General and fine scale oceanographic properties on the Norwegian Continental slope inferred from a moored CTD- and current profiler
by
Ilker Fer1, Øystein Skagseth1,3 and Kjell A. Orvik2
1) Bjerknes Centre for Climate Research, University of Bergen, Norway 2) Geophyscial institute, University of Bergen, Norway
3) Now at Institute for Marine Research, Norway
Project Report to NORSK HYDRO
Contract # 5279548: Indre bølger og seismikk
July, 2005
Summary
Observations were made from a moored profiler recording profiles of CTD and current at
∼1000 m isobath on the Norwegian slope between 125-674 m depth for approximately two months duration. A set of up-down cast is obtained at preset 2.25h intervals. The data set resolves the vertical wavenumber spectrum at several meters to several hundreds of meters and the frequency spectrum upto about 0.5 cycles per hour. The sampling frequency is not adequate to resolve the internal wave continuum and the high frequency events (e.g. nonlinear solitary waves) that might be expected at the site, however resolves the major tidal and interaction bands and is excellent in providing enough ensembles of wavenumber spectra over the dominant semi-diurnal periodicity at the site. The data set is first presented in relation to the environmental forcing (atmosphere and tides) and then possible mixing mechanisms are explored. The data set allows for two independent estimates for mixing: that inferred from a non-linear internal wave interaction model and that inferred from density overturns. The density ratio derived from hydrography suggests the possibility of double-diffusive convection; however it is probably overdriven by enhanced shear-induced mixing at the site.
1. Introduction
Hydrographic measurements in the Norwegian Sea reveal the Atlantic Inflow as a warm and saline wedge-shaped current (Figure 1.). Suitable for Norwegian Sea this water can be defined as T > 5degC and following Helland-Hansen and Nansen (1909) S > 35.0.
Beneath the Atlantic Water is colder and fresher Arctic Intermediate Water (AIW), or Norwegian Sea Deep Water (NSDW) (see e.g. Mork and Blindheim, 2000). The main currents are divided into two distinct branches; 1) a slope branch focused just off the shelf break (typically in the region of moorings S1, S2, and partly SE2, and 2) a western branch in the region of the Arctic Front in vicinity of mooring SE3 (see Fig. 1).
The interface between the AW and AIW is susceptible to considerable variations.
The causal mechanisms for this are not fully resolved, but among the probable candidates are tidal effect, topographic wave effects, and atmospheric forcing. These variations are a major concern for oil exploration, and it has been investigated in detail for the Ormen Lange region (Vikebø et al, J. Marine Systems, 2004; Yttervik and Furnes, DSR, 2005).
Especially breaking of internal waves as these hits the sloping topography has been investigated (Yttervik and Furnes, 2005). Another particular interest has been on the signature of the fine scale variations of the interface on the seismic signals in the ocean, allowing for a novel methods in inferring internal wave spectra from seismic reflection transects (Holbrook and Fer, 2005).
The focus of the report is on measured variations of the interface by a moored Conductivity Temperature Depth (CTD) and current profiler (section 2). This mooring was deployed as part of the Svinøy section monitoring program by the Geophysical Institute, University of Bergen (section 3). The mooring was located about 70 km upstream (i.e. southwest) of the Ormen Lange field. The variations of the interface captured by the mooring here can be interpreted as the open ocean boundary condition for internal waves.
Since this type of measurements are quite new the post recovery processing of the profiling data is described in detail in section 4, and a comparison with independently measured current is contained in part 5. Then relations to the atmospheric forcing and tides are explored in section 6. In section 7 and 8 the general and the fine-scale properties are worked out, and in 9 some concluding remarks are made.
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Figure 1. A typical CTD section from the Svinøy section. The sites marked S1-3, SE1-3 show the location of current meter moorings operated by the GFI, UIB as part of the Svinøy sec. monitoring. The MMP mooring deployed at site SE2.
2. The McLane Moored Profiler
The McLane Moored Profiler (MMP, Fig. 2) is an autonomous platform equipped with a conductivity-temperature-depth (CTD) sensors set and an acoustic current meter (ACM). It is 130.5 cm tall, 33.3 cm wide (port to starboard) and 50.5 cm long (fore to aft). The ACM, protrudes forward 45.2 cm. The MMP weighs approximately 70±1 kg in air weight and 0±0.1 kg in water after ballasting. Both the CTD (Excell 2′′ low-power) and ACM are manufactured by Falmouth Scientific Inc. The instrument profiles up and down along a vertical mooring cable at a pre-programmed profiling interval at a nominal sampling frequency of 1.85 Hz. and a nominal profiling speed of 0.25 m/s. The data streams from the CTD and ACM are not synchronized (see section 4). The MMP is driven by a motor and records data internally. The reader is referred to the technical manual at the manufacturer’s website and several related publications therein (http://www.mclanelabs.com) for a thorough description.
Figure 2. (left) The McLane Moored Profiler (MMP) during deployment at McLane’s 17 meter test well (right) sketch of components of the MMP (courtesy McLane Labs).
3. Deployment and recovery
The McLane profiler mooring was deployed at 13 Dec. 2003 1200 NLT and recovered at 25 Mar. 2004 at 1500 NLT from the R/V Håkon Mosby. The position of the mooring was 63° 06.10′ N, 3°37.20′ E at bottom depth of about 1000m (Fig. 3). The McLane instrument was programmed to profile a complete up and then downcast between 125 m and 674 m every 8000s (~2.25 hours) (Fig. 4). For comparison purposes an Aanderaa RCM was deployed at the lower end of the MMP profiling string, at 810m depth.
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Figure 3. The location of the MMP. The arrows are the vector mean current averaged over 300-450m depth (black, approximately the Atlantic Water layer) and 170-650m depth (red, full depth covered by the MMP) during Period I (see text, the longest near-continuous record of 614 profiles).
Figure 4. An example of the pressure-time history of the casts made by the MMP. Shown are the first 10 profiles of the record starting with upcast, followed by a downcast and another set of measurements approximately half an hour later.
The full depth-time coverage of the MMP deployment is shown in Fig. 5. The portions when data were not available are identified as blank. There are typically 10 data points when averaged into 1-m bins, increasing towards the end of the deployment due to weakening battery, hence slower profiling speed. The relatively continuously sampled portion within the first half of the deployment, identified by arrows in Fig. 5, is referred to as Period I and is further analyzed in the following. Period I comprises a total number of 614 casts.
Figure 5. Depth-time maps of (upper panel) number of data averaged into each 1-m bin, (middle panel) 1-m bin averaged temperature, and (lower panel) salinity covering the whole deployment period. The white portions are those when the instrument returned no data. Period I is identified by two arrows and is analyzed further in this report.
4. Data processing
Prior to analyzing data in oceanographic context there are two distinct tasks in the post-processing. Firstly, the raw acoustic path velocity measurements logged in the ACM data files need to be mapped to velocities in the local Cartesian earth frame. This transformation requires an accurate determination of the heading angle of the ACM sting through compass calibration. The second task is synchronizing the CTD and ACM sensor data streams. While the nominal sample rate of both sensors is 1.85 Hz, they are not phase-locked to prevent drift and they operate independently.
The errors due to slightly different biases, gains and alignments in two horizontal components of the ACM compass (each measures local magnetic flux relative to itself) are accounted for by offset and scale parameters. These are determined by mapping the measurements either from a test or from field data into a unit circle. We have calculated the parameters both from field and test data (spinning the instrument at e.g., 22.5°
increments from a known heading, e.g. North determined by a handheld compass). The test was conducted following the recovery of the instruments on board, hence is biased and affected by the strong magnetic field of the ship and the low battery condition after
∼2 months of service. The test and field corrections coefficients were comparable and we rely on the coefficients derived from the field data. The ACM records velocities along the acoustic axes of its stings. Using the known magnetic deviation for the site of the deployment and the geometry of the stings we calculate the velocity components in mathematical compass coordinates and then rotate into eastward and northward velocities in the true north Cartesian Earth frame.
In order to align the CTD and ACM data streams in time, we follow and slightly revise the procedure suggested by the manufacturer. We compare the vertical velocity, w, measured by the ACM, with dP/dt, the pressure rate that is derived from the CTD pressure measurements. The MMP provides engineering files for each cast, with sufficiently accurate time tags at various pressures. A time record is obtained by matching CTD pressures to time tagged pressures in the engineering record and then linearly interpolating between the known points to fill up the central portion of the record. The ends of the record are extrapolated at the sample rate measured by the interpolation (∼ 1.85 Hz). The pressure rate, dP/dt is calculated and both w and dP/dt time series are passed through a ∼20s cutoff 4th order non-recursive Butterworth low pass filter. Two features, the acceleration near the beginning and the stop near the end, are readily identifiable in both filtered records (an example using field data is shown in Fig 6). Each record is then de-meaned and normalized by one standard deviation. The start and end portions are treated separately. For each portion, lag of maximum correlation between the records are determined. The start and end data indexes are assigned as the first point exceeding the 2.5 times the rms of normalized signal. The ACM record is interpolated to the same time record derived for the P record, between the identified start/end points.
Figure 6. Synchronization of ACM and CTD. An upcast profile is shown. Upper panels are the time rate of change of pressure, dP/dt, derived from CTD and vertical velocity recorded by the ACM. The horizontal axis is the sample number. The lower two rows are expanded views for the first and last 500 samples of the corresponding variable. The start and end points assigned to each record as described in the text are shown by red points. The data are interpolated to a common time based between those points.
Examination of individual full-resolution velocity profiles showed large oscillations in the upper half of the profiling depth, possibly related to the wagging of the profiler. The time rate of change of the sting heading (dH/dt) and the cross-body component of the velocity are expected to be correlated for this behavior. In Fig. 7 we present an example profile of these parameters and the corresponding frequency spectra.
The power spectra are calculated for all casts of Period I (614 casts) and individual spectra are shown together with their ensemble mean for 150-400m depth and 400-650m, separately. The time rate of change of heading shows a significant narrow band peak at ∼ 0.08 Hz at both depth portions (i.e. throughout the profile depth), however it is more energetic in the upper half. The upper half, furthermore, shows a broadband energetic feature at higher frequencies. The 0.08 Hz peak has a strong signature on the cross-body velocity spectra. In addition, the spectra from the upper half has a secondary peak of similar magnitude at ∼0.2 Hz, this is not clearly related to the dH/dt spectra. We further present the effect of the wagging of the MMP on East-North components of the velocity profile and their vertical wavenumber spectra (Fig 8). The artificial oscillations in the upper half of the velocity profiles are clearly identified from an arbitrarily chosen
example. We use 1-h and 1-m gridded data set to calculate the vertical wavenumber spectra from 600 profiles in total. The 0.08 Hz peak in Fig 7. corresponds to a length scale of ∼3 m (∼0.3 cpm) using the nominal profiling speed of 0.25 m/s. This peak is clearly seen on the vertical wavenumber spectra of both east and north components and is more energetic in the upper half of the water column.
The frequency of the observed oscillations and the fact that the oscillations are more pronounced with increasing distance from the bottom is consistent with the eigen- oscillations expected from the structure, which is in analogy with an inverse pendulum.
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Figure 7. Illustration of the noise induced by the wagging of the MMP. The time rate of change of the sting heading (dH/dt) and the cross-body component of the velocity are expected to be correlated for this behavior. Left column is an arbitrarily chosen cast (cast10) and the large oscillations in the upper half of the profile are likely related to the wagging of the instrument. The power spectra covering a set of more than 600 profiles of Period I and their ensemble mean are shown in the right column. Upper panel is the spectra for the cross-body component of the velocity; lower panel is that for the dH/dt. In each panel, upper half (150-400m depth; yellow, mean in red) and lower half (400-650m, gray, mean in black) are shown separately. The significant peak at 0.08 Hz associated with the dH/dt spectra (at both lower and upper part of the profile) has a signature in the velocity spectra.
Figure 8. (left column) A typical velocity profile (east component, black; north component, red). The large oscillations in the upper 200m of the profile are associated with the wagging of the MMP. The 0.08 Hz peak in Fig. 7 corresponds to a length scale of ∼3 m (∼.3 cpm) using the nominal profiling speed of 0.25 m/s. This is the peak seen on the vertical wavenumber spectra. (right column) Vertical wavenumber spectra derived for the upper half (dots), lower half (crosses), and the full depth (lines) for the east (black) and north (red) components. Spectra are ensemble averages over 600 hourly profiles.
In order to remove this artificial contribution to the velocity components, we chose to apply a 20s cutoff 4th order Butterworth low-pass filter to the raw velocity profiles (20 s corresponds to 0.05 Hz and using the nominal profiling speed to a 5 m vertical scale). We then grid the dataset into 1-m vertical bins and 1-h time bins for Period I. The vertical gridding is done by averaging all data points within ±0.5 m of 1-m increment array between 125-675 m. The gridding on the time-axis is done using 1-m vertically averaged individual profiles and using the “griddata” function of MATLAB to
account for the irregular sampling in time (Fig. 4). Because the each profile takes O(1)h and an upcast starts after a delay following a downcast, which on the other hand starts almost immediately after each upcast, the deepest part of the profiling depth is sampled at irregular intervals at ∼0.9h cycle followed by a ∼1.4h, whereas the uppermost depth bin is sampled every ∼0.1h followed by ∼2.25h.
The 1h-1m CTD data are used to derive the potential temperature, θ, salinity, and σθ. Spikes in the conductivity record are detected as the data points exceeding the 2.5 times the standard deviation of the linearly detrended 50m length segments and interpolated prior to calculating salinity. Salinity is further smoothed using a 5-m median filter before calculating the density.
Buoyancy frequency, N(z) ≅ [-g/ρ dρ/dz]2, is calculated using the adiabatic steric anomaly leveling method (Millard et al., 1990). Vertical derivatives; shear (vertical derivative of horizontal components of the velocity du/dz; dv/dz); dT/dz; dS/dz are estimated as the slope of the straight-line fits to 10-m moving windows of 1-m data.
Shear is used in calculations of Richardson number, where as the scalar derivatives are used for density ratio, Rρ, computations (section 6).
5. Comparison between MMP – and RCM currents.
To evaluate the quality of the McLane profiler current record, a comparison with currents from RCM instruments were performed. These data are sampled somewhat differently; the profiler moving vertically along the string at a speed of ~0.25m/s and the RCM at a fixed depth of 810 m. Here we choose to compare averaged profiler currents between 674-624 m (i.e. sampled over about 200 sec.) with the hourly mean RCM currents (Fig. 9). Visually the correspondence between the currents from the two instruments is very good, both with respect to absolute values and directions.
To obtain a more objective measure of the correspondence between the records we define the east and north component of the RCM as:
V1 u1 u1 i v1 v1
where the subscript 1 refers to RCM. Similarly for the MMP current we have :
V2 u2 u2 i v2 v2
where the subscript 2 refers to profiler current. The complex correlation coefficient between these series defined as:
2 2
1 1
2
1
conjV / V conjV V conjV V
=
r ℜ ∑ ∑ ∑
where conj means complex conjugate. The complex correlation coefficient is very high (r=0.91). Even though the RCM also have associated errors, the quality of the RCM instruments has been demonstrated over a wide variety of environments. Thus the close resemblance between these two data sets suggest that the profiler currents are sensible.
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RCM 810m vs MMP 624−674m (upper). scale arrow=10cm/s
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Figure 9. Time series of MMP currents averaged between 624-674m (upper vectors) and RCM currents (lower vectors) for the period 12 Dec 2003 to 12 Jan. 2004. The scale vector represents 10cm/s.
6. Environmental forcing
In traditional oceanographic hydrographic surveys where profiles are repeated at order months (or years) the variations are heavily under-sampled. Thus the cause of the variations are difficult to discern. In contrast, this data set with the relatively high-repeat rate of the MMP profile, provide an excellent opportunity to resolve the actual vertical displacements in relation to the environmental forcing (Figure. 10); however does not resolve the higher frequency internal wave oscillations (upto N ∼ 0.5 – 2 cph).
The MMP observations over the whole deployment period presented in a Hovmoller diagram of potential density show the largest density gradients between 300 and 500 m (Fig. 10, upper). Events of various magnitudes are seen with excursions of the order tens to hundreds of meters. Notably is also the tendency of compressing of the isopycnals when located at the maximum depths and stretching when located at the shallower depths (e.g compare 29 and 24 Dec 2003).
In general sea level pressure (SLP) from the NCEP data in the vicinity of the mooring tend to vary with the sea level variations in Ålesund with the tidal contribution removed (Fig. 10, middle). Thus the inverse barometer effect describes a first order balance, but additional effects may become important: e.g, sea level changes attributed to continental shelf waves is a probable candidate. Dependent on their spatial scale these waves may also contribute to the sea level variations, and thus also the interior pressure gradients, at the mooring site.
The wind at 10m from the NCEP data (Fig. 10, lower) mirror the passage of a series of atmospheric cyclones, with maximum wind speed of ~ 25m/s at 1 Jan. 2004.
Relating the wind to the depth of the AW-AIW interface some qualitative statements can be made: 1) periods of maximum depths of the interface is associated with north(easter)ly winds, 2) and similarly the minimum depths of the interface occur at periods with predominantly southwesterly winds. This seems to hold for the large amplitude events and maybe also for some of the smaller scale events. If so a likely mechanism is through interaction between oceanic Ekman transports over the continental slope that can pile up water toward the coastline. This effectively change the sea level gradient in the continental slope region, that is further compensated for by displacement of the interface (Gill and Schumann, 1974; Skagseth et al., 2004).
The depth mean currents from the MMP show that the sub-tidal variations are large compared to the tidal currents (Fig. 11, upper). The currents show oscillations of similar time scale as for the temperature variations, including also the larger scale event about 1 Jan. 2004 (compare with Fig. 10.upper). No clear relation can be found with the spring-neap tidal cycle at Ålesund (Fig. 11, 2nd lowest), but the variations in the wind field show similar variability (Fig. 11. lower).
Figure 10. MMP observations and environmental forcing. (upper panel) Time series of σθ profiles covering the whole obervation period. (middle panel) Sea level pressure from NCEP at the grid point 65°N, 5°E (blue) and the residual sea level recorded at Ålesund (red). (lower panel) Stick vector plot of NCEP wind at 10-m, scale is shown on the lower right.
The general hydrographic structure in the region is that the warm/saline/light Atlantic water overlies the denser water of more Arctic origin (Fig. 1). Consequently increased portion of the denser Arctic water at the MMP site can be due to both upward or across-slope velocities. The MMP data indicate that the smaller scale variations can be due to horizontal currents (Fig. 12). The large event centered at about 1 Jan 2004 must however be due to some other mechanism, and as discussed probably associated with anomalous vertical velocities.
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Figure 11. Environmental forcing during Period I of the MMP record. (upper panel) Depth mean (125- 675m) hourly and 2-day lowpassed time series of east and north components of velocity recorded by the MMP and (second panel) stick plot of 6h mean depth averaged current. (third panel) NCEP sea level pressure (blue) at the grid point 65°N, 5°E and demeaned tidal water level estimated for Ålesund sea level record (red). (lower panel) 6h NCEP winds at 10m.
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Figure 12. Time series of density at 325 m (solid line) and cumulative across-slope distance (dashed line)
7. MMP observations - General properties
The survey mean (over Period I) CTD profile is shown in Fig. 13. Water column is continuously stratified between 200-500m with a peak buoyancy frequency of about 3 cph (cycles per hour; 1 cph = 2π/3600 s-1; Fig. 14). The Atlantic Water is above 400m with S>35, T>5°C.
The temperature and salinity decrease with increasing depth, hence susceptible to double diffusion. Time averaged profiles of several properties are presented in Fig 14.
The ensemble average (indicated by 〈⋅〉) shear variance (〈Sh2〉) approximately follows the
〈N〉 curve, suggesting internal-wave scaling (WKB scaling). The Richardson number,
〈Ri〉 = 〈N2〉/〈Sh2〉, is less than 2 throughout the profile. Ri O(1) indicates that the TKE generating shear and the suppressing effect of stratification are comparable and a value less than ¼ (in laboratory conditions and in theory) is the necessary condition for generation of K-H billows and shear-induced turbulence. The marginally stable upper 100m should be regarded with caution due to artificial shear induced by the wagging of the instrument. The density ratio, Rρ = [α dθ/dz] / [β dS/dz], where α is the thermal expansion coefficient and β is the haline contraction coefficient, θ is the potential temperature and S is the salinity, is calculated (in this representation) using the survey average θ and S profiles (Fig.14., left panel) and the corresponding local α and β. Double diffusive instabilites are expected for Rρ in the range [0.3, 100] with strong salt fingering for Rρ in the range [1, 2] and diffusive layering for Rρ in range [0.1, 1]. Here, any tentative evidence for double diffusive mixing will be masked by the highly likely shear- related mixing.
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Figure 13. Mean CTD profile derived from all profiles of Period I.
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Figure 14. Time averaged profiles of (first panel) potential temperature (θ) and salinity (S, red); (second panel) east and north (red) components of velocity; (third panel) mean buoyancy frequency (N) and the shear variance (red), (last panel) mean Richardson number (Ri) and density ratio (Rρ, red).
Frequency spectra
Hourly time series at each depth are used to calculate the rotary component frequency spectra of the baroclinic velocity. We removed the depth-mean at all times from all bins to estimate the baroclinic velocity. This will be slightly in error because only between 125-675m of about 1000m water column is sampled. 256 point (10.66 day) half overlapping Hanning windows are used. Spectra for selected 100-m depth ranges centered at 200, 300, 400, and 600 and 20-m depth range centered at 660 (i.e. ∼ the bottommost 20m) are shown in Fig. A5 for the clockwise (CW) and the counterclockwise (CCW) components. The spectra are contrasted to the Garrett-Munk model spectrum (GM, Garrett and Munk, 1972) as presented by Levine et al. (1985) for the corresponding components. The GM model is a function of the inertial frequency (0.0745 cph, here at 63.1 ºN), and the buoyancy frequency, which is implemented as the time-mean over the given depth range (arrows in Fig. 15). At this latitude and with the given sampling (gridding) interval the inertial frequency is not confidently distinguishable from the semi- diurnal lunar (M2) frequency (= 0.0805 cph), therefore we call it the near-inertial range.
In the near-inertial range the CW component is the dominant one, as is typically the case for the Northern hemisphere. The near-inertial peak is the most pronounced, and the rest of the spectrum (the higher frequency continuum) is more or less featureless, with no evidence of non-linear interactions leading to peaks at subharmonics. This is certainly influenced and perhaps masked by the relatively low resolution (1h) gridding of irregularly sampled data (both in time and in depth). At all depths, the CCW component is relatively more energetic at low frequencies. While the shape (f-2 fall off) is comparable to that of GM, the CW level is less energetic.
Vertical wavenumber spectra
Isopycnal displacement, ζ, profiles are calculated relative to the survey averaged potential density profile. Depth of evenly spaced isopycnal surfaces (at 0.005 kg m-3 resolution between the minimum and maximum observed values) are computed via linear interpolation for each profile (every hour), and then filtered using a 5-day boxcar moving window. This method was chosen instead of averaging over the survey, in order to account for the low-frequency trends (e.g. the depression before 31 December).
Displacement of each isopycnal for each cast is calculated relative to its mean depth.
Resulting displacement versus density profiles are converted to displacement versus 1-m resolution depth profiles by linear interpolation. Linear fits to ζ with zero at the surface are subtracted to remove barotropic contributions (Kunze et al., 2002). The observed instantaneous and survey-averaged isopycnal depths (of a chosen subset of isopycnals) as well as the calculated isopycnal displacements are presented in Fig. 16.
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Figure 15. Frequency spectra of CW (black) and CCW (red) rotating velocity components. The GM model is also shown. Each set of spectra is calculated for the target depth as averages over the indicated depth range. The arrows are the time-mean buoyancy frequency averaged over that depth range (used in GM calculation). The inertial frequency and some tidal constituents are indicated.
Daily vertical wavenumber spectra of isopycnal displacements as well as the rotary-component velocity are calculated over the whole profiling depth. Profiles are de- meaned, prior to calculating hourly spectra using 512 point (i.e. 512 m) half-overlapped Hanning windows. Daily spectra are averages over such 24 1-hour spectra and the degree of freedom is more than 48. Horizontal velocity (twice the kinetic energy) spectra are obtained as the sum of clockwise (CW) and counterclockwise (CCW) components of the rotary spectra. The shear (dU/dz) and strain (dζ/dz) spectra are calculated by multiplying the velocity and displacement spectra by wavenumber squared. The corresponding wavenumber spectra, as weekly averages for clarity (dof>336), are shown in Fig. 17. The spectra presented are not scaled by the buoyancy frequency (WKB scaling) and hence may be influenced by the variation of N within this large spectral window.
Figure 16. Time-depth maps of (upper panel) σθ (color) and the survey-mean depth of selected isopycnals (white contours); (lower panel) isopycnal displacement (color) and observed depth of selected isopycnals (white contours). The survey mean in the upper panel is obtained using a 5-day phase-preserving moving boxcar window. The selected isopycnals, in both panels, are 27.35 – 28.05 at 0.05 increments.
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kz (cpm) Φ U + Φ V = 2KE [(cm/s)2 /cpm]
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w1 w2 w3 w4
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Weekly averaged vertical wavenumber spectra
10−3 10−2 10−1 100
10−1 100 101 102
kz (cpm) Φ dζ/dz (1/cpm)
Strain
Figure 17. Weekly averaged vertical wavenumber spectra of (upper left) horizontal velocity, (upper right) shear, (lower right) strain for the four weeks (w1-w4) of Period I. In the lower left panel the ratio of the CW component to the CCW component is shown. The dashed lines in the shear and strain spectra are the corresponding GM model.
The roll-off at high wavenumbers in the velocity and the shear spectra is due to the low-pass filtering (of about 20s) applied in order to reduce the effects of MMP wagging (section 4). The shear spectra are 2-5 times more energetic than the GM model whereas the strain is comparable at scales less than about 50 m. In contrast to the good agreement of the “white” low wavenumber shear spectrum, the strain spectra contain some energy at low wavenumbers, particularly in week 3. The k-1 roll-off of the GM model after a cutoff wavenumber of 0.1 cpm is a modification introduced to the GM model based on a large set of both scalar and velocity observations in the literature. This is commonly interpreted as a manifestation of non-linear internal wave-wave interactions.
Our strain record is reliable at these wavenumbers (because the scalar field is not affected as the velocity field by the wagging of the MMP) and the roll-off with increasing wavenumber is a robust feature of the strain spectra.
For near-inertial frequency internal waves, direction of energy propagation can be inferred from the sense of rotation with depth of the CW and CCW velocity or shear variance. In the Northern Hemisphere near-inertial motions with downward group velocity have CW rotation. Therefore an excess of CW (CCW) variance is often interpreted as downward (upward) energy propagation and the opposite is true for the phase propagation (Leaman and Sanford, 1975). Their ratio around unity indicates vertical symmetry in the sense that the upward and downward propagating energies are comparable (note that GM model assumes vertical symmetry, however dissipation is reported to be relatively insensitive to the departures from symmetry, Polzin et al., 1995).
Values of ratio CW/CCW < 1 are typically interpreted as evidence for generation of near- inertial frequency internal waves (e.g. M2 internal tides) near a topographic feature, because near the generation site internal waves will have an upward energy propagation.
This ratio is presented as a function of wavenumber in Fig. 17 (lower left panel) and values are < 1 for low wavenumbers (corresponding to scales >100m), and particularly for weeks 2 and 4, suggesting a dependence on spring-neap cycle.
8. MMP observations- Finescale properties and mixing
Away from the boundaries, in the stratified ocean interior, the internal wave continuum (frequencies between the local inertial frequency, f, and the local buoyancy frequency, N) is reasonably well represented by the empirical wavenumber-frequency model of GM. This simple representation allowed relating mixing rates to larger-scale observable parameters e.g., shear and strain through models employing nonlinear wave- wave interactions. Away from boundaries, successful parameterizations capture the observed levels of dissipation within a factor of two for both GM (Gregg, 1989) and (with appropriate corrections) non-GM conditions of the ocean (Polzin et al., 1995). The Polzin et al. (1995, referred to a P95) model is based on the vertical wavenumber structure of shear and strain, both of which are resolved in our data set. The parameterization has been proven successful in many applications and was credibly applied for mapping mixing in the Southern Ocean and the Nordic Seas (Naveira Garabato et al., 2004a,b). The P95 model can be formulated as
2 1/ 2
2
1
P95 0 2
0 c
N 0.1 1 1/ R 2
L(f , N) W kg
N k 4 / 3 R 1
ω − ω
⎛ ⎞ ⎛ + ⎞⎛ ⎞ ⎡ ⎤
ε = ε ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠⎜⎝ − ⎟⎠ × ⎣ ⎦
where a non-dimensional energy ratio is incorporated as the ratio of the GM cutoff wavenumber (= 0.1 cpm) to that observed where the integrated N-normalized shear spectrum equals ∼0.7N2 (see e.g., Gregg et al., 2003). Here ε0 = 7.8 ×10-10 is approximately the open-ocean dissipation for canonical GM parameters at 30° N latitude,
N is the observed buoyancy frequency, No is the canonical GM buoyancy frequency (3 cph), and Rω is the observed shear to strain variance ratio. Rω is commonly interpreted as the ratio of horizontal kinetic to available potential energy and Rω = 3 for the GM prescription. Averaged over a single wave’s phase with characteristic frequency ω, Rω≡ [(N2 - ω2)( ω2 + f2)]/[N2(ω2-f2)], where f is the inertial frequency.The last term is L(f, N)
= [f cosh-1(N/f) ]/ [f30 cosh-1 (N0 / f30)] and is latitude dependant through f with f30
evaluated at 30°N. The terms including Rω are corrections for the non-GM conditions and go to unity in a GM field (Rω = 3). We evaluate this expression to get an estimate of turbulent mixing at the measurement site. The vertical diffusivity for mass is then approximated using Kρ = Γε/N2 (Osborn, 1980), where Γ is related to the mixing efficiency and typically Γ = 0.2 (Moum, 1996).
We use 64 point (64 m) half overlapping Hanning windows of hourly velocity and isopycnal displacement profiles to calculate the shear and strain vertical wavenumber spectra for the application of P95 at 32-m vertical resolution. The shear spectra are normalized by the mean buoyancy frequency over the depth of the spectral window (consistent with WKB scaling). The cutoff wavenumber, kc, is estimated as the first wavenumber band when the integrated N-normalized shear variance exceeds 0.7. The ratio Rω is then calculated as the ratio of N-normalized shear variance to strain variance integrated to this kc. At least two wavenumber bands are required for integration. When kc is not resolved or when Rω < 1 (P95 model is not applicable) no data is assigned for that particular 32-m depth bin. Internal wave based mixing models rely heavily on averaging over at least one cycle of the dominant periodicity of the wave field (here semi-diurnal). We therefore present daily averaged results. The inferred values of ε and Kρ are summarized in Fig. 18. The reddish colors of both parameters are significantly elevated above typical open-ocean values and suggest enhanced mixing. The tidal height is presented in the upper panel for reference. There is no clear evidence for spring-neap cycle dominance on mixing.
−100
−50 0 50 100
Tidal Height (cm)
100 200 300 400 500
zσ θ=27.5 (m)
log10ε (W/kg)
−10.5 −10 −9.5 −9 −8.5 −8 −7.5 −7 200
300 400 500 600
Depth (m)
log10K
ρ (m2/s)
−6
−5.5 −5
−4.5 −4
−3.5 −3
12/13 12/20 12/27 01/03 01/10
200 300 400 500 600
Depth (m)
Date (mm/dd)
Figure 18. Summary of the mixing parameter estimates using P95 parameterization. The tidal height (mean level removed) recorded in Ålesund is shown in the upper panel (blue). The red curve in all panels is the depth of the σθ = 27.75, shown for reference. Spectral estimates of dissipation, ε, over half overlapping 64- m windows are averaged daily (over two semi-diurnal cycles). The vertical diffusivity is estimated using Osborn’s model with Γ = 0.2. Date ticks are placed every 1 day.
Another independet measure of mixing can be estimated using Thorpe-scale analysis. In a stratified fluid, a parcel of fluid has to move a vertical distance which as a statistical mean can be represented by the Ozmidov scale, LO = (ε/N3)1/2, in order to convert all its kinetic energy into potential energy (Ozmidov, 1965). Using conventional CTD profiles, Thorpe (1977) developed a method to estimate the length scales of overturns associated with gravitational instabilities in a stratified turbulent flow- so called Thorpe scale. The Thorpe scale, LT, can then be calculated as the root mean square (rms) value of all nonzero displacements that each parcel of fluid has to move vertically from the initial to the reordered profile within the depth span covering the overturn. LT is reported to be proportional to LO,typically c = LO/LT ∼ 0.8 (Dillon 1982). This gives an
estimate of ε independent of internal wave models: ε= (cLT)2N3. Vertical eddy diffusivity can again be estimated on the basis of the turbulent mass flux, using Osborn’s (1980) model: Kρ = Γε/N2.
It is generally preferred to assume that density overturns can be represented by the overturns in potential temperature to eliminate relatively high instrumental noise in the conductivity cell as well as the systematic noise due to mismatches in time response of temperature and conductivity probes or the thermal inertia of the conductivity cells.
However, to avoid spurious inversions, density should be used when salinity is the stratifying agent or different water masses are present. Furthermore a threshold for the corresponding variable should carefully be chosen to ignore overturn events associated with the noise. In our application of Thorpe scale analysis we will use 1-m averaged individual casts. We deliberately avoid using 1h gridded data to get the best estimate associated with observed density overturns. The 1-m finite differences of density profiles and potential temperature profiles are analyzed to detect a threshold for noise (Figs. 19- 20). A very conservative choice is 0.05 K for temperature and 0.005 kg/m3 for density, corresponding approximately to twice the rms of each record. Displacements associated with fluctuation values less than these thresholds are set to zero. We estimated Thorpe scales and associated mixing using both θ and σθ (Fig. 21). LT are calculated as rms of non-zero Thorpe displacements over 32-m length segments, to be consistent with the P95 model. The buoyancy frequency, N, is calculated over each 32-m bin from the reordered, gravitationally stable density profiles. Then ε and Kρ are computed using c = 0.8 and Γ = 0.2. The mixing parameters inferred from Thorpe scale analysis of density profiles are presented in Fig. 22 (those from temperature profiles yield comparable values). Because of the large threshold to determine an overturning event only enhanced mixing patches are captures. Values of diffusivity less than about 10-4 m2/s are not resolved. Because this method is independent from any internal wave periodicity, estimates are not averaged in time. The values derived from the P95 model and the Thorpe scale analysis compare well qualitatively (and also quantitatively when individual patches of high mixing are averaged and smoothed out in daily representation as it is in P95).
0 0.5 1 1.5 2 2.5 3 x 105
−0.1
−0.05 0 0.05 0.1
∆σθ (kg m−3 )
0 0.5 1 1.5 2 2.5 3
x 105
−1
−0.5 0 0.5
∆θ (°C)
Data point
Figure 19. 1-m differences of 1-m averaged (upper panel) density profiles and (lower panel) potential temperature profiles. Red-line envelope the threshold (∼ 2 times the rms value over all occurrences) attributed to the noise for Thorpe scale calculations. All individual profiles of Period I are used.
−6 −4 −2 0
0 0.5 1 1.5 2 2.5
3x 104
↓
log10(|∆σθ|) (kg m−3)
Number of occurences
−6 −4 −2 0
0 0.5 1 1.5 2 2.5x 104
↓
log10(|∆θ|) (°C)
Figure 20. Histogram of (log10) absolute value of (left) density differences and (right) potential temperature differences of 1-m averaged individual profiles. The arrows show the corresponding thresholds selected for Thorpe scale calculations.
LT (m)
0 4 8 12 16 20 200
300 400 500 600
Depth (m)
LT using σθ profiles
LT (m)
0 4 8 12 16 20
12/13 12/20 12/27 01/03 01/10
200 300 400 500 600
Depth (m)
LT using θ profiles
Date (mm/dd)
Figure 21. Thorpe scales calculated as rms of Thorpe displacements over 32-m length windows using (upper panel) density profiles (lower panel) potential temperature profiles. The red curve in each panel is the depth of the σθ = 27.75, shown for reference.
ε (W/kg)
−9.5 −9
−8.5 −8
−7.5 −7
−6.5 −6 200
300 400 500 600
Depth (m)
Kρ (m2/s)
−4.5 −4
−3.5 −3
−2.5 −2
−1.5
12/13 12/20 12/27 01/03 01/10
200 300 400 500 600
Depth (m)
Date (mm/dd)
Figure 22. (upper panel) Dissipation and (lower panel) vertical diffusivity derived from Thorpe scales calculated via density profiles. The parameters are inferred at 32-m segments for each individual casts of MMP (over Period I). The values in the colorbar are in log10. The red curve in each panel is the depth of the σθ = 27.75, shown for reference.
9. Concluding remarks
The MMP profiler system returned a unique data set that allows for examination of vertical wavenumber and frequency domain (of both the CTD and horizontal velocity) simultaneously. The sampling strategy greatly overcomes the undersampling issue inherent in conventional hydrographic time series, albeit the geographical undersampling remains (one mooring location). The profiler allows estimates to be made of important non-dimensional parameters, such as the Richardson number, shear-to-strain ratio and density ratio, over many tidal cycles and over a large portion of the water column.
The additional Andereaa RCM current meter record lends confidence on the MMP current record. Inferred time series averaged over the bottom 50-m portion of the MMP profiling range are contrasted to the RCM current time series at ∼130 m below the MMP. The correlation was found to be significant.
The Atlantic Water- Arctic Intermediate Water interface is severely displaced (O(100 m)) by the passage of several cyclones throughout the recording period. A first order mechanism is observed in which the change in sea level gradient induced by the Ekman transport is compensated for by displacement of the interface.
Mixing is inferred using two independent methods. The non-linear internal wave interaction model utilizing shear-strain vertical wavenumber structure leads to values of vertical diffusivity (at the AW-AIW interface) an order of magnitude larger than typical open-ocean values. There was no clear evidence suggestive of the spring-neap cycle dependency. The survey-average vertical profile of shear variance follows the stability profile. This suggests a scaling by internal wave and supports the mixing estimates inferred from the internal-wave field. The second method provides estimates of mixing from density overturns detected with significant confidence. Due to the inherent noise in density calculations, only events with large eddy diffusivities can be resolved. Results from both methods compare favorably.
References
Dillon, T.M., 1982. Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 9601-9613.
Garrett, C.J. and W.H. Munk, 1972. Space-time scales of internal waves. Geophys. Fluid Dyn., 2, 225-264.
Gill, A.E., and H. Schumann, 1974), The generation of long shelf waves by wind, J.
Phys. Oceanogr., 4, 83-90.
Gregg, M.C., 1989. Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94, 9686-9698.
Gregg, M.C., T.B. Sanford and D.P. Winkel, 2003. Reduced mixing from the breaking of internal waves in equatorial waters. Nature, 422, 512-515.
Helland-Hansen, B., and F. Nansen, 1909, The Norwegian Sea: Its Physical Oceanography based upon Norwegian Research 1900-1904, Part 1, No. 2, Fiskeridir. Skr. Ser. Havunders., Vol.3, 390pp
Holbrook, W.S. and I. Fer, 2005, Ocean internal wave spectra inferred from seismic reflection transects. Geophys. Res. Lett., in press.
Kunze, E., L.K. Rosenfeld, G.S. Carter and M.C. Gregg, 2002. Internal waves in Monterey submarine canyon. J. Phys. Oceanogr., 32, 1890-1913.
Leaman, K.D. and T.B. Sanford, 1975. Vertical energy propagation of inertial waves: A vector spectral analysis of velocity profiles. J. Geophys. Res., 80, 1975-1978.
Levine, M.D., C.A. Paulson and J.H. Morison, 1985. Internal waves in the Arctic Ocean:
Comparison with lower-latitude observations. J. Phys. Oceanogr., 15, 800-809.
Millard, R.C., W.B. Owens and N.P. Fofonoff, 1990. On the calculation of the Brunt- Väisäla frequency. Deep-Sea Res., 37, 167-181.
Mork, K.A., and J. Blindheim, 2000, Variations of the Atlantic inflow to the Nordic Seas, 1955-1996. Deep-Sea Res., I, 47, 1035-1047.
Moum, J.N., 1996. Efficiency of mixing in the main thermocline. J. Geophys. Res., 101, 12,057-12,069.
Naveira Garabato, A.C., K.I.C. Oliver, A.J. Watson and M.-J. Messias, 2004a. Turbulent dipaycnal mixing in the Nordic Seas. J. Geophys. Res., 109, C12010,
doi:10.1029/2004JC002411.
Naveira Garabato, A.C., K.L. Polzin, B.A. King, K.J. Heywood and M. Visbeck, 2004b.
Widespread intense turbulent mixing in the Southern Ocean. Science, 303, 210- 213.
Orvik, K.A., Ø. Skagseth, and M. Mork, 2001, Atlantic inflow to the Nordic Seas.
Current structure and volume fluxes from moored current meters, VM-ADCP and SeaSoar-CTD observations, Deep-Sea Res. I, 48, 937-957.
Osborn, T.R., 1980. Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 83-89.
Ozmidov, R.V., 1965. On the turbulent exchange in a stably stratified ocean.
Atmos.Oceanic Phys., 8, 853-860.
Polzin, K.L., J.M. Toole and R.W. Schmitt, 1995. Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr., 25, 306-328.
Skagseth, Ø., K.A. Orvik and T. Furevik, 2004, Coherent variability of the Norwegian Atlantic Slope Current derived from TOPEX/ERS altimeter data. Geophys. Res.
Let., 31, L14304, doi:1029/2004GL020057
Thorpe, S.A., 1977. Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond.
A, 286, 125-181.
Vikebø, F., J. Berntsen and G. Furnes (2004) Numerical studies of current responses at Ormen Lange to a travelling storm, J. Mar. Syst., 45, 205-220
Yttervik, R., and G. Furnes ( 2005) Current measurements on the continental slope west of Norway in an area with a pronounced two-layer profile, Deep-Sea Res., I, 52, 161-178