Seasonal variation of turbulent diapycnal mixing in the northwestern ...

GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L23604, doi:10.1029/2010GL045418, 2010

Seasonal variation of turbulent diapycnal mixing in the northwestern Pacific stirred by wind stress Zhao Jing1 and Lixin Wu1 Received 9 September 2010; revised 20 October 2010; accepted 29 October 2010; published 3 December 2010.

[ 1 ] Profiles of potential density obtained from CTD measurements along the northwestern Pacific section at 137°E are used to estimate both mean and seasonal variations of turbulent diapycnal mixing based on both a Thorpe‐scale method and a finescale parameterization method. In general, away from the bottom, the estimated mean value along this section is about O(10 −4 m 2 /s), indicating much stronger mixing in the Northwestern Pacific than in the stratified mid‐latitude interior ocean. It is further found that the diffusivity can even exceed 10−4 m2/s around the rough topography. The turbulent diapycnal mixing in the upper ocean also displays a distinct seasonal variation with the amplitude decreasing with depth, bearing a statistically significant correlation with surface wind stress forcing. Our study here provides evidence for the important role of energy input from wind stress in sustaining the deep ocean mixing. Citation: Jing, Z., and L. Wu (2010), Seasonal variation of turbulent diapycnal mixing in the northwestern Pacific stirred by wind stress, Geophys. Res. Lett., 37, L23604, doi:10.1029/2010GL045418.

[4] Given rough and complicated topography in the Northwestern Pacific, one might anticipate large mixing rates in this region. In addition, with a great amount of wind‐induced energy flux there [Gill et al., 1974; Alford, 2001], the mixing in the upper ocean may also display a distinct seasonality due to a strong seasonal variation of the wind stress. The accumulated CTD profiles along the Northwestern Pacific section at 137°E provide a unique opportunity to estimate both mean and seasonal variation of the diapycnal mixing in that region. Here we will employ both Thorpe‐scale method and finescale parameterization method to calculate the turbulent diapycnal diffusivity based on the historical CTD observations.

2. Methodology and Data 2.1. Thorpe‐Scale Method [5] The most common model for turbulent diapycnal diffusivity K is suggested by Osborn [1980] as: K ¼G

1. Introduction [2] With the traditional one‐dimensional advection– diffusion model, Munk [1966] argued that the observed abyssal stratification requires an average diapycnal diffusivity K∼O(10−4 m2/s). However, the last three decades of microstructure measurements have indicated a much smaller diapycnal diffusivity value, i.e., O(10−5 m2/s), in the stratified mid‐latitude ocean interior away from boundaries [Gregg, 1987]. Therefore, it has been argued that the diapycnal mixing may be enhanced near rough topography and some other places. Researches in the last two decades have found much stronger turbulent mixing over ridges [Finnigan et al., 2002; Althaus et al., 2003; Klymak et al., 2006], seamounts [Kunze and Toole, 1997; Lueck and Mudge, 1997], canyons [St. Laurent et al., 2001; Carter and Gregg, 2002], as well as hydraulically controlled passages [Roemmich et al., 1996; Polzin, 1996; Ferron et al., 1998]. [3] Temporal variability of the mixing can be also expected due to the varying energy input by tides and wind [Wunsch and Ferrari, 2004]. Studies have found the spring‐ neap cycle of the tide can modulate the turbulent dissipation significantly [St. Laurent et al., 2001; Finnigan et al., 2002; Klymak et al., 2008]. However, the seasonality of the mixing still remains poorly assessed and understood due to limited data. 1 Physical Oceanography Laboratory, Ocean University of China, Qingdao, China.

Copyright 2010 by the American Geophysical Union. 0094‐8276/10/2010GL045418

" N2

ð1Þ

where G is mixing efficiency and typically taken to be 0.2 [Osborn, 1980], N buoyancy frequency, and " turbulence dissipation rate which can be estimated from density overturns [Thorpe, 1977; Alford and Pinkel, 2000] as: " ¼ a2  L2T  N 3

ð2Þ

where a = 0.8 is a constant of proportionality [Dillon, 1982], and LT is the Thorpe scale [Thorpe, 1977]. [6] Both spatial resolution of the measurements and noise of the instruments may impose constraints on the overturn detection. In this paper, the overturn size criteria proposed by Galbraith and Kelley [1996], the modified profile preprocessing method and R0 criterion proposed by Gargett and Garner [2008] are employed to reject those spurious overturns. 2.2. Finescale Parameterization Method [7] The diapycnal diffusivity can be also expressed in terms of finescale strain as [Gregg et al., 2003]  ¼ K0

hz2 i2

2 2 GM hz i

h2 ðR! Þjð f =N Þ

ð3Þ

where hx 2z i represents the finescale internal wave strain variance, GMhx2z i strain variance of GM model, with both evaluated by following Kunze et al. [2006a], Rw shear/strain variance ratio, and f the Coriolis parameter. [8] The strain spectrum may be contaminated by both background stratification and CTD noise, which means that

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Figure 1. (a) Depth‐latitudinal distribution of the time‐mean turbulent diffusivity based on a finescale parameterization method using data from WOCE. (b) Vertically averaged diffusivity (from 300 m–2700 m) against latitude (grey solid) as well as the mean‐square bottom roughness following Jayne and St. Laurent [2001] (blue solid). The dashed line represents the section‐mean value for both variables. The units for diffusivity and roughness are m2/s and m respectively.

the method is not applicable in the presence of sharp pycnoclines as well as in a weakly stratified region. As profiles of horizontal velocity are not available, it is difficult to estimate Rw. Here Rw is set to 7 based on the results estimated by Kunze et al. [2006a]. 2.3. Data [9] We take CTD profiles at 137°E from both Japan Oceanographic Data Center (JODC) and WOCE hydrographic data bank, which respectively cover 30°N–34°N and 3°N–34°N. For the data from the JODC, only profiles with vertical resolution ≤1 m as well as the uncertainties for temperature and salinity respectively less than ±0.005°C and ±0.0005 psu are used. As a result, a total of 325 profiles spanning from 1998 to 2007 can be retained. For the data from WOCE, there are 258 CTD profiles in total with the vertical resolution of 2 m. Finally, all the profiles are broken into 300‐m segments to evaluate the segment‐averaged diffusivity. The shallowest segment, i.e., 0 m–300 m, is discarded due to the presence of sharp pycnoclines. The daily sea surface wind stress spanning from year 1998 to year 2009 from the NCAR/NCEP Reanalysis will be also used.

3. Results [10] We first estimate the time‐mean diapycnal diffusivity K based on the WOCE observations by applying a finescale parameterization method. It should be noted that a Thorpe‐ scale method is not applicable to the WOCE data because of the limit of the vertical resolution of the data (2 m). Two

remarkable features can be identified (Figure 1). First, around the rough topography (e.g., around 8°N, 25°N and 34°N) the diffusivity is found to exceed 10−4 m2/s (Figures 1a and 1b), which is probably due to the dissipation of internal tides generated by barotropic flow [Egbert and Ray, 2001; Wunsch and Ferrari, 2004]. Second, away from the bottom, the estimated mean diffusivity in the Northwestern Pacific is about 7.4 × 10−5 m2/s, much stronger than that in the mid‐latitude ocean interior. Such a strong mixing mainly results from the enhanced mixing around the topography. In addition, the great amount of wind‐induced near‐inertial energy flux and wind work on the strong western boundary current may also play some important roles [Gill et al., 1974; Alford, 2001]. [11] The WOCE CTD measurements reveal some important characteristics of the mean diapycnal mixing in the Northwestern Pacific; however, they can not be used to assess the seasonal variations of diapycnal mixing because of limitation of the sampling number. To assess the seasonal variations, we further analyze the CTD data from the JODC, which has more profiles at each station and a higher vertical resolution, but unfortunately the available data only covers a narrow spatial segment (30°N–34°N), which is just south of the Japan Island. In this region, the seafloor is nearly flat with depth exceeding 4000 m from 30°N to 33°N and then rapidly elevates to less than 1500 m at 34°N. [12] Both Thorpe‐scale and finescale parameterization method indicate a diapycnal diffusivity within 10−5 m2/s– 10−4 m2/s above 3000‐m depth at 30°N–33°N and exceeding 10−4 m2/s above the slope at 33°N–34°N (Figures 2a and

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Figure 2. Depth‐latitudinal distribution of the time‐mean turbulent diffusivity derived from JODC data based on (a) Thorpe‐scale estimates and (b) finescale parameterization estimates. (c) Ratio of turbulent diffusivity by finescale parameterization estimates to that by Thorpe‐scale estimates at Station A and B. 2b). In general, the results derived from the JODC data are consistent with those derived from the WOCE data. [13] These two independent methods can be also cross‐ validated to reduce the uncertainties of the estimations. Here, we treat the section 30°N–33°N as one station, i.e., station A, the section 33°N–34°N as station B, and then evaluate diffusivity at these two stations to reduce the random fluctuations due to the insufficient samplings. The two estimates agree reasonably well at the station A with the deviations within a factor of 2 (Figure 2c), suggesting a robustness of the estimations. At the station B, the values obtained by finescale parameterization estimates are larger than these obtained by Thorpe‐scale method at all depth, with the deviations within a factor of 4 (Figure 2c). This probably results from fluctuations in the background stratification under 300‐m depth inherent in some profiles, which may lead to serious overestimations by finescale parameterization method due to the spectral leakage [Kunze et al., 2006a]. Nevertheless, the enhanced diapycnal diffusivity with a value larger than 10−4 m2/s near the southern coast of Japan is robust. [14] To analyze the seasonal variation of turbulent diapycnal diffusivity, we compare the individual mean values of diffusivity for each season. However, random fluctuations as well as short time‐scale variations of mixing, e.g., the spring–neap cycle caused by tidal forcing [St. Laurent et al., 2001; Finnigan et al., 2002; Klymak et al., 2008], may lead to some uncertainties. Here, we use a statistic test in which the null hypothesis is that there is no seasonal variation inherent in the diapycnal mixing. The null hypothesis can be rejected if there are at least two seasons (e.g., winter and summer) at which the 90%‐confidence intervals of diffusivity have no overlapping. [15] Here we only analyze the seasonal variation at the station A using a Thorpe‐scale method because the estimates are more robust and there are more profiles available. It can be seen that the diapycnal diffusivity displays a distinct seasonality (Figure 3), with a maximum in winter and

minimum in spring and summer. In the upper 900 m, the diapycnal diffusivity in winter is about seven‐folds of that in spring or summer (Figures 3a and 3b). While the seasonality of diapycnal mixing persists in the deep ocean, the amplitude of the seasonal variation decreases with depth. At depths of 900–1500 m, the amplitude ratio decreases to about 4 and 3 (Figures 3c and 3d). A similar seasonal variation can be also found based on the finescale parameterization method, although the amplitudes are somewhat weaker than the Thorpe‐scale estimations (not shown). [16] Much of the oceanic mixing occurs through internal wave breaking. One of the major energy sources for the internal wave breaking is the surface wind forcing [Wunsch and Ferrari, 2004]. Therefore, the seasonality of mixing in the upper ocean may result from the varying energy input by wind. Figure 4a indicates a significant correlation between the diapycnal diffusivity estimated by a Thorpe‐scale method and the surface wind stress, with the coefficient reaching 0.38 (statistically significant at 99% confidence level using a student test). To further demonstrate the relation of diffusivity with the surface wind forcing at seasonal timescale, we calculate the mean diffusivity at each season and align with the seasonal mean surface wind stress (Figure 4b). Strong (weak) mixing corresponds to strong (weak) wind stress in winter (spring and summer).

4. Summary and Discussion [17] Both Thorpe‐scale method and finescale parameterization method are used to estimate the turbulent diapycnal diffusivity along the Northwestern Pacific section at 137°E. Several phenomena have been found as follows. [18] 1. In the region away from the bottom, the estimated diffusivity is about O(10−4 m2/s), indicating a much stronger mixing in the Northwestern Pacific than in the stratified mid‐latitude ocean interior.

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Figure 3. Seasonal changes of the turbulent diffusivity at different depths of Station A by a Thorpe‐scale method. (a) 300– 600 m, (b) 600–900 m, (c) 900–1200 m, and (d) 1200–1500 m. Results are not shown at depths larger than 1500 m because the sampling number is not enough to make a robust detection. The errorbar represents the 90%‐confidence interval based on a lognormal distribution. [19] 2. The enhanced mixing has been found around the topography, which is probably due to the dissipation of internal tides. [20] 3. A distinct seasonal variation of turbulent diapycnal mixing has been found in the upper ocean with the amplitude of the variation decreasing with depth. The seasonality is likely driven by the annual cycle of the surface wind stress. [21] Tidal dissipation is one of the primary energy sources that support diapycnal mixing in the oceanic interior, especially in the deep ocean. However, it is estimated that the total tidal dissipation rate in the open ocean is on the order of 0.7–0.9 TW, which may only contribute 50% of the energy required for sustaining diapycnal mixing in the subsurface ocean [Munk and Wunsch, 1998]. Therefore, it has been argued that a large portion of the remainder may be supplied by the wind field [Wunsch and Ferrari, 2004]. So

far both modeling and observational studies haven’t reached consensus. Danioux et al. [2008] analyzed 3D propagation of the wind‐forced near‐inertial motions in a fully turbulent flow field with a numerical model and revealed that the wind energy may have a significant impact on small‐scale mixing in the deep interior ocean. However, by examining the near‐inertial energy budget in a realistic 1/12° model of the North Atlantic Ocean driven by synoptically varying wind forcing, Zhai et al. [2009] found that nearly 70% of the wind‐induced near‐inertial energy at the surface is lost to turbulent mixing within the top 200 m, therefore the wind forcing can not stir diapycnal mixing at greater depth. Kunze et al. [2006a] found no dependence of diffusivity on winds, but in their study there are only a few profiles available at each station. Alford and Gregg [2001] found that a surface‐ generated near‐inertial wave can penetrate at least to 300 m, the maximum depth of their observations. Based on histor-

Figure 4. (a) Scatterplot of vertically integrated diffusivity from 300 m to 1500 m at Station A by a Thorpe‐scale method against surface wind stress as well as the linear fit (blue dashed). (b) Vertically integrated diffusivity from 300 m to 1500 m by a Thorpe‐scale method and climatological wind stress at each season. 4 of 5

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ically accumulated profiles along 137°E with adequate vertical and temporal coverage, our study here indicates that the surface wind can control the seasonal variations of the deep ocean mixing with depth extending to more than 1000‐ m, pointing to the important roles of wind‐input energy flux in supporting the deep ocean mixing. [22] Acknowledgments. This work is supported by Chinese National Key Basic Research Program (2007CB411800) and Chinese National Natural Science Foundation Distinguished Young Investigator Project (40788002).

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