T. M. Shaun Johnston and Daniel L. Rudnick

Transcription

1 Trapped diurnal internal tides, propagating semidiurnal internal tides, and mixing estimates in the California Current System from sustained glider observations, T. M. Shaun Johnston and Daniel L. Rudnick Scripps Institution of Oceanography, University of California, San Diego, 95 Gilman Dr # 213, La Jolla, CA, , USA shaunj@ucsd.edu, (858) Abstract From , along 3 repeated cross-shore transects (California Cooperative Oceanic Fisheries Investigations lines 66.7, 8, and 9) in the California Current System, shear and strain profiles from 66 glider missions are used to estimate mixing via finescale parameterizations from a dataset containing over 52 profiles. Elevated diffusivity estimates and energetic diurnal (D 1 ) and semidiurnal (D 2 ) internal tides are found: (a) within 1 km of the coast on lines 66.7 and 8 and (b) over the Santa Rosa- Cortes Ridge (SRCR) in the Southern California Bight (SCB) on line 9. While finding elevated mixing near topography and associated with internal tides is not novel, the combination of resolution and extent in this ongoing data collection is unmatched in the coastal ocean to our knowledge. Both D 1 and D 2 internal tides are energy sources for mixing. At these latitudes, the D 1 internal tide is subinertial. On line 9, D 1 and D 2 tides are equally energetic over the SRCR, the main site of elevated mixing within the Preprint submitted to Deep-Sea Res. II January 3, 214

2 SCB. Numerous sources of internal tides at the rough topography in the SCB produce standing and/or partially-standing waves. On lines 66.7 and 8, the dominant energy source below about 1 m for mixing is the D 1 internal tide, which has an energy density 2 the D 2 internal tide. On line 8, estimated diffusivity, estimated dissipation, and D 1 energy density peak in summer. The D 1 energy density shows an increasing trend from Its amplitude and phase are mostly consistent with topographically-trapped D 1 internal tides travelling with the topography on their right. The observed offshore decay of the diffusivity estimates is consistent with the exponential decay of a trapped wave with a mode-1 Rossby radius of 2 3 km. Despite the variable mesoscale, it is remarkable that coherent internal tidal phase is found. Keywords: mixing parameterizations, internal tides, seasonal cycle, cross-shore decay Introduction Mixing in the thermocline is produced mainly by breaking internal waves [Gregg, 1989; MacKinnon et al., 213], which are forced predominantly by tides and winds [Alford, 23; Ferrari and Wunsch, 29; Garrett and Kunze, 27]. Much of the internal wave energy is in low vertical modes (i.e., in waves with horizontal wavelengths of 1 km or more) and propagates away from generation sites [Alford, 23; Zhao and Alford, 29]. Smaller-scale internal waves may break near their generation site and contribute to mixing [Alford and Gregg, 21; Gregg et al., 1986; Klymak et al., 26; Nakamura et al., 21]. Here, we consider the contribution of not only the freely-propagating 2

3 semidiurnal (D 2 ) internal tide [Garrett and Kunze, 27], but also the subinertial diurnal (D 1 ) internal tide, which is topographically-trapped near its generation site. The latter topic has received much less attention in the literature. In our study area in the coastal ocean off of California, D 1 internal tides are often more energetic than D 2 in our observations and previous work around the Southern California Bight (SCB) [Beckenbach and Terrill, 28; Kim et al., 211; Nam and Send, 211]. Poleward of 3, D 1 internal waves are subinertial and evanescent, since the Coriolis frequency (f) is >1 cycle day 1. Considerable mixing may arise due to topographically-trapped internal tides because they likely dissipate in the same area where they are forced [Nakamura et al., 21; Padman and Dillon, 1991], although alongshore propagation is possible with dissipation elsewhere at the topography. Such mixing may contibute to water mass formation [Tanaka et al., 21] and higher primary productivity [Tanaka et al., 213]. Energy loss from the D 1 barotropic tide is a maximum around the Pacific rim [Egbert and Ray, 23]. A local maximum in this dissipation is found along the west coast of North America beyond 3 N. The sink for this energy is likely the topographically-trapped D 1 internal tide, which in turn dissipates turbulently. To assess the contributions of topographically-trapped D 1 and freelypropagating D 2 internal tides to mixing in the coastal ocean, we use an extensive dataset to estimate diffusivity using parameterizations based on observed current shear and/or isopycnal strain [Gregg, 1989; Gregg et al., 23; Polzin et al., 1995]. Six years of sustained glider observations in the California Current System (CCS) along three repeated California Coopera- 3

4 tive Oceanic Fisheries Investigations (CalCOFI) cross-shore transects (lines 66.7, 8, and 9 in Figure 1) provide over 52 profiles, at O(1 m) vertical and 3-km horizontal resolution from the continental slope to 3 5 km offshore [Davis et al., 28; Todd et al., 211a, 212]. With this unique combination of spatial and temporal coverage, we can examine the seasonal and cross-shore structure of mixing estimates and internal tides. For example, D 1 internal tides may control the cross-shore decay scale at the continental slope and the seasonal cycle of mixing at the northern end of the SCB. At the Santa Rosa-Cortes Ridge (SRCR), a prominent feature of the SCB, D 1 and D 2 internal tides have similar energies and may contribute equally to mixing. Next, we provide some background on mixing parameterizations (Section 2.1), previous observations of mixing in the SCB and other coastal locations (Section 2.2), and possible energy sources for mixing (internal waves and frontogenesis in Sections 2.3 and 2.4). In Section 3, our methods are described including a basic outline of the mixing parameterizations with further details in Appendix A. Section 4 shows an example transect from line 9 and time-mean transects (i.e., binned in depth and cross-shore distance) of the data and harmonic fits from lines 8 and 9 (line 66.7 is similar to line 8). In Section 5, depth-mean diffusivity estimates are binned in time or crossshore distance and then are related to similarly averaged internal tides and mesoscale flows. A seasonal cycle is composited for line 8 (Section 5.4). A discussion and summary of our findings follow in Sections 6 and 7. 4

5 Background 2.1. Finescale mixing parameterizations Direct measurements of either mixing via tracer release or turbulent fluctuations via specialized microstructure instruments occur of necessity during infrequent research cruises of usually several weeks duration. Only recently have moored microstructure measurements become possible [Moum et al., 213]. However, finescale or O(1-m) scale profiles of shear and strain are readily available from many platforms including the gliders described in this paper. Turbulent dissipation (ɛ) and diapycnal diffusivity (K ρ ) can be estimated from these finescale measurements using parameterizations based on the idea of a downscale energy transfer via weakly interacting internal waves [Gregg, 1989; Gregg et al., 23; Kunze et al., 26; MacKinnon et al., 213; Polzin et al., 1995]. Assuming there is a steady state transfer, by measuring the finescale variance in shear and strain, we estimate the downscale energy transfer or dissipation at a scale much larger than the actual turbulence. The parameterizations relate ɛ to the ratio of the observed finescale variance to the variance in the the empirical Garrett-Munk (GM) spectra of the internal wave field. The GM spectrum is used to compare internal wave energy levels in locations with different stratification and latitude. For example, over the SRCR, a site of internal tidal generation, some example shear and strain spectra are within a factor of three of GM (Appendix A). For further comparison, the mission-mean spectrum from glider measurements east of Luzon Strait, which averages over regions of both weak and strong internal wave activity, is consistent with a level of 4 times GM [Rudnick et al., 213]. These values 5

6 appear reasonable and reinforce the well-known utility of the GM spectrum in a wide variety of conditions. Finescale parameterizations have been applied to diverse data sets over large areas with appreciable tidal and inertial signals [Kunze et al., 26; MacKinnon et al., 213; Waterhouse et al., 213; Whalen et al., 212]. These methods under a variety of conditions are considered accurate to a factor of 2 4 at best [MacKinnon et al., 213, and references therein] compared to specialized microstructure instruments, which measure the actual turbulent fluctuations [Klymak and Nash, 29; Thorpe, 25]. In this paper, we estimate mixing in the coastal ocean using such parameterizations (Section 3.3 and Appendix A) Previous observations of mixing in coastal waters With rough topography, varying stratification, and numerous local and remote sources of internal waves in our study region, considerable spatial and temporal variability of mixing is expected. Using our methods, we can examine variability in the cross-shore direction along with tidal and seasonal variability, which complements previous moored or ship-based process studies, which have greater temporal resolution, but are limited in temporal or spatial extent. Such variability in mixing over a semidiurnal tidal period, over a springneap cycle, and over variable topography is found in a bay situated between two distinct sources of internal tides near Oahu, Hawaii [Alford et al., 26; Martini et al., 27]. Also the two sources of internal tides are of unequal strength and produce partially-standing internal waves. This interference pattern varies over the spring-neap cycle and with varying stratification at 6

7 or between the sources. Models generally have greater turbulence at boundaries, but do not reproduce observed midwater column mixing with a variety of turbulence parameterizations [Wijesekera et al., 23]. In the coastal waters off Oregon, the superposition of shear from inertial and semidiurnal internal waves with shear from a coastal current in thermal wind balance leads to midwater column mixing, when none of the individual components would trigger a shear instability [Avicola et al., 27]. It is now more common for regional models to include both mesoscale and tidal phenomena, but assessment of their mixing parameterizations is lacking perhaps due to a lack of sufficient temporal and spatial extent of observations for comparison. The depth-mean mixing estimates (excluding the mixed layer but including the thermocline to a depth of 362 m) in this paper may prove useful in this respect. Previous tracer release experiments and microstructure measurements in the SCB show elevated K ρ at the steep topography, which can be as high as O(1 4 m 2 s 1 ) [Gregg and Kunze, 1991; Ledwell and Bratkovich, 1995; Ledwell and Hickey, 1995; Ledwell and Watson, 1991]. This value is much larger than away from the topography, where the mean thermocline values is: K ρ 1 5 m 2 s 1 [Gregg, 1987]. Limited velocity measurements do not identify the processes leading to this mixing near topography, but either trapped D 1 or freely-propagating D 2 internal tides are likely candidates Internal waves Shear and strain from internal waves produce instabilities and mixing [Alford and Pinkel, 2]. Below we briefly cover some features of nearinertial, D 1, and D 2 internal waves relevant to the SCB and mixing. In 7

8 general, shear in the internal wave band is dominated by NIW [Alford and Gregg, 21; Pinkel, 1985]. In the SCB, wind stress variance is greatest from March June [Table 1 in Hickey, 1979]. The region near Point Conception at the northern edge of the SCB displays a local maximum in a model of wind work to inertial motions in the mixed layer, i.e. a precursor to NIW generation in the thermocline [Figure 2 in Simmons and Alford, 212]. The magnitude of this input is similar to stormier climates near 45 N on the west coast of North America. Trapped D 1 internal tides are often more energetic than D 2 internal tides in the SCB. These waves may have considerable impact on mixing as noted earlier (Section 1) because there are likely numerous sites of generation and dissipation in close proximity at rough topography [Tanaka et al., 213]. Elsewhere, at a seamount in the North Pacific near 32 N, dissipation is strong enough to dissipate the trapped D 1 motions within 3 days, which makes for a strongly forced and damped system [Kunze and Toole, 1997]. In the SCB, surface drifters in this area show diurnal/inertial oscillations with decay scales of 1 days [Poulain, 199]. There are numerous sources of D 2 internal tides along the continental slope and over the rough topography of the SCB [Beckenbach and Terrill, 28; Buijsman et al., 212]. Internal tidal generation may produce local mixing [Johnston et al., 211a; Klymak et al., 26]. Propagating internal tides may encounter topography, scatter to smaller scales, and break [Johnston and Merrifield, 23; Johnston et al., 23; Kelly et al., 212; Martini et al., 211; Nash et al., 24]. 8

9 Fronts Other relevant sites of elevated mixing includes fronts [Hoskins and Bretherton, 1972; Johnston et al., 211b], which are ubiquitous in the SCB [e.g., Davis et al., 28; Powell, 213]. Frontogenesis can lead to mixing at depth on the dense, cyclonic side of fronts where the gradients (i.e., shear and strain) are largest [Hoskins and Bretherton, 1972]. It is unclear what are the relative contributions to mixing from frontogenesis or internal waves which are trapped, reflected, or refracted at the front [Johnston et al., 211b]. Elevated mixing at fronts can lead to enhanced primary productivity [Hales et al., 29; Li et al., 212] Three possible issues are noted with respect to estimating mixing at fronts. First, if mixing at fronts is not due to internal waves, then the mixing parameterizations used here do not apply. Second, there is some question of how much the internal wave field is modified in the vicinity of background shear and whether the empirical GM spectrum (Section 3.3) is applicable [Munk, 1981]. Third, we note persistent fronts at locations where internal tides are strong on both lines 8 and 9, which unfortunately hampers discrimination of their effects. For the first two issues, we note our spectra resemble GM (Appendix A), which provides reasonable confidence in our approach. These parameterizations essentially use a Richardson number criterion as an indicator of mixing and have proven useful across a wide range of conditions (Section 2.1). 9

10 Methods 3.1. Data Since 26/27, three cross-shore transects have been almost continuously covered by underwater gliders to 5-m depth [Davis et al., 28; Todd et al., 211b]. These transects follow CalCOFI lines 66.7, 8, and 9 which begin near Monterey Bay, Point Conception, and Dana Point and extend 3 55 km offshore (Figure 1). One glider mission lasts about 1 days, with each cross-shore transect taking about 3 weeks (Figure 2). In this analysis, over 19 density and velocity profiles from October 26 to December 212 are used on each of line 8 and 9. This dataset comprises 27 glider missions on line 9 and 22 on line 8. From April 27 to December 212, over 14 profiles from 17 glider missions on line 66.7 are used. Data plots are available for these missions at In Figure 2, the example transect is from mission 12831, where the identifier comprises a two-digit year (12 for 212), a one-digit hexadecimal month (8 for August), a three-digit glider serial number (3 for Spray 3), and a two-digit mission number (1 in this case). A Spray glider moves vertically through the ocean by inflating/deflating an external bladder, while wings provide lift to move the glider forward resulting in a sawtooth pattern in depth and time (or horizontal distance) [Sherman et al., 21]. The payload comprises: (a) a pumped Sea-Bird Electronics (SBE) 41CP conductivity-temperature-depth instrument (CTD) from which potential temperature (θ), salinity (S), in situ density (ρ), and potential density (σ θ ) are obtained (Figures 2a b); (b) a Seapoint chlorophyll a (chl a) fluorometer; and (c) a Sontek 75 khz acoustic Doppler profiler 1

11 (ADP) aligned to measure horizontal velocities in five 4-m vertical range bins [Davis, 21; Todd et al., 211b]. Data are obtained on ascents, when the CTD experiences clean flow. For the purposes of this paper, data and times are averaged in 31 vertical bins, which are 16-m tall, non-overlapping, and centered from 1 49 m. A dive cycle to 5 m and back to the surface is completed every 3 hours, which gives a Nyquist frequency of 1/6 cycle hour 1 and is sufficient to sample D 2 signals (Section 3.2). During a dive cycle, a glider moves about 2.7 km through the water. Vertical displacements are obtained from density differences from a lowpassed mean (Figure 2c): η(z, t) = g σ θ σ θ N d (1) where z is the vertical coordinate (up is positive), t is time, g is gravitational acceleration, denotes a running mean over the subscripted intervals-i.e., 1.5 days, σ θ = σ θ σ θ 1.5 d is the density deviation from the 1.5-day lowpassed mean, and N 2 is the buoyancy frequency. The 1.5-day mean is roughly equivalent to a 3-km mean. Due to this averaging window, η and other variables calculated below with similar averaging will vary slowly in time over periods of O(1 day or 2 km) as in Figure 2c. Some further details of sampling with a slowly-moving glider are covered in Section 3.2. Strain, z η, is calculated from a first difference (Figure 2d). Velocity profiles are made similar to lowered acoustic Doppler current profiles from ships [Visbeck, 22]. Depth-mean currents are obtained from a combination of Global Positioning System fixes and a glider s measured attitude [Todd et al., 29]. The depth-mean current and ADP-measured, 11

12 glider-relative velocities are combined in a linear system of equations that is solved by a least squares method for water velocities [Todd et al., 211b]. Referencing objectively-mapped and vertically-integrated ADP-measured shear to the depth-mean current produces similar results [Davis, 21]. Hereafter, horizontal currents (u and v) are given in the cross-shore and alongshore directions (Figures 3a b), which are positive onshore (x) and to the approximately north-northwest of the transects (y). The coordinates are defined separately for each of lines 66.7, 8, and 9. Glider tracks differ from these lines when: (a) depth-mean currents are strong and contrary to the desired glider course and (b) during launch and recovery of gliders near the coast. We calculate shear components, i.e. z u and z v, from first differences (Figures 3c d). We note elevated shear variance below m due to a decrease in acoustic scatterers. Quantities related to shear variance below 362 m are excluded from further consideration, most notably (a) the D 1 and D 2 velocity bandpasses (Section 3.2) and (b) the diffusivity estimates, which depend on shear variance squared (Section 3.3 and Appendix A). However, we still show mean cross-shore sections of u, v, and Rossby number (Ro) with data below 362 m, since the noise is at high vertical wavenumber and thus affects shear more strongly than velocity. Using full-depth data produces minor quantitative differences in diffusivity estimates by including shear measurements with lower signal-to-noise ratio, but none of the qualitative conclusions change. Using this cutoff produces better agreement between shear- and strain-based mixing parameterizations (method described in Section 3.3). Horizontal gradients of density and currents are calculated after smooth- 12

13 ing the density and currents over 3 km (e.g., Figure 3e). This procedure is needed because spectra show noise (i.e., internal waves) in density gradients and geostrophic currents at wavelengths shorter than about 3 km when calculated along depth surfaces [Rudnick and Cole, 211]. Since we only measure the x v component of relative vorticity (ζ), we estimate Ro = ζ/f x v/f (Figure 3e) and so the actual Ro could be twice as large if there is solid body rotation, where x v = y u. The fluorometer is uncalibrated and suffers from offsets from mission to mission, but for any given mission the spatial pattern is qualitatively accurate even though the magnitude is not. Fluorometer voltage is multiplied by 3 to obtain an uncalibrated number similar to chl a concentrations in mg m 3 to illustrate relative changes Mixed layer depth is calculated with σ θ =.1 kg m 3 from the nearsurface value [Johnston and Rudnick, 29] Energy density and fluxes With relatively slow-moving gliders ( 2 km/day), we estimate tidal and near-inertial signals similar to Johnston et al. [213]. Space-time confusion arises since relatively high frequency signals (i.e., internal waves with frequencies from f to N) are projected into spatial variations [Rudnick and Cole, 211]. The projection is caused by two effects (smearing because the glider moves slowly and aliasing because the glider profiles at a frequency in the internal wave band) and cannot be undone, but still allows for an estimate of these harmonic signals. A moving 1.5-day ( 3-km) window is used, which discriminates between D 1 and D 2, but cannot distinguish near-inertial motions from D 1 since the 13

14 frequency resolution is 2/3 cycle day 1. In essence, this method is a bandpass filter. Harmonic analysis of η, u, and v using M 2 and K 1 frequencies is applied over the moving 1.5-day window producing the harmonics for displacement (η ), for example, as follows (Figure 4): η (z, t) = A η cos[ω(t t o ) + φ η ] (2) The amplitude is: A η (z, t) = η r + i η i, where η r = A η cos φ η and η i = A η sin φ η are the real and imaginary components of the fit to cos[ω(t t o )] and sin[ω(t t o )]. The phase is: φ η (z, t) = tan 1 (η i /η r ). The M 2 and K 1 periods are: T = and hours. The radial frequency is: ω = 2π/T. The reference time, t o, for phase calculations is Coordinated Universal Time (UTC) on 1 January 21, roughly the midpoint of the data. Velocity fits are made in complex form, u + i v. Inertial motions have T = 23.2 to 2.9 hours from 31 to 35 N. Later when mean phases are shown, they are calculated from the means of the real and imaginary components. Energy density and fluxes in D 1 and D 2 frequency bands are calculated from amplitudes as: E(z, t) = ρ t (A 2 u + A 2 v + N 2 t A 2 η)/4 (3) where time averages, t, are mission means [Lee et al., 26]. Kinetic energy (E k ) comprises the first two terms, while potential energy (E p ) is the last term. No attempt has been made to remove barotropic components, but the results of the harmonic analysis appear dominated by baroclinic structurei.e., internal waves (Figure 4). Energy fluxes require full-depth measurements 14

15 and so mode-1 fits of the harmonics are used where depths exceed 362 m: η, ũ, and ṽ, where the tilde denotes the modal fit [Johnston et al., 213]. Data are extended using the World Ocean Atlas 29 analysis for depths greater than 5 m [Antonov et al., 21; Locarnini et al., 21] and bathymetry from Smith and Sandwell [1997]. The mode-1 pressure perturbation, p, is calculated from η [Johnston et al., 213]. Lastly, mode-1 D 1 and D 2 energy fluxes are obtained based on both density and velocity measurements: [F x (z, t), F y (z, t)] = p ũ, p ṽ 1.5 d (4) with averages over 1.5 days or 3 km. The mode fit is performed from m in depth, even though modes are orthogonal only over the full water depth and can lead to flux errors of about 4%. Limits of the modal decomposition are explained in more detail in Johnston et al. [213] Finescale mixing parameterizations As noted in Section 2.1, the advantage of these parameterizations is that turbulence estimates can be made from standard Doppler current and CTD profiles. The physical basis of these finescale mixing parameterizations relies on a steady downscale energy transfer from large-scale weakly interacting waves to small-scale breaking internal waves to turbulence. For a GM internal wave field, this transition occurs at roughly 1 m, but this cutoff is adjusted based on Richardson number. The white wavenumber spectrum of either shear or strain drops off at wavenumbers above the cutoff. In our case, the cutoff is placed at 1/4 cycles m 1, where noise in the ADP-measured 15

16 shear becomes apparent. Details of the calculations are in Appendix A. We produce two estimates of K ρ : one from observed shear and strain (K sh ) and the other from strain alone (K st ) with an assumed shear-to-strain ratio. The observed shear-to-strain ratio is larger than the GM value and so K st will be an underestimate by a factor of up to 2 (Appendix A). We only show ɛ calculated from both shear and strain Bin means In much of the following analysis of temporal and spatial variability (Sections 4 and 5), data are binned in cross-shore distance and time, x and t. These results are used to describe time-mean, cross-shore sections along with the seasonal cycle of the currents, density structure, internal tides, and mixing. To form time-mean cross-shore sections, bin sizes are x = 1 km. Data located >15 km away from the nominal transect are not considered, which mainly occurs on launch and recovery, but also when there the depth-mean cross-transect (i.e., alongshore) currents exceed.25 m s 1. Derived quantities (e.g., x σ or N 2 ) are calculated first and then binned. Bin means in depth and x are shown for some data and amplitudes and phases from the harmonic fits. Bin-mean phases are calculated from the bin means of real and imaginary components. Bin means of depth-integrated fluxes and depthmean energies are shown. The former emphasizes mode-1 content, while the latter better represents higher modes (i.e., smaller-scale vertical structure). Temporal bins are t = 6 days, which is enough time to cover slightly more than two cross-shore transects. When binning is both in t and x, x is increased to 2 km. These values for x and t bins are similar to decorrelation 16

17 scales used in objective maps of the same data [Todd et al., 211b]. A composite seasonal cycle for line 8 is constructed by binning data by month. A time series for line 8 is made by binning data from x = -1 to km in 6 day increments. Lines 66.7 and 9 show little indication of seasonal cycle in K ρ and so we do not show similar calculations there Cross-shore and depth structure of the mesoscale and internal tides: an example section and time means 4.1. Overview In this section, we are primarily concerned with examining D 1 and D 2 variability near the continental slope on line 8 and the SRCR on line 9. The mesoscale current and density structures are also described. First, we examine a single example transect on line 9 to illustrate the type of data obtained from a glider (Section 4.2). Second, we apply harmonic analysis to u, v, and η. Third, time-mean transects are then examined to better identify mesoscale and internal tidal flows for lines 8 and 9 (Sections 4.3 and 4.4). Several features are noted on the example transect on line 9 including (Figures 2 4): (a) larger displacements above the SRCR; (b) greater strain within the SCB; (c) considerable mesoscale variability in Ro; (d) a front over the SRCR; and (e) stronger D 1 and D 2 motions in the SCB but especially at the SRCR. The time-mean transects describe the expected cross-shore structure of the CCS, confirm the features described earlier in this paragraph, and further display consistent tidal phase near these internal tidal generation sites (Figures 5 8). These characteristics are used to distinguish NIW from D 1 internal tides, identify D 1 trapping, and illustrate D 2 propagation. 17

18 An example from line 9 An example of a shoreward transect on line 9 during mission from 3 27 September 212 illustrates typical data (Figures 2 3). Tick marks along the upper axis of Figure 2b show glider dives roughly every 3 km. While the transect is not synoptic, mesoscale structure and internal waves are apparent. Increased internal wave activity over the SRCR (topography near x = -19 km) produces vertical displacements seen in T, S, σ θ, and η (Figures 2a c). Larger strain is found near the topography and within the SCB (x > -2 km, Figure 2d). A front is found near the SRCR, as evidenced by increased cross-shore gradients of θ, S, and σ θ there (Figures 2a b). Both internal wave oscillations and mesoscale structure are seen in the currents (Figure 3a b). With a glider moving at 2 km/day, 5 and 1 oscillations in currents over 1 km indicate D 1 and D 2 motions. Both upand downward phase propagation is present in the shear, which indicates a combination of down- and upward propagating internal wave energy (Figures 3c d), but shear does not appear particularly elevated near the topography in this transect. The magnitude of Ro exceeds.4 near the coast (Figure 3e), but may be up to twice as large (Section 3.1). Internal tides appear larger near the SRCR and within the SCB. In particular, D 1 and D 2 η are larger (Figures 4e f). Velocities can be equally strong further offshore, especially for D 1, which could be due to NIW (Figures 4a d). NIW currents impinging on topography would produce larger displacements near the topography as would trapped D 1 internal tides (Figure 4e), while freely-propagating D 2 internal tides should show larger η radiating away from the topography higher and lower in the water column, as possibly seen in Fig- 18

19 ure 4f. Larger D 1 v and η preferentially on one side of the SRCR suggest topographic trapping, a process which is examined in more detail below Time-mean, cross-shore transects: lines 66.7 and 8 The time-mean, cross-shore structure displays the canonical, mid-latitude eastern boundary current system with a coastal upwelling front, a poleward undercurrent, and equatorward flow further offshore (Figure 5) [Hill et al., 1998]. Data from all missions are averaged in time to produce a time-mean, x-z section for all three lines. Lines 66.7 and lines 8 are qualitatively similar with coastal upwelling (shoaling isopycnals and stratification, a density front, and elevated chl a) and a northward undercurrent with anticyclonic ζ (Ro < ) inshore of the current s core (Figures 5a f, h ; only line 8). To avoid repetition, figures for line 66.7 are not shown. Typically >2 data points are in each bin, but more profiles per unit cross-shore distance are collected near shore where (a) dives are sometimes shallower than 5 m and (b) currents are stronger and gliders attempt to stay on track by crossing the current at an angle (Figures 5g, i). The continental slope is steep: at x = -3 km the water depth is over 5 m, but by x = -1 km the water depth reaches 3 km (Figure 5j). Harmonic analyses of η, u, and v show considerable D 1 and D 2 motions (Figure 6, left and right sides). We will show: (a) the D 1 waves near topography are consistent with trapped internal tides, which decay offshore and propagate with the topography on the right; and (b) the D 2 waves propagate offshore from numerous sources, which interfere and produce partiallystanding waves. The time-mean D 1 amplitudes are largest (a) within 3 4 km of the coast 19

20 due to trapped D 1 internal tides and (b) in the upper 1 m presumably due to NIW (Figures 6a, c). A η exceeds 12 m in places, which is not much larger than an open ocean GM root-mean-squared η of 7 m. A u is the magnitude of the tidal velocity amplitude, A 2 u + A 2 v. D 1 motions will be more visible as currents, since internal waves become more horizontal as ω approaches f. The spatial extent of surface-intensified A u suggest NIW, which are ubiquitous. Over the slope and below 5 m, A η decays to background values over about 7 km in the cross-shore direction. This decay is consistent with the baroclinic Rossby radius of 2 km (a decay to 5% of background levels occurs over 6 km) and trapped D 1 internal tides. The decay of A u is not as apparent as with A η. D 1 phases are useful for distinguishing NIW from internal tides. φ η is relatively constant near the continental shelf and slope where amplitudes are large (i.e., in a triangular region in the lower right of Figure 6g, where x > -1 km). In the same small region, A u is also large and φ v is also relatively constant (Figure 6e). Over most of the water column away from the surface and topography, φ v shows relatively little change compared with φ η. The D 1 phase differences (φ η φ u and φ η φ v ) are useful indicators of the direction of wave propagation. For a two-layer flow, when the lower layer s η and velocity have phase differences of /18 (i.e., in phase/out of phase), the wave propagates in the positive/negative direction [See Figure 6.3 in Gill, 1982]. Phase differences of ±9 imply standing waves. Depthmean phase differences are obtained from m to avoid NIW influence near the surface and emphasize deeper D 1 internal tidal motions. The depth mean of complex amplitude for each quantity (η, u, and v) is calculated at 2

21 each cross-shore distance, the angle is computed, and then we difference two such angles (Figure 6i). With this method, regions with higher amplitudes are emphasized. For x > -1 km, where D 1 amplitudes are largest (not including the surface), φ η φ u is near ±9, which yields no cross-shore energy propagation and is consistent with trapped waves (Figure 6i). On the other hand, φ η φ v is near (x = -12 to -3 km, Figure 6i), which implies northward phase propagation for a mode-1 wave. The combination of these phase results with elevated amplitudes near the slope indicate a topographically-trapped baroclinic wave travelling with the topography on its right. Next, D 2 harmonic fits are used to illustrate cross-shore propagation in contrast with D 1 above. One internal tidal generation site appears to be at the shelf edge and another, deeper one over the slope is near x = -8 km with waves propagating both onshore and offshore from there. Canyons, submarine ridges, and a seamount are found near 34 N, 121 E (or x = -8 km) and are somewhat visible in Figure 1b. D 2 A u is large near the topography, in the upper 1 m, and also about 15 km away from the slope (Figure 6b). This distance corresponds to a D 2 wavelength and suggests a surface reflection of a tidal beam [Cole et al., 29; Johnston et al., 211a; Martin et al., 26]. A η also suggests a beam-like structure emanating upward from topography near x = -8 km (Figure 6d). Several regions of on- and offshore phase increase are found in φ u and φ η (Figures 6f and h), which produce roughly 75 km-long sections of on- and offshore propagation, with φ η φ u = and 18 (Figure 6j). Onshore propagation (φ η φ u = ) is found for x > -7 km consistent with generation at the slope. A standing wave (φ η φ u 21

22 = -9) is found further offshore (-14 km < x < -7 km), which suggests at least two sources of propagating waves Time-mean, cross-shore transect: line 9 The time-mean, cross-shore structure along line 9 is consistent with previous observations in the SCB [e.g., Davis et al., 28; Hickey, 1979; Todd et al., 211b]. Inshore of the continental slope near x = -26 km, the topography comprises several ridges and basins in the SCB unlike lines 66.7 and 8 which have narrow shelves (Figures 1, 5j, and 7j). Like line 8, there is a nearshore shoaling of isopycnals and stratification at a coastal front near x = -2 km, where chl a is also larger (Figures 7a d). Flows in most of the SCB, from the coast to x -15 km, are generally northward, while southward flows are found in the California Current offshore of the slope in the upper 1 m with the northward California Undercurrent below 1 m (Figure 7f). Near the SRCR, a narrow region of southward flow is found along with anticyclonic Ro (Figures 7f, h). Cyclonic Ro bands are found on either side, which may assist with D 1 trapping by making the effective vorticity larger (Figure 7h) [Kunze and Toole, 1997]. Ro is small in this time mean, but values on a single section can be large (Figure 3e). A front associated with the inshore boundary of the California Current is found above SRCR with a broader lateral extent of chl a compared to the coastal front (Figures 7a, b, d). More profiles are obtained near the two ridges where dives are often shallower, but typically >15 data points are in each bin (Figures 7g, i). Similar to line 8, higher D 1 and D 2 amplitudes are found near the topography on line 9, but, unlike line 8, the higher amplitudes are at topography within the SCB, mainly at the SRCR and not at the coast (Figures 22

23 a d). The complex topography provides numerous generation sites for internal tides. Increasing phase indicates a few areas of propagating waves, but large regions of slowly-varying phase show standing or partially-standing waves are dominant features (Figures 8e j). D 1 amplitudes are larger on the east side of the SRCR (in the San Nicolas Basin, near x = -18 km) consistent with an interpretation of trapped D 1 internal tides propagating southward with the ridge on their right (Figures 8a, c). Within 5 km of the east side of the ridge, φ η and φ v appear distinct from the surrounding phases (Figures 8e, g). A small region within 1 2 km of the SRCR has φ η φ v = 18 ( ) indicating southward (northward) phase propagation on the east (west) side of the ridge (Figure 8i). We discount NIW currents impinging on topography as the dominant signal below the upper 5 m because they would produce large mean amplitudes on both sides of SRCR and the ridge near x = -5 km. D 2 has larger amplitudes on both sides of the SRCR especially for displacements (Figures 8b, d). D 2 A η is also larger near x = -35 and -5 km, about one and two D 2 wavelengths from the SRCR (Figure 8d). Smaller displacements are seen at two other ridges near x = -5 and -1 km. As with the D 1 band, D 2 phases vary slowly, consistent with standing or partiallystanding waves (Figures 8f, h). Phase differences show small regions of propgating, standing, or partially-standing waves (Figure 8j) Summary On line 8, trapped D 1 internal tides are shown with: (a) largest amplitudes near topography, (b) slowly-varying phase in the same locations, and (c) phase differences which are consistent with northward propagation, and 23

24 (d) the coast is on the waves right consistent with a trapped wave. D 2 internal tides show propagation away from two sources, the shelf edge and rough topography on the slope. The phase differences show a combination of propagating and standing waves. On line 9, the amplitudes and phases at the SRCR provide evidence for trapped D 1 internal tides rather than NIW: (a) larger amplitudes on the east side of the SRCR, (b) distinct phases there, and (c) some suggestions of propagation with the ridge on the right. Numerous D 2 wave sources over the complex topography of the SCB yield patterns dominated by partiallystanding waves. Line 8 s time-mean, cross-shore structure shows a coastal upwelling front, a poleward undercurrent, and equatorward flow further offshore. Line 9 displays a similar time-mean, cross-shore structure offshore of the the slope/srcr. Most of the flow in the SCB is poleward with a weaker upwelling front at the coast Depth-mean mixing estimates and internal tides: spatial and temporal variability 5.1. Overview Within the context of the internal-wave, frontal/mesoscale, and mean flows (Section 4), depth-mean K ρ and ɛ estimates from all available glider profiles are presented for each of the three lines (Section 5.2). Then, bin means in time and space are used to better describe the temporal and spatial variability of these estimates. The cross-shore structure is described in the mean (Section 5.3). On line 8, patterns are found over the >6-year record 24

25 along with a seasonal cycle (Section 5.4). No seasonal cycle is found on the other lines. In particular, we illustrate these patterns of variability in the mixing estimates, internal tidal energies and fluxes, gradients and density at fronts, and chl a using depth means. This section covers three analyses: (a) the time- and depth-mean cross-shore structure for all lines, (b) the depth mean on line 8 for the region near the coast (x > -1 km) shown as a time series, and (c) the depth mean on line 8 shown as a composite annual cycle (i.e., x versus month). These three analyses rely on depth means over somewhat different depths and so we summarize for each calculation the relevant depths and reasons before proceeding with the results. For analysis a, depth-mean K ρ and ɛ are averaged from below the mixed layer to 362 m, the depth of the deepest reliable shear measurements (Section 3.1 and Appendix A). σ θ and x σ θ emphasize fronts by averaging from 1 9 m. Chl a is averaged over the same depth range for the same purpose and also because there is little signal below that depth. Depth-mean rather than depth-integrated E is calculated to emphasize high mode internal waves. Its depth mean is from 58 m up to a maximum of 362 m to minimize NIW influence and to more closely compare with mixing estimates. Depth-integrated mode-1 fluxes are calculated from data which covers m. For analyses b c, averaging intervals are as noted above, but σ θ and N 2 depth means are from m to show the annual cycle in upwelling. Further details on the binning are in Section

26 Depth-mean mixing estimates To demonstrate the resolution and extent of the data, we show depthmean diffusivity estimates from all profiles on all three lines where both shear and strain are available (Figure 9). The spatial patterns on all three lines are consistent with locations of elevated D 1 and/or D 2 energy either near the shelf/slope or over the rough topography of the SCB (Figures 6a d and 8a d). With a 1.5-day window, there is some smearing of these patterns over 3 km, a typical distance covered by a glider in this time and so this pattern of mixing near topography is likely more localized in space than we describe below. On line 9, the overall pattern of the parameterized dissipation and diffusivity shows highest values over the SRCR with ɛ > 1 8 W kg 1 and K ρ > 1 4 m 2 s 1 from both shear-strain and strain-only estimates (Figure 9c). Secondary maxima are seen at x -1 and -5 km near two other ridges (Figures 1b, 7j, and 9c). Another, intermittent local maximum is near x -35 km at a possible D 2 downgoing beam (Figures 8d and 9c). K sh estimates from line 66.7 and 8 display an offshore decay to background values within 1 km of the coast (Figures 9a b). Diffusivity estimates appear more sporadic on line Sampling density near the coast is sometimes lower because gliders are deployed and recovered from coastal locations off of the nominal lines, which are excluded from consideration because y > 15 km (Section 3.4 and Appendix A). Thus, typically 2 of 4 transects on one mission will closely follow the line near the coast. Also estimates are not made, when a profile extends less than 96 m below the mixed layer depth, a condition which is more likely to occur in shallow coastal 26

27 waters. Patterns of ɛ are almost identical to K sh, which in turn are very similar to K st and so we only show K sh at this point. Section 5.3 will further demonstrate this similarity. The spatial patterns of K sh and K st agree within a factor of 2, which reflects a factor of 2 difference in the correction for shearto-strain ratio from observations and GM (h in Appendix A). This result suggests the independent measurements of shear and strain are in reasonable agreement (Section 3.3 and Appendix A). Since these K ρ estimates follow the statistics of ( z u 2 + z v 2 ) 2 (Appendix A), the probability distribution functions roughly resemble a lognormal distribution (figure not shown). The ratio log(k sh /K st ) has a mean value of log(1.7) and a standard deviation of log(1.6) and the ratio of K sh /K st is <2 with a standard deviation < Depth- and time means of the cross-shore transects In this section, we use the depth- and time-mean, cross-shore structure of mixing, internal tides, density, and chl a to assess the energetics and relevance of our mixing estimates. First, on lines 66.7 and 8, the offshore decay of K sh is similar from values near the coast of 1 4 m 2 s 1 to 1 5 m 2 s 1 offshore (x < -1 km, Figure 1a). K st is within one standard deviation of K sh, but appears to under-/overestimate off-/onshore. A similar decay is found on both lines 66.7 and 8 for ɛ (Figure 1b). Due to the similarity with line 8 in the cross-shore mean, most of the description of K sh below covers only lines 8. As in Section 4.3, on line 8, the coastal upwelling front is near x = -5 km, where maxima in chl a and its variance are seen (Figures 1c d). Depth-integrated D 1 mode-1 energy flux is small (<1 W m 1 ) and displays no clear pattern, which is expected for an evanescent internal wave 27

28 (figure not shown). The depth-integrated D 2 mode-1 energy flux converges shoreward from x = -12 km (Figure 1f), while the depth-mean energy densities increases for D 1 and D 2 shoreward of x = -5 and -1 km (Figure 1e). D 1 energy density is 2 greater than D 2. Data coverage as noted earlier drops off closer to shore (Figures 1g h), yielding more uncertain mixing estimates there (Figures 1a b). In summary, turbulence estimates and D 1 energy peak in the same location. This result along with those in Section 4.3 indicate trapped D 1 internal tides are the dominant source of mixing on line 8. The decay away from topography of the D 1 signal and K ρ estimates are similar and suggest trapped D 1 waves may be the main contributor to mixing. The mode-1 baroclinic Rossby radius (= c/f, where c is the mode-1 phase speed) within about 1 km of the coast varies from km. An exponential decay in x reaches 5% of the value at the coast over a distance of km. The larger distances are consistent with the decay scales of D 1 E and K ρ on line 8, while the smaller distances are appropriate for the shallower waters in the SCB on line 9 as we will show later in this section. For line 8, we make rough estimates of the energy budget within 1 km of the coast. The energy lost from D 1 and D 2 internal tides should balance the dissipation. We neglect any contribution from NIW or fronts. We argue the most energetic D 1 component is due to trapped internal tides. These topographically-trapped waves propagate northward with the coast on their right. If we assume 1% of their depth-mean energy within 1 km of the coast is locally dissipated over a tidal cycle (1 day) that yields a depth-integrated dissipation in roughly 1-m deep water as:

29 J m 3 1 m / 864 s 6 mw m 2. The D 2 mode-1 flux convergence: is roughly F x / x = 48 W m 1 / 12 km = 4 mw m 2. The very crude estimate of energy lost by D 1 and D 2 internal tides is comparable to an order of magnitude estimate of the depth-integrated dissipation (calculated from depth-mean ɛ in Figure 1b): ρɛh = 1 3 kg m W kg m = 1 mw m 2. Many of the factors included in this paragraph could be increased and decreased easily by factors of 2 or more given their variations within 1 km of the coast. Therefore, we conclude as an order of magnitude estimate, that there is 1 mw m 2 energy lost from the D 1 and D 2 bands to produce the estimated dissipation of 1 mw m 2. On line 9, elevated mixing estimates appear where D 1 and D 2 energy densities are largest over the SRCR (x = -25 to -15 km, Figures 11a, b, and e). There may be contributions from a persistent front (Figure 11c). K sh has a maximum of m 2 s 1 across the SRCR and the slope. A decay to background values of <1 5 m 2 s 1 in deep water is found (x < -3 km, Figure 11a). The offshore decay occurs over 1 km similar to lines 66.7 and 8, but the onshore decay is more sudden (near x = -15 km, Figures 11a, b, and e). This result would be consistent with an offshore increase in Rossby radius and extent of D 1 trapped internal tides. Again K st is an underestimate compared to K sh in deep water. Similar features are found in ɛ with slightly elevated values over other ridges at x = -1 and -5 km (Figures 11a b). We also note a persistent density front near x -2 km, where chl a and its variability are elevated (Figures 11c d). Depth-integrated D 2 mode-1 baroclinic energy fluxes are small in the SCB and only increases offshore of the continental slope (x < -25 km, Figure 11f). Data coverage 29