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  • View in gallery

    Seasonal variability of the input of wind power Π (W m−2) in the North Pacific for (a) January–March, (b) April–June, (c) July–September, and (d) October–December averaged over 36 years with the climatology MLD (ΠClim explained in section 2a). The color bar indicates the Π scales (W m−2).

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    Horizontal maps of the correlation coefficient r estimated from monthly data at each grid point (the sample number in each grid is 120). (a) The r between wind power inputs Π50m and ΠMOAA and (b) r between the ΠClim and ΠMOAA. The color bars at the right side indicate the r scale. In (a), the blue box is defined as the western area, the red box as the central area, and the green box as the eastern area.

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    Time series of the input of the wind power Π for the (a) western, (b) central, and (c) eastern parts of the North Pacific. Thin and thick black lines are results for Π50m and ΠMOAA, respectively.

  • View in gallery

    Spatial distributions of EOF first and second modes of Π: first mode from (a) the input of wind power Π50m and (b) ΠClim, and second mode from (c) Π50m and (d) ΠClim. The color bars at the top of (a) and (b) indicate the EOF scale (W m−2) for Π50m and ΠClim, respectively. The color boxes are defined in Fig. 2a. The time series of are the principal component of the EOF first mode (thick solid) and second mode (dashed) from (e) Π50m and (f) ΠClim. Year 1980 represents an average over November 1979 to March 1980.

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    Horizontal maps of the regression coefficient of wind power input Π from November to March defined by the Eq. (3) for (left) the first mode and (right) the second mode of the EOF, showing (a),(b) November; (c),(d) December; (e),(f) January; (g),(h) February; and (i),(j) March. The color bar at the right side of (f) indicates the regression coefficient scale.

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    The wavelet power spectrum of (a) the principal component of the EOF first mode and (b) the EOF second mode from the Morlet wavelet. The solid line is the 95% confidence level for a red-noise process (lag-1 autocorrelation, α = 0.72). The period longer than the dashed line indicates the period where edge effects of the time series become important. The color bar indicates the scale of log2(wavelet power spectrum).

  • View in gallery

    Horizontal maps of wind power input Π (color) and sea surface pressure (black lines) averaged over (a) November 2014 to March 2015 and (b) November 2015 to March 2016. The contour interval is 4 hPa, and the thick black line shows 1012 hPa for reference. Here, sea surface pressure from the NCEP–NCAR reanalysis (Kalnay et al. 1996) is used. The color bar at the right side indicates the Π scale (W m−2). The red line in (a) indicates the initial position of the Argo float array.

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    Time series of (a) input of wind power averaged over 5 days and zonally between 165° and 175°W and (b)–(h) vertical diffusivities inferred from the float array. White and red dots and slanted crosses in (a) indicate the meridional position of each float. The squares in (a) indicate positions of the first profile for each float. The letters in (a) indicate the panel where vertical diffusivities inferred by these float data are shown. The inverted triangles at the top of (b)–(h) indicate the profiling dates. The color bars at the right side of (a) and (e) indicate the Π (W m−2) and log10Kρ (m2 s−1) scales, respectively.

  • View in gallery

    Horizontal maps of the inferred diffusivities in the interval 700–1000 dbar for (a) January–March, (b) April–June, (c) July–September, and (d) October–December averaged over 10 years. In (a) the box definitions are as in Fig. 2a. In (b) the thin contour lines indicate the bottom topography with a contour interval of 2000 m. The color bar at the right side of (d) indicates the log10Kρ scale (m2 s−1).

  • View in gallery

    Time series of monthly (a) Π, (b) inferred vertical diffusivities, and (c) numbers of profiles used to obtain the average diffusivities shown in (b). Blue lines indicate the western area, red lines the central area, and green lines the eastern area (Fig. 9a). Asterisks show the temporal average of the monthly values from November to March.

  • View in gallery

    Scatterplots of bootstrap mean of ΠMOAA vs (a) Kρ and (b) ε. Samples were taken from November to March over the western (blue), central (red), and eastern (green) areas. The crosses at each data point indicate the 95% confidence intervals. In each panel, the solid black line is the linear regression line obtained by the Deming method, , where coefficients ( and ) are averages from the bootstrap method. The black dashed lines show the 95% confidence interval of obtained from the bootstrap method.

  • View in gallery

    Time series of the inferred vertical diffusivities from (a) the float deployed at 45°N (Fig. 8b) with a 2-dbar vertical resolution and (c) that with a 20-dbar resolution. (b),(d) Histograms obtained from the time series in (a) and (c), respectively. (e)–(h) As in (a)–(d), but for a different float deployed at 30°N (Fig. 8h). The color bar at the right side of panel (g) indicates the log10Kρ scale (m2 s−1). The arithmetic means are 1.7 × 10−6, 1.2 × 10−6, 1.1 × 10−5, and 8.7 × 10−6 for (b), (d), (f), and (h), respectively. The geometric means are 1.5 × 10−6, 6.6 × 10−7, 6.3 × 10−6, and 3.5 × 10−6 for (b), (d), (f), and (h), respectively. The medians are 1.5 × 10−6, 6.7 × 10−7, 5.7 × 10−6, and 3.6 × 10−6 for (b), (d), (f), and (h), respectively.

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Wind-Induced Mixing in the North Pacific

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  • 1 Research and Development Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan
  • | 2 Project Team for Risk Information on Climate Change, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
  • | 3 Research and Development Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan
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Abstract

Temporal variability of the winter input of wind energy flux (wind power) and its relationship to internal wave fields were examined in the North Pacific. The dominant long-term variability of the wind power input, estimated from a mixed layer slab model, was inferred from an empirical orthogonal function analysis, and it was found that variability partly corresponded to the strength and movement of the Aleutian low. Responses of the internal wave field to the input of wind power were examined for two winters with a meridional float array along 170°W at a sampling interval of 2 dbar. Time series of the vertical diffusivities inferred from density profiles were enhanced during autumn and winter. After comparing diffusivities inferred from densities sampled at 2- and 20-dbar intervals, Argo floats with a vertical resolution of 20 dbar were used to detect spatial and temporal variability of storm-related mixing between 700 and 1000 dbar in the North Pacific over a period of 10 years. Horizontal maps of inferred seasonal diffusivities suggested that the diffusivities were enhanced in autumn and winter. However, it is unlikely that there is a simple linear relationship between the input of wind power and the inferred mixing.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. Inoue, rinoue@jamstec.go.jp

Abstract

Temporal variability of the winter input of wind energy flux (wind power) and its relationship to internal wave fields were examined in the North Pacific. The dominant long-term variability of the wind power input, estimated from a mixed layer slab model, was inferred from an empirical orthogonal function analysis, and it was found that variability partly corresponded to the strength and movement of the Aleutian low. Responses of the internal wave field to the input of wind power were examined for two winters with a meridional float array along 170°W at a sampling interval of 2 dbar. Time series of the vertical diffusivities inferred from density profiles were enhanced during autumn and winter. After comparing diffusivities inferred from densities sampled at 2- and 20-dbar intervals, Argo floats with a vertical resolution of 20 dbar were used to detect spatial and temporal variability of storm-related mixing between 700 and 1000 dbar in the North Pacific over a period of 10 years. Horizontal maps of inferred seasonal diffusivities suggested that the diffusivities were enhanced in autumn and winter. However, it is unlikely that there is a simple linear relationship between the input of wind power and the inferred mixing.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. Inoue, rinoue@jamstec.go.jp

1. Introduction

It is widely recognized that atmospheric storms efficiently generate inertial oscillations in the surface mixed layer (ML) of the ocean. After the oscillations are generated, a part of the energy in the ML radiates to the ocean interior as near-inertial internal waves and eventually dissipates (Gill 1984; D’Asaro et al. 1995; Alford et al. 2016). It has also been hypothesized that this mixing is important in maintaining stratification in the abyssal ocean (Munk 1966; Munk and Wunsch 1998). Estimates of the global inertial energy flux into the surface ML (hereinafter the input of wind power or wind power input) obtained with the slab ML model (Pollard and Millard 1970; D’Asaro 1985) have indicated that there is a seasonal variability of the wind power input in midlatitudes; the input is high in autumn and winter because of storm tracks (Alford 2001; Watanabe and Hibiya 2002; Alford 2003; Watanabe et al. 2005). Analysis of mooring datasets has also revealed a seasonal cycle of the near-inertial, internal-wave kinetic energy within oceans (Alford and Whitmont 2007; Silverthorne and Toole 2009). A recent estimation of vertical diffusivities inferred from a finescale internal-wave strain parameterization by using global Argo floats has indicated that the inferred diffusivities increase in autumn and winter (Whalen et al. 2012).

In the North Pacific, storm tracks develop in autumn and winter, and the positions of the storm tracks and their properties depend on the variability of the Aleutian low. For example, Nakamura (1992) has shown that atmospheric baroclinic wave activity is positively correlated with the maximum jet speed, but it is negatively correlated when the jet speed exceeds a threshold. Chang (2001) has further shown that the intensity of storm tracks in midwinter is negatively correlated with the jet strength in the upper troposphere and has explained the dynamics by using an eddy energy budget. It is also known that the center of the Aleutian low tends to move eastward when the low is strong (Overland et al. 1999; Rodionov et al. 2007). The position and strength of the Aleutian low also show decadal or longer variability as well as interannual variability (Sugimoto and Hanawa 2009; Di Lorenzo et al. 2015). It has been suggested that, on decadal or longer time scales, the strength and zonal shift of the Aleutian low are associated with the Pacific–North American teleconnection pattern and that the meridional shift is associated with the west Pacific teleconnection pattern (Sugimoto and Hanawa 2009). It has also been suggested that the El Niño–Southern Oscillation affects those teleconnection patterns, in which case it may affect the Aleutian low (Zhang et al. 1997; Alexander et al. 2002; Di Lorenzo et al. 2015).

Because the mixed layer depth (MLD) and stratification affect the input of wind power and the propagation of internal waves, it is possible that variability of the Aleutian low can change internal wave fields by altering ocean states as well as by causing differences in wind fields. The variability of the Aleutian low changes sea surface temperatures (SSTs) and affects the ocean through spinup of gyre circulation. When the Aleutian low is strong, the surface ML becomes deep and cold in the central North Pacific because of enhanced surface cooling, entrainment at the ML base, and Ekman transport. This change appears as the first mode of the empirical orthogonal function (EOF) of SST variability in the North Pacific and is called the Pacific decadal oscillation (e.g., Newman et al. 2003). The sea surface height anomaly caused by the Aleutian low propagates via Rossby waves to the west, where it changes the dynamic state of the Kuroshio Extension (Oka and Qiu 2012; Qiu et al. 2014). This change is a prominent decadal oscillation of the western boundary region and changes stratification and MLDs as well as subtropical and central mode water formation through eddy activity (Qiu and Chen 2005; Oka et al. 2012).

Although Alford (2003) found an increase of the wind power input over 50 years that is qualitatively consistent with the increasing trend of the number of extratropical cyclones, further studies are required to understand the spatial and temporal variability of the winter input of wind power and its relation to wind-driven, near-inertial internal wave fields on interannual, decadal, and multidecadal time frames and basinwide spatial scales. To understand the spatial and temporal variability of the input of wind power in the North Pacific, we examined the relationship between the input of wind power estimated from the ML slab model and the variability of the MLD and wind forcing. Application of an EOF analysis to a 36-yr time series of the wind power input allowed us to discern a relationship between the wind power input and the variability of large-scale structures such as the Aleutian low. Finally, to find the relationship between the surface wind forcing and internal wave fields, we then compared the variability of the wind power input with inferred vertical diffusivities and the rate of dissipation of turbulent kinetic energy estimated from the density strain fields observed by Argo floats.

2. Data and methods

a. Input of wind power

To estimate the flux of wind-induced inertial energy into the ocean (input of wind power), we numerically integrated the slab mixed layer model (Pollard and Millard 1970; D’Asaro 1985),
e1
Here, ZI = uI + I is the complex expression of the horizontal current velocity, where the subscript I indicates the inertial frequency. The parameter ω = r + if, where r = 1/(4 days), is a linear damping constant that presumably represents damping processes such as the radiation of near-inertial internal waves from the base of the ML (e.g., D’Asaro 1985; Plueddemann and Farrar 2006). The parameter f is the local Coriolis frequency. We used results obtained from latitudes higher than 20°N because the model assumption that r/f is much less than 1.0 might be violated near the equator (Alford 2003). The parameter X = (τx + y)/ρ is the complex expression of the wind stress for zonal (τx) and meridional (τy) directions, respectively, where ρ is the sea surface density. The parameter H is the MLD. The input of wind power (W m−2, the inertial energy flux per unit area) was obtained from the kinetic energy equation by multiplying the complex conjugate to Eq. (1) (D’Asaro 1985),
e2

We used the ERA-Interim wind dataset at 10 m above the sea surface with spatial and temporal resolutions of 0.75° × 0.75° and 6 h, respectively (Dee et al. 2011) to integrate Eq. (1) for 36 years, beginning in 1979. The surface wind stress was calculated by using the bulk transfer formula of Large and Pond (1981). The fact that the local inertial period at midlatitudes becomes comparable to the temporal resolution of the wind stress causes an underestimation of the wind-induced near-inertial power. We therefore amplified wind speeds with time scales shorter than 8 days following the method of Niwa and Hibiya (1999). We used three different MLDs to elucidate the effects of different MLDs on seasonal and interannual variability. The first was a fixed MLD of 50 m (Π50m). The second was the climatological MLD (ΠClim) derived from monthly composites of the Grid Point Value of the Monthly Objective Analysis using Argo data (MOAA GPV; Hosoda et al. 2008) between 2005 and 2014. The MOAA GPV, which has been available since 2004, gives monthly temperature and salinity data on a 1° × 1° horizontal grid by using a two-dimensional optimal interpolation on constant pressure surfaces. The third is the monthly MLD estimated from the MOAA GPV (ΠMOAA). In the last two cases, the MLD was defined to be the depth at which the density exceeded the value at 10 m by 0.125 kg m−3. The estimated MLD was linearly interpolated onto the wind data points.

The input of wind power integrated over the area shown in Fig. 1 was 25.3 ± 4.8 GW in winter (Fig. 1a), 10.4 ± 2.1 GW in spring (Fig. 1b), 10.6 ± 2.7 GW in summer (Fig. 1c), and 31.5 ± 5.4 GW in autumn (Fig. 1d). We found that the global power input during 1989–95 with an MLD of 50 m was 0.27 TW, less than the 0.6 TW estimated by Watanabe and Hibiya (2002) with a different wind product. Since Jiang et al. (2005) and Rimac et al. (2013) have pointed out the dependence of the estimated wind power input on wind products, the effects of the dependence on spatial and temporal variability, especially by using the high-resolution dataset such as Climate Forecast System Reanalysis (Saha et al. 2010), may deserve future study.

Fig. 1.
Fig. 1.

Seasonal variability of the input of wind power Π (W m−2) in the North Pacific for (a) January–March, (b) April–June, (c) July–September, and (d) October–December averaged over 36 years with the climatology MLD (ΠClim explained in section 2a). The color bar indicates the Π scales (W m−2).

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

b. Japanese Argo floats and meridional float array

To assess the variability of the internal wave fields around the thermocline, we made use of density data from the global Argo floats and followed the method used by Whalen et al. (2012) (appendix A) with the following exceptions. The Japan Agency for Marine-Earth Science and Technology (JAMSTEC) and the Japanese Meteorological Agency have deployed more than 1200 Argo floats over the past 15 years, mainly in the western North Pacific, with a vertical resolution of 20 dbar around the depth of the thermocline (500–1000 dbar). However, the threshold of the vertical resolution used by Whalen et al. (2012) for calculating the density strain was 15 dbar. All of the Japanese float data were therefore discarded by Whalen et al. (2012). To include those float data in the density profiles observed under storm tracks, we set the threshold of the vertical resolution to 20 dbar to allow us to study variability of internal wave fields in the main thermocline around the western North Pacific. We also note that in the western North Pacific, the frontal structure between Oyashio and Kuroshio waters generates numerous intrusions down to the depth of the salinity minimum layer (e.g., Talley et al. 1995; Yasuda et al. 1996). These intrusions can create density strains with vertical scales similar to those of internal waves. By using the deeper layer for estimating the vertical density strain, we could therefore avoid potential contamination from intrusive features associated with frontal structures. Note that those intrusions are generated by either sub- or superinertial motion, which are impossible to separate in the vertical profile of one Argo float.

To understand the effects of the vertical resolution difference and to ensure that the variability of the density strain observed by floats with a resolution of 20 dbar represented that of internal wave fields, we have deployed a meridional float array along 170°W since July 2014. The resolution of this array is 2 dbar, and appendix B provides a comparison between results obtained with 2-dbar and degraded 20-dbar resolutions. In this float array, seven Navis floats [World Meteorological Organization (WMO) numbers 4902137, 4902138, 4902139, 4902140, 4902141, 4902142, and 4902143] have been deployed between 30° and 45°N at 2.5° intervals. They are controlled by a two-way iridium communication system. The floats park at 1000 dbar, simultaneously come to the sea surface every 10 days, and observe the density between 4 and 2000 dbar with a sampling interval of 2 dbar. Some floats have a shorter sampling period (up to 1 day for profiling to 2000 dbar or 30 min for profiling the upper 50 dbar) to capture frontal or mixed layer restratification processes. The buoyancy engine in some Navis floats did not work properly during this experiment, and the floats eventually drifted at the sea surface. At those sites, we added new floats in July 2015 (WMO numbers 4902356 and 4902359). We also made use of one Navis float deployed by the U.S. National Oceanic and Atmospheric Administration (WMO number 4901662; we started using profiles on and after the profiling number 45); for that float, the vertical resolution was 2 dbar, the profiling occurred 4 days ahead of array measurements, and only real-time quality control was applied. For the other JAMSTEC floats in the array, the delayed quality control of the Global Argo network was applied (Wong et al. 2015).

3. Results

a. Variability of the input of wind power

1) Temporal variability of the MLD

First, effects of the seasonal variability of the MLD on the input of wind power (Π) defined in Eq. (2) were examined based on the correlation coefficient between Π50m and ΠMOAA during 2005–14 at each grid point (Fig. 2a). The region of low correlation might reflect the importance of MLD variability. On the basis of the horizontal distribution of the correlation, we divided the North Pacific (30°–45°N) into three areas: a western area bounded by 145°–165°E, a central area bounded by 170°E–170°W, and an eastern area bounded by 160°–140°W. The correlation was lowest in the western North Pacific, where a deep ML forms in late winter (Fig. 3a). The correlation was high in the eastern North Pacific (Fig. 2a), which suggests that the seasonal variability of the MLD was not as important for the input of wind power in the eastern North Pacific (Fig. 3c). This conclusion for the eastern North Pacific is different from that of D’Asaro (1985), who found that in the eastern North Pacific the input of wind power was highest in October, when the MLD was shallow, and lower in late winter, even though winds showed a similar strength in winter. However, the study area of D’Asaro (1985) was mainly northeast of our eastern box, where the correlation was relatively low.

Fig. 2.
Fig. 2.

Horizontal maps of the correlation coefficient r estimated from monthly data at each grid point (the sample number in each grid is 120). (a) The r between wind power inputs Π50m and ΠMOAA and (b) r between the ΠClim and ΠMOAA. The color bars at the right side indicate the r scale. In (a), the blue box is defined as the western area, the red box as the central area, and the green box as the eastern area.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

Fig. 3.
Fig. 3.

Time series of the input of the wind power Π for the (a) western, (b) central, and (c) eastern parts of the North Pacific. Thin and thick black lines are results for Π50m and ΠMOAA, respectively.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

Effects of the interannual variability of the MLD on the input of wind power were also examined based on the correlation between ΠClim and ΠMOAA (Fig. 2b). The correlation coefficient at each grid point was estimated from the monthly average input of wind power between 2005 and 2014. Because the correlation between ΠClim and ΠMOAA was high and time series of ΠMOAA was not long enough to study the time scale longer than long-term variability, we therefore assume that ΠClim can be used to study the temporal variability of the wind power input with time scales longer than the seasonal cycle. Since below 300 dbar the vertical resolution of the MOAA was relatively coarse, ~100 dbar (Hosoda et al. 2008), it is possible that the variability of the deep ML could not be resolved by the MOAA. Effects of interannual variability of the MLD on the wind power input might require further study.

2) Temporal variability of winds

On the basis of the assumption, we used 36 years of wind data to examine the temporal and spatial variability of the inputs of wind power with time scales longer than the seasonal cycle by comparing Π50m with ΠClim. To remove seasonal variability, the input of wind power was averaged from November to March, and then an EOF analysis was applied. Note that we excluded October from the average because occasionally tropical typhoons occur in the western North Pacific in that month. We used a spatial running mean (7 grid points times 0.75° = 5.25°) for zonal and meridional directions on the averaged Π fields before the EOF analysis. We found that the spatial structure was similar in two cases for both modes of the EOF (Fig. 4): there was a monopole structure in the first mode (centered at about 170°W, which corresponds to the longitude of the float array) and a bipole structure in the second mode (northwest–southeast). Differences in contributions from the first mode and second mode were not as distinct in ΠClim (19.1% and 14.1%, respectively) as in Π50m (29.3% and 18.4%, respectively). The center of the monopole structure shifted southeastward in the first mode. Because the MLD is much deeper than 50 m in the western North Pacific, this shift may be associated with the winter ML deepening. As defined earlier, the western area (30°–45°N, 145°–165°E) corresponded to a positive region in the second mode (Figs. 4c,d). The central area (30°–45°N, 170°E–170°W) was near the center of the first mode (Figs. 4a,b) and a mixture of positive and negative values in the second mode (Figs. 4c,d). The eastern area (30°–45°N, 160°–140°W) was a negative region in the second mode (Figs. 4c,d).

Fig. 4.
Fig. 4.

Spatial distributions of EOF first and second modes of Π: first mode from (a) the input of wind power Π50m and (b) ΠClim, and second mode from (c) Π50m and (d) ΠClim. The color bars at the top of (a) and (b) indicate the EOF scale (W m−2) for Π50m and ΠClim, respectively. The color boxes are defined in Fig. 2a. The time series of are the principal component of the EOF first mode (thick solid) and second mode (dashed) from (e) Π50m and (f) ΠClim. Year 1980 represents an average over November 1979 to March 1980.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

Because the EOF analysis was applied to data averaged between November and March, we cannot specify whether the pattern was created by very strong rare events or continuous events over several months. To detect a contribution from monthly variability, we made use of a regression of the principal component of each EOF mode, (Figs. 4e, f), on the monthly wind power input time series between November and March. This regression was defined as follows:
e3
Here, Πmon(t) is the monthly wind power input for November to March during 36 years at each grid point, is the monthly wind power input for November to March averaged over 36 years, and is given for each year, where the EOF is estimated from the input of wind power averaged from November to March. Note that was normalized so that the standard deviation became 1. The same spatial running mean used in the EOF analysis was applied to Π. The spatial distribution of the regressions (Fig. 5) suggests that variability of the Aleutian low in December is important for the first mode in the central and eastern North Pacific, and a similar structure appeared in February. The variability in February was also important for the second mode in the central North Pacific. We also note that the reduction of the importance of January for the first mode might be related to the midwinter reduction of storm activity as explained by Chang (2001).
Fig. 5.
Fig. 5.

Horizontal maps of the regression coefficient of wind power input Π from November to March defined by the Eq. (3) for (left) the first mode and (right) the second mode of the EOF, showing (a),(b) November; (c),(d) December; (e),(f) January; (g),(h) February; and (i),(j) March. The color bar at the right side of (f) indicates the regression coefficient scale.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

3) Relation to long-term variability

Although our dataset was too short to resolve time scales longer than a decade, a wavelet analysis (Torrence and Compo 1998) that we applied to the indicated that the first mode and second mode were possibly dominated by bidecadal and decadal (or less than decadal) scales, respectively (Figs. 4e,f and 6). Note that, according to Sugimoto and Hanawa (2009), with the exception of interannual variability, the intensity and zonal position of the Aleutian low change on a bidecadal scale, and the meridional position changes on a decadal scale. Because the regression analysis suggested that the spatial pattern was created by an accumulation of events for several months, the wavelet analysis suggested that the time scales might be longer than or equal to a decade, and the represents a large-scale feature, so we expect that the might be comparable to a climate index. Correlation coefficients between the North Pacific Index (NPI) averaged from November to March (Trenberth and Hurrell 1994) and the first mode and second mode of the from ΠClim were estimated to be −0.71 (p < 0.05) and 0.30 (p = 0.07), respectively. Therefore, the first mode might be associated with the NPI, which characterizes long-term variability of the Aleutian low.

Fig. 6.
Fig. 6.

The wavelet power spectrum of (a) the principal component of the EOF first mode and (b) the EOF second mode from the Morlet wavelet. The solid line is the 95% confidence level for a red-noise process (lag-1 autocorrelation, α = 0.72). The period longer than the dashed line indicates the period where edge effects of the time series become important. The color bar indicates the scale of log2(wavelet power spectrum).

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

b. Internal wave variability

1) Argo float array along 170°W

Horizontal maps of the average sea level pressure and wind power input between November 2014 and March 2015 and those between November 2015 and March 2016, which corresponded to the float array observation period, showed that there was an interannual zonal shift of the maximum input of wind power (Fig. 7). This shift may have been partly associated with changes in the center position and intensity of the Aleutian low caused by variability on some time scale, including the variability that appeared in the EOF first and second modes (Figs. 4, 6). For example, both the first and second modes were negative in 2015 (Fig. 4f). Combined with the spatial structure of ΠClim (Figs. 4b,d), those modes could create a weakened pattern of the wind power input in the central Pacific (Fig. 7a). It is also possible that the interannual variability of the input of wind power can change the spatial pattern of internal wave fields in the main thermocline because the inertial oscillation of the ML propagates into the ocean interior as near-inertial internal waves (e.g., Fig. 3 in Simmons and Alford 2012).

Fig. 7.
Fig. 7.

Horizontal maps of wind power input Π (color) and sea surface pressure (black lines) averaged over (a) November 2014 to March 2015 and (b) November 2015 to March 2016. The contour interval is 4 hPa, and the thick black line shows 1012 hPa for reference. Here, sea surface pressure from the NCEP–NCAR reanalysis (Kalnay et al. 1996) is used. The color bar at the right side indicates the Π scale (W m−2). The red line in (a) indicates the initial position of the Argo float array.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

A time series of the inferred vertical diffusivities estimated from Navis floats deployed along 170°W between 30° and 45°N showed that the vertical diffusivities inferred from the density strain were enhanced during autumn and winter, and this timing also corresponds to the interannual variability of the input of wind power (Fig. 8). There were periods when the local input of wind power could not explain the larger inferred diffusivities (e.g., February 2015 at latitudes of 40°–45°N; Fig. 8c). The inferred diffusivities in the main thermocline also showed meridional structures that were smaller in the north but higher in the south. The float array also suggests that the internal wave breaking near 30°N (Figs. 8f,h) may be enhanced by storm events during autumn and winter because the inferred diffusivities were larger in the winter of 2015/16, when the input of wind power was stronger (e.g., October 2015 at 34°N), and we suspect that near-inertial waves were generated and propagated toward the equator.

Fig. 8.
Fig. 8.

Time series of (a) input of wind power averaged over 5 days and zonally between 165° and 175°W and (b)–(h) vertical diffusivities inferred from the float array. White and red dots and slanted crosses in (a) indicate the meridional position of each float. The squares in (a) indicate positions of the first profile for each float. The letters in (a) indicate the panel where vertical diffusivities inferred by these float data are shown. The inverted triangles at the top of (b)–(h) indicate the profiling dates. The color bars at the right side of (a) and (e) indicate the Π (W m−2) and log10Kρ (m2 s−1) scales, respectively.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

2) Spatial and seasonal variability in the North Pacific

On the basis of the variability in the time series of the inferred vertical diffusivities, we suggested that the Argo float array observed seasonal and interannual variability of internal wave fields caused by variability of the wind power input on a similar time scale. To confirm the seasonal variability and to investigate the spatial variability, we inferred the horizontal distributions of the vertical diffusivities for each season from all Argo floats sampled between 2005 January and 2015 September with vertical resolutions finer than 20 dbar in the depth range of 700–1000 dbar. We plotted average values when there were more than 10 samples within each 5° × 5° grid (Fig. 9). This approach was also used by Whalen et al. (2015), who averaged values within 1.5° square bins at depths of 500–1000 m. Even if our average bin size was coarser than that of Whalen et al. (2015), our horizontal map also indicated that mixing was enhanced around bottom topographies. Because of the coarse resolution and greater numbers of float data, our horizontal map had more spatial coverage and showed seasonal variability. In all seasons, the inferred diffusivities were enhanced around the Izu–Ogasawara ridge, the Hawaiian Islands, the Emperor Seamounts, and the Aleutian Islands. Larger inferred diffusivities were observed in the averaged area at latitudes of 25°–30°N near the Hawaiian Islands and the Izu–Ogasawara ridge, and the inferred diffusivities were slightly increased around the Murray Fracture zone, the Moonless Seamounts, and the Molokai Fracture zone around 140°W of those latitudes. These larger inferred diffusivities might correspond to the southward enhancement of the inferred diffusivities apparent in the Argo float array data (Fig. 8). The inferred diffusivities were also enhanced in autumn and winter, especially in the western North Pacific, an enhancement that might correspond to the seasonal variability of the input of wind power (Fig. 1). Perhaps in part because of those spatial patterns, the inferred vertical diffusivities were dominated by a spatial pattern characterized by larger values in the western North Pacific and smaller values to the east. The float distributions were sparse in the eastern area and south of the Okhotsk Sea.

Fig. 9.
Fig. 9.

Horizontal maps of the inferred diffusivities in the interval 700–1000 dbar for (a) January–March, (b) April–June, (c) July–September, and (d) October–December averaged over 10 years. In (a) the box definitions are as in Fig. 2a. In (b) the thin contour lines indicate the bottom topography with a contour interval of 2000 m. The color bar at the right side of (d) indicates the log10Kρ scale (m2 s−1).

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

3) Interannual variability in the North Pacific

Time series of inputs of wind power and inferred diffusivities in each region (Fig. 10) suggested that the values averaged from November to March in the central and western areas were slightly smaller during 2009–11 than during other years. Profile numbers in the eastern area were close to zero when inputs of wind power were similar to those in the central and western areas (e.g., 2005–08 and 2010), but the profile numbers increased after 2013, when the wind power inputs were weaker. Therefore, the weaker inferred mixing in the eastern area in Fig. 9 might have been caused by biased sampling during the weaker wind forcing. To assess the dependence of mixing on wind forcing, we compared inferred mixing parameters with the wind power input and used a bootstrap method to find a statistically significant relationship between them. The regression slope between the wind power input (independent variable) and either the inferred diffusivities or dissipation rates (dependent variables) was calculated from the averaged values of the input of wind power and the dependent variable by using the Deming method (Deming 1943), wherein the slope was weighted based on the standard deviation of the averaged values. Averages between November and March were calculated from samples that were randomly taken from a population with the same size as the actual population. This procedure was repeated 10 000 times (Fig. 11), and an average slope was obtained from the 10 000 slopes. After combining all data from the North Pacific, we found that almost all the slopes were positive and significant (p < 0.05) for inferred diffusivities and inferred dissipation rates, based on a t test. However, because this pattern was also associated with the spatial pattern of weak mixing in the eastern North Pacific during the period of weak wind forcing, it was difficult to conclude that the level of inferred mixing would increase when the input of wind power increased.

Fig. 10.
Fig. 10.

Time series of monthly (a) Π, (b) inferred vertical diffusivities, and (c) numbers of profiles used to obtain the average diffusivities shown in (b). Blue lines indicate the western area, red lines the central area, and green lines the eastern area (Fig. 9a). Asterisks show the temporal average of the monthly values from November to March.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

Fig. 11.
Fig. 11.

Scatterplots of bootstrap mean of ΠMOAA vs (a) Kρ and (b) ε. Samples were taken from November to March over the western (blue), central (red), and eastern (green) areas. The crosses at each data point indicate the 95% confidence intervals. In each panel, the solid black line is the linear regression line obtained by the Deming method, , where coefficients ( and ) are averages from the bootstrap method. The black dashed lines show the 95% confidence interval of obtained from the bootstrap method.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

4. Discussion

In the previous section, we could not detect a linear relationship between the wind power input and the level of inferred mixing. To seek possible reasons, we examined the assumptions that underlie the analysis of the statistical relationship between the input of wind power and inferred mixing. Under the Boussinesq and hydrostatic approximations, the near-inertial energy budget for the upper ocean can be written as (Zhai et al. 2009)
e4
Here, the subscript i represents a near-inertial component and is the horizontal kinetic energy of a near-inertial motion. The variables pi, ui, ρi, and wi are the pressure perturbation, three-dimensional velocity, density perturbation, and vertical velocity of near-inertial motions, respectively. The parameters g, τ, ρ0, and Kυ are the acceleration of gravity, horizontal surface wind stress, reference density, and vertical viscosity, respectively. The integral is a volume integration for the upper ocean, is the energy flux of near-inertial motion through the side and bottom boundaries for a given area, is the areal integration of the input of wind power at the sea surface for a given area, and is the conversion from kinetic to potential energy. The integral is the viscous dissipation of near-inertial motion and can be written via the turbulent kinetic energy balance as follows:
e5
Here, is the buoyancy flux due to diapycnal mixing and γ is the mixing efficiency (Osborn 1980). The integral includes any other process such as the removal of energy due to nonlinear energy transfers to other frequencies. If we assume that the input of wind power can be compared with ε (dissipation rate of turbulent kinetic energy) as well as Kρ (vertical diffusivity), there needs to be a close balance between the second and fourth terms on the right-hand side of Eq. (4). However, it is possible that the spatial (western, central, and eastern areas) and temporal (November–March) averaging schemes did not reduce the contributions of other factors (e.g., horizontal propagation) and therefore failed to highlight this balance. The analysis also presumed that mixing between 700 and 1000 dbar was representative of mixing throughout the water column. However, it has been suggested that only a part (10%–30%) of near-inertial energy in the ML is transferred into the main thermocline (Furuichi et al. 2008; Zhai et al. 2009; Alford et al. 2012). We could not estimate ε in the mixed and subsurface layers for the volume integration in Eq. (4), where most of the energy dissipates, and the balance in Eq. (5) may not hold in the ML.

For spatial distributions, Jing and Wu (2014) have reported that inferred diffusivities could be enhanced in the western North Pacific because of the relatively strong eddy activity there; such enhancement could partly explain the westward intensification of the inferred diffusivities. Therefore, it is possible that the Aleutian low may modify internal wave fields by changing the dynamic state of the Kuroshio Extension (Oka and Qiu 2012; Qiu et al. 2014). This possibility deserves further study. In the eastern North Pacific, although interannual zonal variability of the large wind power input was apparent (Fig. 7), inferred mixing was weak. This might stem from insufficient sampling, because the input of wind energy was high before 2008, but the number of float profiles increased during and after 2008 (Fig. 10c). The low inferred mixing level might have been caused by the tendency for the density strain estimated from 20 dbar to underestimate Kρ and ε in low-mixing patches (appendix B). However, the first mode of the EOF of the wind power input (Fig. 4) indicated that the dominant variability could be associated with the Aleutian low at a time scale longer than a decade, and with this time scale, the Aleutian low moves eastward when the central pressure of the Aleutian low is low (Sugimoto and Hanawa 2009). The input of wind power as well as the inferred mixing in the interior ocean of the eastern North Pacific might be large when the central pressure of the Aleutian low is low. Therefore, even if the inferred mixing was weak in the eastern North Pacific in this study, it may be important to monitor this region.

Finally, it has been hypothesized that low-mode internal waves generated below the storm tracks propagate to low latitudes and, once the frequency of those waves becomes twice the local Coriolis frequency, the low-mode waves transmit their energy into near-inertial waves with a smaller vertical scale as a result of parametric subharmonic instability (PSI; e.g., Nagasawa et al. 2000), which was not considered in the comparison because of the limited averaged area. However, the enhanced Kρ around 30°N cannot be explained by the wind forcing between 30° and 45°N (Figs. 8a,h) through this mechanism because the Coriolis frequency at 45°N is not twice the Coriolis frequency at 30°N. Note that 28.8°N is the critical latitude of the M2 tide, where the frequency of the M2 tide is twice the local Coriolis frequency and it is also possible that mixing is enhanced by PSI (e.g., MacKinnon et al. 2013). Therefore, the implication may be that the wind-induced, near-inertial waves interacted with low-mode M2 internal tides, and mixing was enhanced. A comparison of wind forcing and mixing in the thermocline based on consideration of internal wave dynamics as well as validation of the strain parameterization is deserving of further study.

5. Summary

In this analysis, spatial and temporal variability of the near-inertial input of wind power and its relationship to internal wave strain fields in the North Pacific were examined.

An EOF analysis was applied to 36 years of the wind power input averaged from November to March. The first mode of the EOF had a monopole structure (centered at around 170°W), and the second mode had a bipole structure (northwest–southeast). A wavelet analysis suggested that the dominant time scale could be bidecadal for the first mode and decadal or interdecadal for the second mode. That there was a correlation between the first mode and the NPI also suggests that there was a relation between the input of wind power and variability of the Aleutian low.

Horizontal maps of the annual input of wind power showed that there was an interannual zonal shift of the maximum input of wind power. This shift might change the spatial pattern of internal wave fields in the main thermocline and, therefore, mixing. To examine this possibility, a meridional float array along 170°W with a sampling interval of 2 dbar was deployed. We found that time series of the vertical diffusivities inferred from a density strain parameterization (Gregg and Kunze 1991; Wijesekera et al. 1993) were enhanced during autumn and winter, as previously shown by Whalen et al. (2012). The inferred diffusivities were higher in the southern part of the meridional array around 30°N, and they were enhanced in 2016, when the wind power input was relatively large.

From the results of the float array, we surmised that Argo floats with vertical resolutions of 20 dbar can detect spatial and temporal variability of the relatively stronger storm-related mixing in the North Pacific (appendix B). We used a vertical resolution of 20 dbar as the threshold for calculating vertical diffusivities from density strains so that we could use results from Japanese Argo floats, which were discarded in a previous study owing to the vertical resolution around the depth of the main thermocline (700–1000 dbar in this study). Horizontal maps of inferred diffusivities for each season suggested that the inferred diffusivities were enhanced around bottom topographies (Whalen et al. 2015). This enhancement might correspond to the southward enhancement seen in the Argo floats array. The inferred diffusivities were also enhanced in autumn and winter. We compared the input of wind power with the inferred diffusivities and dissipation rates of turbulent kinetic energy in the western, central, and eastern North Pacific at latitudes of 30°–45°N. It is unlikely that there was a simple linear relationship between the input of wind power and the inferred mixing. Therefore, the implication is that the inferred mixing may be related to the input of wind power, but the relationship may be complex.

Acknowledgments

We are indebted to the captain, crew, chief scientist, and other scientists on R/V Hakuho-Maru (chief scientist H. Ogawa, University of Tokyo) and R/V Hokuho-Maru (chief scientist H. Kidokoro, Tohoku National Fisheries Research Institute) for their successful deployments of the profiling float array. We thank K. Sato, M. Hirano, and H. Hosoda at JAMSTEC and H. Nakajima, K. Kato, T. Iino, and I. Takahashi at Marine Works Japan, Ltd. for support during the float observations. R. Inoue was partly supported by a Grant-in-Aid for Scientific Research on Innovative Areas (MEXT KAKENHI-JP15H05818). S. Osafune was partly supported by a Grant-in-Aid for Scientific Research on Innovative Areas (MEXT KAKENHI-JP15H05819). We thank S. Kouketsu at JAMSTEC for fruitful discussions and two anonymous reviewers and E. Kunze at North West Research Associates for insightful suggestions. All Argo float data are publically available through the websites http://www.usgodae.org/argo/argo.html and http://www.coriolis.eu.org/. Wavelet software was provided by C. Torrence and G. Compo; it is available at http://paos.colorado.edu/research/wavelets/. The North Pacific Index averaged over November to March is distributed by Trenberth and Hurrell at https://climatedataguide.ucar.edu/climate-data/north-pacific-np-index-trenberth-and-hurrell-monthly-and-winter.

APPENDIX A

Internal Wave Activity

The density data from floats were linearly interpolated to every 2 or 20 dbar. We then calculated the density strain (Kunze et al. 2006; Whalen et al. 2012),
ea1
Here, N2 is the square of the buoyancy frequency (s−2) estimated from the float conductivity–temperature–depth data. The parameter is a fitted N2 estimated from temperature and salinity profiles smoothed with a second-order polynomial fit in the data window. The data window had a length of 200 dbar between 700 and 1000 dbar and was specified at 100-dbar intervals, with a 100-dbar overlap (i.e., 700–900 dbar and 800–1000 dbar). This depth range was chosen to avoid artifacts in the calculation of density strain possibly caused by mode waters and intrusions often observed in the western North Pacific. The parameter is the average of over the data window. The vertical wavenumber spectrum of the density strain Sstr(kz) was then calculated and vertically integrated over the wavenumbers that could be associated with the internal wave band:
ea2
where min(kz) is the minimum wavenumber (cpm) of integration determined from the data window and max(kz) is the cutoff wavenumber, which satisfies the equation
ea3
If max(kz) could not be obtained from the float density observations because of inadequate vertical resolution (e.g., 0.25 cpm for the iridium floats and 0.025 cpm for the Argos floats), those wavenumbers were substituted for max(kz).
Finally, an internal-wave strain parameterization (Gregg and Kunze 1991; Wijesekera et al. 1993) with a latitudinal dependence (Polzin et al. 1995; Gregg et al. 2003) was used to convert Eq. (A2) into expressions for the turbulent kinetic energy dissipation rate ε (W kg−1) and vertical diffusivity Kρ (m2 s−1) (Whalen et al. 2012) as follows:
ea4
ea5
Here ε0 = 6.73 × 10−10 (W kg−1) and N0 = 5.24 × 10−3 (s−1) are reference turbulent kinetic energy dissipation rate and buoyancy frequency, respectively. The parameter ξzGM is the strain of the Garrett–Munk internal wave field (Garrett and Munk 1975) integrated over the same wave band as Eq. (A2). The parameter h(Rω) characterizes the dependence of the internal waves Rω on the ratio of available potential energy and horizontal kinetic energy. In this study, we assumed Rω = 3 (e.g., Kunze et al. 2006), and hence we used h(Rω = 3) = 1. The parameter represents the dependence of ε on latitude (e.g., Gregg et al. 2003). The parameter γ is the mixing efficiency and was assumed to be 0.2 (Osborn 1980). Note that recent studies (Chinn et al. 2016; Ijichi and Hibiya 2017) discuss the limitations of the strain parameterization for low-frequency internal waves.

APPENDIX B

Vertical Resolution of Argo Floats

We examined the effects of the vertical resolution of density sampling on the estimation of diffusivity. We estimated inferred diffusivities from densities with resolutions of 2 dbar and sparsely resampled with resolutions of 20 dbar in weak (~45°N between July 2014 and March 2015) and strong inferred mixing regions (~30°N between July 2014 and October 2015) and compared the time series (Fig. B1). A visual inspection of the time series indicated that the spatial and temporal distributions of patches of high inferred mixing were similar. However, the blue-colored areas (approximately corresponding to Kρ < 10−5 m2 s−1 in Fig. B1) were darker in the low-resolution estimation, the implication being that the inferred diffusivities in the patches of weak inferred mixing tended to be underestimated if the vertical resolution was coarse. The histograms from the two estimates confirmed that the 20-dbar resolution tended to underestimate diffusivity when the strain was small (the float that drifted around 45°N; Figs. B1a–d). In contrast, differences between the two resolutions became small when the inferred mixing was strong (the float that drifted around 30°N; Figs. B1e–h), possibly because the highest wavenumber for integration of the power spectrum was almost resolved by the 20-dbar resolution when the power spectrum density of strain was high. Because our interest was not in the absolute magnitude but rather in the spatiotemporal patterns of the relatively strong, storm-related mixing in the North Pacific, we assumed that we could use Argo floats with a vertical resolution of 20 dbar to discern spatiotemporal patterns.

Fig. B1.
Fig. B1.

Time series of the inferred vertical diffusivities from (a) the float deployed at 45°N (Fig. 8b) with a 2-dbar vertical resolution and (c) that with a 20-dbar resolution. (b),(d) Histograms obtained from the time series in (a) and (c), respectively. (e)–(h) As in (a)–(d), but for a different float deployed at 30°N (Fig. 8h). The color bar at the right side of panel (g) indicates the log10Kρ scale (m2 s−1). The arithmetic means are 1.7 × 10−6, 1.2 × 10−6, 1.1 × 10−5, and 8.7 × 10−6 for (b), (d), (f), and (h), respectively. The geometric means are 1.5 × 10−6, 6.6 × 10−7, 6.3 × 10−6, and 3.5 × 10−6 for (b), (d), (f), and (h), respectively. The medians are 1.5 × 10−6, 6.7 × 10−7, 5.7 × 10−6, and 3.6 × 10−6 for (b), (d), (f), and (h), respectively.

Citation: Journal of Physical Oceanography 47, 7; 10.1175/JPO-D-16-0218.1

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