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Abstract
Surface expressions of internal tides constitute a significant component of the total recorded tide. The internal component is strongly modulated by the time-variable density structure, and the resulting perturbation of the recorded tide gives a welcome look at twentieth-century interannual and secular variability. Time series of mean sea level h SL(t) and total recorded M 2 vector a TT(t) are extracted from the Honolulu 1905–2000 and Hilo 1947–2000 (Hawaii) tide records. Internal tide parameters are derived from the intertidal continuum surrounding the M 2 frequency line and from a Cartesian display of a TT(t), yielding a ST = 16.6 and 22.1 cm, a IT = 1.8 and 1.0 cm for surface and internal tides at Honolulu and Hilo, respectively. The proposed model a TT(t) = a ST + a IT cosθ IT(t) is of a phase-modulated internal tide generated by the surface tide at some remote point and traveling to the tide gauge with velocity modulated by the underlying variable density structure. Mean sea level h SL(t) [a surrogate for the density structure and hence for θ IT(t)] is coherent with a IT(t) within the decadal band 0.2–0.5 cycles per year. For both the decadal band and the century drift the recorded M 2 amplitude is high when sea level is high, according to δ a TT = O(0.1δh SL). The authors attribute the recorded secular increase in the Honolulu M 2 amplitude from a TT = 16.1 to 16.9 cm between 1915 and 2000 to a 28° rotation of the internal tide vector in response to ocean warming.
Abstract
Surface expressions of internal tides constitute a significant component of the total recorded tide. The internal component is strongly modulated by the time-variable density structure, and the resulting perturbation of the recorded tide gives a welcome look at twentieth-century interannual and secular variability. Time series of mean sea level h SL(t) and total recorded M 2 vector a TT(t) are extracted from the Honolulu 1905–2000 and Hilo 1947–2000 (Hawaii) tide records. Internal tide parameters are derived from the intertidal continuum surrounding the M 2 frequency line and from a Cartesian display of a TT(t), yielding a ST = 16.6 and 22.1 cm, a IT = 1.8 and 1.0 cm for surface and internal tides at Honolulu and Hilo, respectively. The proposed model a TT(t) = a ST + a IT cosθ IT(t) is of a phase-modulated internal tide generated by the surface tide at some remote point and traveling to the tide gauge with velocity modulated by the underlying variable density structure. Mean sea level h SL(t) [a surrogate for the density structure and hence for θ IT(t)] is coherent with a IT(t) within the decadal band 0.2–0.5 cycles per year. For both the decadal band and the century drift the recorded M 2 amplitude is high when sea level is high, according to δ a TT = O(0.1δh SL). The authors attribute the recorded secular increase in the Honolulu M 2 amplitude from a TT = 16.1 to 16.9 cm between 1915 and 2000 to a 28° rotation of the internal tide vector in response to ocean warming.
Abstract
This study summarizes results of an analysis of the TOGA drifting buoy observations in the Southern Hemisphere. The data were first quality controlled for gross errors and then screened against climatology and products from national weather centers. The characteristic space scales of the SLP, SST, and air temperature fields for the summer months of December, January, and February, and the winter months of June, July, and August were determined next. Typical decorrelation distances for all fields were between 1200–2800 km with the correlations being generally isotropic. This information suggests that roughly 30–40 fully functional buoys evenly distributed over the southern oceans from 15° to 60°S should be able to resolve the major scales of Southern Hemisphere climate change.
Abstract
This study summarizes results of an analysis of the TOGA drifting buoy observations in the Southern Hemisphere. The data were first quality controlled for gross errors and then screened against climatology and products from national weather centers. The characteristic space scales of the SLP, SST, and air temperature fields for the summer months of December, January, and February, and the winter months of June, July, and August were determined next. Typical decorrelation distances for all fields were between 1200–2800 km with the correlations being generally isotropic. This information suggests that roughly 30–40 fully functional buoys evenly distributed over the southern oceans from 15° to 60°S should be able to resolve the major scales of Southern Hemisphere climate change.
Abstract
An attempt is made to quantify the impact of stochastic wave–induced shears on salt fingers associated with internal waves in the ocean. The wave environment is represented by the superposition of Fourier components conforming to the Garrett–Munk (GM) spectrum with random initial phase distribution. The resulting time series of vertical shear are incorporated into a finger-resolving numerical model, and the latter is used to evaluate the equilibrium diapycnal fluxes of heat and salt. The proposed procedure makes it possible to simulate salt fingers in shears that are representative of typical oceanic conditions. This study finds that the shear-induced modification of salt fingers is largely caused by near-inertial motions. These relatively slow waves act to align salt fingers in the direction of shear, thereby rendering the double-diffusive dynamics effectively two-dimensional. Internal waves reduce the equilibrium vertical fluxes of heat and salt by a factor of 2 relative to those in the unsheared three-dimensional environment, bringing them close to the values suggested by corresponding two-dimensional simulations.
Abstract
An attempt is made to quantify the impact of stochastic wave–induced shears on salt fingers associated with internal waves in the ocean. The wave environment is represented by the superposition of Fourier components conforming to the Garrett–Munk (GM) spectrum with random initial phase distribution. The resulting time series of vertical shear are incorporated into a finger-resolving numerical model, and the latter is used to evaluate the equilibrium diapycnal fluxes of heat and salt. The proposed procedure makes it possible to simulate salt fingers in shears that are representative of typical oceanic conditions. This study finds that the shear-induced modification of salt fingers is largely caused by near-inertial motions. These relatively slow waves act to align salt fingers in the direction of shear, thereby rendering the double-diffusive dynamics effectively two-dimensional. Internal waves reduce the equilibrium vertical fluxes of heat and salt by a factor of 2 relative to those in the unsheared three-dimensional environment, bringing them close to the values suggested by corresponding two-dimensional simulations.
Abstract
Moored observations of temperature and current were collected on the inner continental shelf off Point Sal, California, between 9 June and 8 August 2015. The measurements consist of 10 moorings in total: 4 moorings each on the 50- and 30-m isobaths covering a 10-km along-shelf distance and an across-shelf section of moorings on the 50-, 40-, 30-, and 20-m isobaths covering a 5-km distance. Energetic, highly variable, and strongly dissipating transient wave events termed internal tide bores and internal solitary waves (ISWs) dominate the records. Simple models of the bore and ISW space–time behavior are implemented as a temperature match filter to detect events and estimate wave packet parameters as a function of time and mooring position. Wave-derived quantities include 1) group speed and direction; 2) time of arrival, time duration, vertical displacement amplitude, and waves per day; and 3) energy density, energy flux, and propagation loss. In total, over 1000 bore events and over 9000 ISW events were detected providing well-sampled statistical distributions. Statistics of the waves are rather insensitive to position along shelf but change markedly in the across-shelf direction. Two compelling results are 1) that the probability density functions for bore and ISW energy flux are nearly exponential, suggesting the importance of interference and 2) that wave propagation loss is proportional to energy flux, thus giving an exponential decay of energy flux toward shore with an e-folding scale of 2–2.4 km and average dissipation rates for bores and ISWs of 144 and 1.5 W m−1, respectively.
Abstract
Moored observations of temperature and current were collected on the inner continental shelf off Point Sal, California, between 9 June and 8 August 2015. The measurements consist of 10 moorings in total: 4 moorings each on the 50- and 30-m isobaths covering a 10-km along-shelf distance and an across-shelf section of moorings on the 50-, 40-, 30-, and 20-m isobaths covering a 5-km distance. Energetic, highly variable, and strongly dissipating transient wave events termed internal tide bores and internal solitary waves (ISWs) dominate the records. Simple models of the bore and ISW space–time behavior are implemented as a temperature match filter to detect events and estimate wave packet parameters as a function of time and mooring position. Wave-derived quantities include 1) group speed and direction; 2) time of arrival, time duration, vertical displacement amplitude, and waves per day; and 3) energy density, energy flux, and propagation loss. In total, over 1000 bore events and over 9000 ISW events were detected providing well-sampled statistical distributions. Statistics of the waves are rather insensitive to position along shelf but change markedly in the across-shelf direction. Two compelling results are 1) that the probability density functions for bore and ISW energy flux are nearly exponential, suggesting the importance of interference and 2) that wave propagation loss is proportional to energy flux, thus giving an exponential decay of energy flux toward shore with an e-folding scale of 2–2.4 km and average dissipation rates for bores and ISWs of 144 and 1.5 W m−1, respectively.
Abstract
The inner shelf is a region inshore of that part of the shelf that roughly obeys Ekman dynamics and offshore of the surf zone. Importantly, this is where surface and bottom boundary layers are in close proximity, overlap, and interact. The internal tide carries a substantial amount of energy into the inner shelf region were it eventually dissipates and contributes to mixing. A part of this energy transformation is due to a complex interaction with the bottom, where distinctions between nonlinear internal waves of depression and elevation are blurred, indeed, where polarity reversals of incoming waves take place. From an intensive set of measurements over the inner shelf off central California, we identify salient differences between onshore pulses from waves with properties of elevation waves and offshore pulses from shallowing depression waves. While the velocity structures and amplitudes of on/offshore pulses 1 m above the seafloor are not detectably different, onshore pulses are both more energetically turbulent and carry more sediments than offshore pulses. Their turbulence is also oppositely skewed: onshore pulses slightly to the leading edges, offshore pulses to the trailing edges of the pulses. We consider in turn three independent mechanisms that may contribute to the observed asymmetry: propagation in adverse pressure gradients and the resultant inflection point instability, residence time of a fluid parcel in the pulse, and turbulence suppression by stratification. The first mechanism may largely explain higher turbulence in the trailing edge of offshore pulses. The extended residence time may be responsible for the high and more uniform turbulence distribution across onshore compared to offshore pulses. Stratification does not play a leading role in turbulence modification inside of the pulses 1 m above the bed.
Abstract
The inner shelf is a region inshore of that part of the shelf that roughly obeys Ekman dynamics and offshore of the surf zone. Importantly, this is where surface and bottom boundary layers are in close proximity, overlap, and interact. The internal tide carries a substantial amount of energy into the inner shelf region were it eventually dissipates and contributes to mixing. A part of this energy transformation is due to a complex interaction with the bottom, where distinctions between nonlinear internal waves of depression and elevation are blurred, indeed, where polarity reversals of incoming waves take place. From an intensive set of measurements over the inner shelf off central California, we identify salient differences between onshore pulses from waves with properties of elevation waves and offshore pulses from shallowing depression waves. While the velocity structures and amplitudes of on/offshore pulses 1 m above the seafloor are not detectably different, onshore pulses are both more energetically turbulent and carry more sediments than offshore pulses. Their turbulence is also oppositely skewed: onshore pulses slightly to the leading edges, offshore pulses to the trailing edges of the pulses. We consider in turn three independent mechanisms that may contribute to the observed asymmetry: propagation in adverse pressure gradients and the resultant inflection point instability, residence time of a fluid parcel in the pulse, and turbulence suppression by stratification. The first mechanism may largely explain higher turbulence in the trailing edge of offshore pulses. The extended residence time may be responsible for the high and more uniform turbulence distribution across onshore compared to offshore pulses. Stratification does not play a leading role in turbulence modification inside of the pulses 1 m above the bed.
Abstract
Cross-shore heat flux (CHF) spatiotemporal variability in the subtidal (ST), diurnal (DU), and semidiurnal (SD) bands is described for 35 days (summer 2015) from collocated vertical measures of temperature and currents obtained by moorings deployed from 50- to 7-m water depths near Pt. Sal, California. The CHF is largest in the ST and SD bands, with nearly zero contribution in the DU band. The sum of CHF and surface heat flux (SHF) account for 31% and 17% of the total change in heat storage on the midshelf and inner shelf, respectively. The ST CHF for the midshelf and inner shelf is mostly negative and is correlated with upwelling-favorable winds. A mostly positive SD CHF on the midshelf and inner shelf decreases linearly in the shoreward direction, is correlated with wind relaxations, and is attributed to warm-water internal tidal bores (WITBs) that are observed to propagate to the edge of the surf zone. A negative SD CHF is correlated with upwelling-favorable winds on the midshelf at 15–25-h time lags, and is believed to be associated with cold-water internal tidal bores. The WITBs have characteristics of progressive waves on the midshelf and transition to partially standing waves on the inner shelf potentially reducing the SD CHF contribution on the inner shelf. Heat accumulation over the midshelf and inner shelf is primarily driven by WITBs and SHF, which is largely balanced by cumulative cooling by ST processes over the midshelf and cumulative cooling by alongshore heat flux (AHF) over the inner shelf.
Abstract
Cross-shore heat flux (CHF) spatiotemporal variability in the subtidal (ST), diurnal (DU), and semidiurnal (SD) bands is described for 35 days (summer 2015) from collocated vertical measures of temperature and currents obtained by moorings deployed from 50- to 7-m water depths near Pt. Sal, California. The CHF is largest in the ST and SD bands, with nearly zero contribution in the DU band. The sum of CHF and surface heat flux (SHF) account for 31% and 17% of the total change in heat storage on the midshelf and inner shelf, respectively. The ST CHF for the midshelf and inner shelf is mostly negative and is correlated with upwelling-favorable winds. A mostly positive SD CHF on the midshelf and inner shelf decreases linearly in the shoreward direction, is correlated with wind relaxations, and is attributed to warm-water internal tidal bores (WITBs) that are observed to propagate to the edge of the surf zone. A negative SD CHF is correlated with upwelling-favorable winds on the midshelf at 15–25-h time lags, and is believed to be associated with cold-water internal tidal bores. The WITBs have characteristics of progressive waves on the midshelf and transition to partially standing waves on the inner shelf potentially reducing the SD CHF contribution on the inner shelf. Heat accumulation over the midshelf and inner shelf is primarily driven by WITBs and SHF, which is largely balanced by cumulative cooling by ST processes over the midshelf and cumulative cooling by alongshore heat flux (AHF) over the inner shelf.
Automated Detection, Classification, and Tracking of Internal Wave Signatures Using X-Band Radar in the Inner ShelfAbstract
A method based on machine learning and image processing techniques has been developed to track the surface expression of internal waves in near–real time. X-band radar scans are first preprocessed and averaged to suppress surface wave clutter and enhance the signal-to-noise ratio of persistent backscatter features driven by gradients in surface currents. A machine learning algorithm utilizing a support vector machine (SVM) model is then used to classify whether or not the image contains an internal solitary wave (ISW) or internal tide bore (bore). The use of machine learning is found to allow rapid assessment of the large dataset, and provides insight on characterizing optimal environmental conditions to allow for radar illumination and detection of ISWs and bores. Radon transforms and local maxima detections are used to locate these features within images that are determined to contain an ISW or bore. The resulting time series of locations is used to create a map of propagation speed and direction that captures the spatiotemporal variability of the ISW or bore in the coastal environment. This technique is applied to 2 months of data collected near Point Sal, California, and captures ISW and bore propagation speed and direction information that currently cannot be measured with instruments such as moorings and synthetic aperture radar (SAR).
Abstract
A method based on machine learning and image processing techniques has been developed to track the surface expression of internal waves in near–real time. X-band radar scans are first preprocessed and averaged to suppress surface wave clutter and enhance the signal-to-noise ratio of persistent backscatter features driven by gradients in surface currents. A machine learning algorithm utilizing a support vector machine (SVM) model is then used to classify whether or not the image contains an internal solitary wave (ISW) or internal tide bore (bore). The use of machine learning is found to allow rapid assessment of the large dataset, and provides insight on characterizing optimal environmental conditions to allow for radar illumination and detection of ISWs and bores. Radon transforms and local maxima detections are used to locate these features within images that are determined to contain an ISW or bore. The resulting time series of locations is used to create a map of propagation speed and direction that captures the spatiotemporal variability of the ISW or bore in the coastal environment. This technique is applied to 2 months of data collected near Point Sal, California, and captures ISW and bore propagation speed and direction information that currently cannot be measured with instruments such as moorings and synthetic aperture radar (SAR).
Abstract
We present observations of shoaling nonlinear internal bores off the coast of central California. The dataset includes 15 moorings deployed during September–October 2017 and cross-shore shipboard surveys. We describe the cross-shore structure and evolution of large-amplitude internal bores as they transit from 9 km (100-m depth) to 1 km offshore (10 m). We observe that two bores arrive each semidiurnal period, both propagating from the southwest; of the total, 72% are tracked to the 10-m isobath. The bore speeds are subtidally modulated, but there is additional bore-to-bore speed variability that is unexplained by the upstream stratification. We quantify temporal and cross-shore variability of the waveguide (the background conditions through which bores propagate) by calculating the linear longwave nonrotating phase speed c o and using the nonlinearity coefficient of the Korteweg–de Vries equation α as a metric for stratification. Bore fronts are generally steeper when α is positive and are more rarefied when α is negative, and we observe the bore’s leading edge to rarefy from a steep front when α is positive offshore and negative inshore. High-frequency α fluctuations, such as those nearshore driven by wind relaxations, contribute to bore-to-bore variability of the cross-shore evolution during similar subtidal waveguide conditions. We compare observed bore speeds with c o and the rotating group velocities c g , concluding that observed speeds are always faster than c g and are slower than c o at depths greater than 32 m and faster than c o at depths of less than 32 m. The bores maintain a steady speed while transiting into shallower water, contrary to linear estimates that predict bores to slow.
Abstract
We present observations of shoaling nonlinear internal bores off the coast of central California. The dataset includes 15 moorings deployed during September–October 2017 and cross-shore shipboard surveys. We describe the cross-shore structure and evolution of large-amplitude internal bores as they transit from 9 km (100-m depth) to 1 km offshore (10 m). We observe that two bores arrive each semidiurnal period, both propagating from the southwest; of the total, 72% are tracked to the 10-m isobath. The bore speeds are subtidally modulated, but there is additional bore-to-bore speed variability that is unexplained by the upstream stratification. We quantify temporal and cross-shore variability of the waveguide (the background conditions through which bores propagate) by calculating the linear longwave nonrotating phase speed c o and using the nonlinearity coefficient of the Korteweg–de Vries equation α as a metric for stratification. Bore fronts are generally steeper when α is positive and are more rarefied when α is negative, and we observe the bore’s leading edge to rarefy from a steep front when α is positive offshore and negative inshore. High-frequency α fluctuations, such as those nearshore driven by wind relaxations, contribute to bore-to-bore variability of the cross-shore evolution during similar subtidal waveguide conditions. We compare observed bore speeds with c o and the rotating group velocities c g , concluding that observed speeds are always faster than c g and are slower than c o at depths greater than 32 m and faster than c o at depths of less than 32 m. The bores maintain a steady speed while transiting into shallower water, contrary to linear estimates that predict bores to slow.
Abstract
Broadly distributed measurements of velocity, density, and turbulence spanning the inner shelf off central California indicate that (i) the average shoreward-directed internal tide energy flux
Abstract
Broadly distributed measurements of velocity, density, and turbulence spanning the inner shelf off central California indicate that (i) the average shoreward-directed internal tide energy flux
Abstract
Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨F E ⟩, and energy flux divergence ∂ x ⟨F E ⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂ x ⟨F E ⟩, we also interpret our estimate of ∂ x ⟨F E ⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨F E ⟩, and ∂ x ⟨F E ⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.
Abstract
Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨F E ⟩, and energy flux divergence ∂ x ⟨F E ⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂ x ⟨F E ⟩, we also interpret our estimate of ∂ x ⟨F E ⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨F E ⟩, and ∂ x ⟨F E ⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.
