecutive segments of 5120 data points, each corresponding to a bin height of about 6 m. For each segment, the frequency power spectrum was calculated and multiplied by the average descending velocity to obtain the corresponding vertical wavenumber power spectrumϕ (m). The turbulent dissipation rate at each depth is calculated by integrating φ (m) from 1 cpm to the highest wavenumber m0 free from the instrument's vibration noise such that
where νis the kinematic viscosity. The turbulent dissipation rates thus calculated are then averaged over each of the 200-m-depth bins. For more details about the processing of XCP data and microstructure data mentioned above, readers are referred toNagasawa et al. [2002, 2007].
3. Calculation of “α” and “β” as a Measure of Spectral Distortion From the GM Model
 We now introduce “α” and “β” representing the ratios of the local internal wave energy integrated over the “high-frequency band” (2f < ω < N) and over the “low-frequency band” (f < ω < 2f), respectively, to their corresponding values from the GM spectrum. These parameters are obtained by solving the equations,
where [VzGM 2]2f-N and [VzGM 2] f-2f ([ξzGM 2]2f-N and [ξzGM 2] f-2f) are the fine-scale vertical shear variances (vertical strain variances) in theGMspectrum integrated over the “high-frequency band” and over the “low-frequency band”, respectively (GM76 model [seeGregg et al., 1993]). The distortion of the local internal wave spectrum from the GM prescription can be measured in terms of these parameters.
4. Results and Discussions
 From the results of microstructure measurements near the Aleutian Ridge, we find that both α and β (blue and red bars in Figure 3a, for α and β, respectively) are relatively small, namely, less than 5. This indicates that the local internal wave spectra near the Aleutian Ridge do not deviate noticeably from the GM prescription.
 In contrast, the microstructure measurements near the Emperor Seamounts (Figures 3b and 3c) and the Izu-Ogasawara Ridge (Figures 3d and 3e) indicate large α and β, which are distinct both from each other and from the Aleutian Ridge measurements. These large values imply that the local internal wave spectra significantly depart from the GM prescription in both the level and shape. Of special notice is that α becomes much larger than β near the ocean floor at Station H1 (Figure 3b), which, as shown in Figure 1, is above the Emperor Seamounts. Motivated by this result, we scatter plot α and β for all the depth bins below 500 m depth classified by the height above the ocean floor (Figure 4a). There is a clear bias in the local internal wave spectra toward higher frequencies nearer to the ocean floor. One possible explanation for this is that high frequency internal waves are generated by tidal interaction with features on the ocean floor [Iwamae and Hibiya, 2012; Iwamae et al., 2009]. On the other hand, although both α and βnear the Izu-Ogasawara Ridge are also large,β becomes much larger than α, in contrast to the internal wave field near the Emperor Seamounts (Figures 3d and 3e). This is consistent with the results of the previous numerical and field studies [Hibiya et al., 1996, 1998, 2002; Hibiya and Nagasawa, 2004; Furuichi et al., 2005] that, at latitudes 20°–30°, parametric subharmonic instabilities(PSI) efficiently transfer energy from the low vertical wavenumber semidiurnal internal tide to the high vertical wavenumber near-inertial frequency portion of the local internal wave spectrum. Actually, the scatter plot ofα and β classified by latitudes shows that the local internal wave spectra at latitudes 20°–30° tend to be biased toward lower frequencies (Figure 4b).
 Next, we compare the turbulent dissipation rates estimated using G89, W93, and GHP (εG89, εW93, εGHP) with those directly measured using microstructure profiler VMP-5500 (εVMP) where
f0 = 7.27 × 10−5 s−1, N0 = 5.24 × 10−3 s−1, VzGM 2 (ξzGM 2) the fine-scale vertical shear variance (vertical strain variance) in theGM spectrum [Gregg et al., 1993] (Figure 3). Note that we employ ε0 = 1.8 × 10−10 m2s−3 instead of the conventional value (ε0 = 7.0 × 10−10 m2s−3 [e.g., Gregg, 1989]), because we find that ε0 = 7.0 × 10−10 m2s−3 overestimates εVMP even when the local internal wave spectrum does not deviate from the GM prescription (i.e., 0.5α < β < 2α, see Figure 3f). The result that ε0 adjusted by a factor of 4 yields the best fit to εVMPfor the undistorted GM-like internal wave spectrum is fairly robust for different upper limits of vertical wavenumbers (0.02 cpm < m < 0.05 cpm) for the integration of shear and strain spectra. Bearing in mind that the exact reason for this small value of ε0 should be clarified in the future, we focus our attention here on the distortion of the internal wave spectrum from the GMprescription with its effect on the fine-scale parameterizations of turbulent dissipation rates.
 The plots of geometrically averaged εVMP for various ranges of α and βover the Aleutian Ridge, the Emperor Seamounts, and the Izu-Ogasawara Ridge show that mixing hotspots can be found at large values ofα and β: a primary one with higher values at 3 < α < 6 and 9 < β < 18 and the other secondary ones with lower values at 6 < α < 9 and 6 < β < 9 and at 9 < α < 18 and 3 < β < 6 (Figure 5a), respectively. This indicates that the internal wave fields in the mixing hotspots are not necessarily following the GM prescription. Of special notice is that both G89 and W93 can significantly overestimate and/or underestimate turbulent dissipation rates at these mixing hotspots; in particular, the ratio of the geometrical average of εG89 to that of εVMP becomes 1.53 for 3 < α < 6 and 9 < β < 18 and 0.74 for 9 < α < 18 and 3 < β < 6, whereas the ratio of the geometrical average of εW93 to that of εVMP becomes 0.8 for 3 < α < 6 and 9 < β < 18 and 1.48 for 9 < α < 18 and 3 < β < 6 (Figures 5b and 5c).
 Such discrepancies between the predicted and observed turbulent dissipation rates are much reduced when GHP is employed; the ratio of the geometrical average of εGHP to that of εVMP becomes 1.13 for 3 < α < 6 and 9 < β < 18 and 1.1 for 9 < α < 18 and 3 < β < 6, both approaching unity (Figure 5d). It is thus found that using GHP parameterization avoids existing overestimates and/or underestimates in predicting turbulent dissipation rates in the mixing hotspots where internal wave fields deviate from the GM prescription.
 Using a fine-scale parameterization to predict turbulent dissipation rates based on fine-scale vertical shear [Gregg, 1989; G89] or fine-scale vertical strain [Wijesekera et al., 1993; W93] can significantly overestimate or underestimate the turbulent dissipation rates near prominent topographic features in the world's oceans [Hibiya et al., 2007]. One possible explanation for this is that the internal wave spectra near topographic features greatly diverge from the Garrett-Munk (GM) prescription. Although the parameterization proposed by Polzin et al.  (GHP) takes into account the effect of this spectral distortion, assessment of its applicability to the real ocean has not been fully carried out.
 In this study, we have first evaluated “α” and “β” representing the ratios of spectral amplitudes averaged in the high frequency (2f < ω < N) and low frequency (f < ω < 2f) bands, respectively, to the corresponding values in the GMspectrum using the depth profiles of fine-scale vertical shear and strain simultaneously measured near mixing hotspots. We have found thatα/β ≫ 1 at mixing hotspots immediately above the Emperor Seamount (38°N, 170°E) where high frequency internal waves are thought to be efficiently generated by tidal interactions with the rough ocean floor, whereas α/β≪ 1 at mixing hotspots near the Izu-Ogasawara Ridge (28°N, 144°E) where high vertical wavenumber near-inertial current shears are thought to be created viaparametric subharmonic instabilities. Next, the efficacy of the existing fine-scale parameterizations,G89, W93, and GHP in evaluating the turbulent dissipation rates near mixing hotspots has been assessed. Although a dissipation coefficient ε0much smaller than the conventional value has been utilized to produce the observed turbulent dissipation rates for the GM-like internal wave field, we have found that GHP most accurately estimates turbulent dissipation rates by adequately correcting the overestimates (or underestimates) and underestimates (or overestimates) of turbulent dissipation rates byG89 (or W93) for α/β ≪ 1 and for α/β ≫ 1, respectively.
 Apart from the ambiguity of the dissipation coefficient ε0, this study warns us that using the fine-scale parameterization based only on vertical shear or vertical strain might lead to a significant distortion in the broad mapping of turbulent dissipation rates [Hibiya et al., 2006; Whalen et al., 2012]. In order to complete the assessment of fine-scale parameterizations of turbulent dissipation rates, however, we are planning more extensive simultaneous measurements of fine-scale vertical shear and strain and turbulent dissipation rates, the results of which will be reported elsewhere.
 The authors would like to express their gratitude to the captain and the officers and crew of T/V Oshoro-Maru of the Faculty of Fisheries of Hokkaido University and the scientific parties on board for their help in carrying out the microstructure measurements. Thanks are extended to two anonymous reviewers for invaluable comments on the paper.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.