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- Author or Editor: Colin Y. Shen x

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## Abstract

It is shown that each term that represents vorticity flux convergence or divergence in the quasigeostrophic potential vorticity equation can be inverted to obtain fluid acceleration associated with that term, and the same can be obtained for the vortex stretching term. The computed acceleration in the form of a “force potential” shows precisely how the process given by each vorticity term changes the flow field and contributes to its evolution, such as formation and propagation of current features. This complements the standard vorticity diagnostic, which evaluates the magnitudes of the terms only. Application to some simple unstable flows is presented.

## Abstract

It is shown that each term that represents vorticity flux convergence or divergence in the quasigeostrophic potential vorticity equation can be inverted to obtain fluid acceleration associated with that term, and the same can be obtained for the vortex stretching term. The computed acceleration in the form of a “force potential” shows precisely how the process given by each vorticity term changes the flow field and contributes to its evolution, such as formation and propagation of current features. This complements the standard vorticity diagnostic, which evaluates the magnitudes of the terms only. Application to some simple unstable flows is presented.

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## Abstract

The Boussinesq long-wave equations in constituent form are generalized to encompass both the irrotational long-wave dynamics and the rotational current dynamics. For irrotational long waves, the generalized equations are shown to represent both the weakly nonlinear and fully nonlinear Boussinesq-type wave equations given previously in the literature. The generalized equations are of additional interest in that they are effectively model equations for a weakly nonhydrostatic wave/current system, in which the conventional hydrostatic ocean current/wave model is a limiting case. The derived equations are related to the surface flow variables that are accessible to synoptic surface wave/current measurements such as those available from radar remote sensing.

## Abstract

The Boussinesq long-wave equations in constituent form are generalized to encompass both the irrotational long-wave dynamics and the rotational current dynamics. For irrotational long waves, the generalized equations are shown to represent both the weakly nonlinear and fully nonlinear Boussinesq-type wave equations given previously in the literature. The generalized equations are of additional interest in that they are effectively model equations for a weakly nonhydrostatic wave/current system, in which the conventional hydrostatic ocean current/wave model is a limiting case. The derived equations are related to the surface flow variables that are accessible to synoptic surface wave/current measurements such as those available from radar remote sensing.

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## Abstract

The seasonal thermocline in the Sargasso Sea near 30°45′N, 71°45′W was measured in July 1981 using a towed thermistor army with ∼0.5 m horizontal and vertical resolution. A 200-km long section of the survey path is analyzed for overturn occurrences and the relationship of these occurrences to the ambient flow field. Our analysis shows that the probability of an overturn occurrences increases when the Richardson number of the ambient field decreases. This increase is most rapid when the Richardson number is of order unity. Our assessment of overturn processes based on calculated conditional probabilities indicates that both sheer instability and advective instability are important to the generation of the overtures observed in our experiment while the symmetric instability is not.

## Abstract

The seasonal thermocline in the Sargasso Sea near 30°45′N, 71°45′W was measured in July 1981 using a towed thermistor army with ∼0.5 m horizontal and vertical resolution. A 200-km long section of the survey path is analyzed for overturn occurrences and the relationship of these occurrences to the ambient flow field. Our analysis shows that the probability of an overturn occurrences increases when the Richardson number of the ambient field decreases. This increase is most rapid when the Richardson number is of order unity. Our assessment of overturn processes based on calculated conditional probabilities indicates that both sheer instability and advective instability are important to the generation of the overtures observed in our experiment while the symmetric instability is not.

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## Abstract

Observations of mesoscale ocean eddies from the 1973 Mid-Ocean Dynamics Experiment (MODE) are used to calculate, by objective analysis, the modal coefficients, which are functions of horizontal position and time, in a representation based on the two most energetic vertical modes—the barotropic and first baroclinic. The gross energy levels associated with these modes are calculated and found to be generally consistent with previous estimates. Modal coupling statistics are also estimated: these are the volume integral modal energy exchange rate and the spatially lagged covariances between modal streamfunction and velocity fields. The former is found to be approximately zero and the latter have significant extrema at lag distances comparable to an eddy radius. Furthermore, the dominant contribution to these coupling signals comes from the time-averaged (over a little more than two months) mesoscale field, which from lengthy moored observations we can identify as an instantaneous realization of the very low frequency “secular scale” described by Schmitz (1978). Forecasts from this observational representation in a two-mode, quasi-geostrophic numerical model with no horizontal energy flux into the region of interest (an extreme statement of our observational ignorance of mesoscale processes outside the MODE region) consistently fail to preserve either these covariance relations or the secular scale mesoscale component for any significant time, with a possible exception of the zero energy transfer rate in a small ]∼(100 km)^{2}[, data dense region for a brief time (∼10–15 days). Since these forecast failures occur on a time short compared to a turbulent predictability time, it is proposed that a missing, and observationally undocumented, process of exterior influence (such as radiation from the Gulf Stream region) is probably required to adequately model the mesoscale modal coupling in the MODE region.

## Abstract

Observations of mesoscale ocean eddies from the 1973 Mid-Ocean Dynamics Experiment (MODE) are used to calculate, by objective analysis, the modal coefficients, which are functions of horizontal position and time, in a representation based on the two most energetic vertical modes—the barotropic and first baroclinic. The gross energy levels associated with these modes are calculated and found to be generally consistent with previous estimates. Modal coupling statistics are also estimated: these are the volume integral modal energy exchange rate and the spatially lagged covariances between modal streamfunction and velocity fields. The former is found to be approximately zero and the latter have significant extrema at lag distances comparable to an eddy radius. Furthermore, the dominant contribution to these coupling signals comes from the time-averaged (over a little more than two months) mesoscale field, which from lengthy moored observations we can identify as an instantaneous realization of the very low frequency “secular scale” described by Schmitz (1978). Forecasts from this observational representation in a two-mode, quasi-geostrophic numerical model with no horizontal energy flux into the region of interest (an extreme statement of our observational ignorance of mesoscale processes outside the MODE region) consistently fail to preserve either these covariance relations or the secular scale mesoscale component for any significant time, with a possible exception of the zero energy transfer rate in a small ]∼(100 km)^{2}[, data dense region for a brief time (∼10–15 days). Since these forecast failures occur on a time short compared to a turbulent predictability time, it is proposed that a missing, and observationally undocumented, process of exterior influence (such as radiation from the Gulf Stream region) is probably required to adequately model the mesoscale modal coupling in the MODE region.

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## Abstract

A time-dependent physical model whose initial condition is only approximately known can predict the evolving physical state to only within certain error bounds. In the prediction of weather, as well as its ocean counterpart, quantifying this uncertainty or the predictability is of critical importance because such quantitative knowledge is needed to provide limits on the forecast accuracy. Monte Carlo simulation, the accepted standard for uncertainty determination, is impractical to apply to the atmospheric and ocean models, particularly in an operational setting, because of these models’ high degrees of freedom and computational demands. Instead, methods developed in the literature have relied on a limited ensemble of simulations, selected from initial errors that are likely to have grown the most at the forecast time. In this paper, the authors present an alternative approach, the polynomial chaos method, to the quantification of the growth of uncertainty. The method seeks to express the initial errors in functional form in terms of stochastic basis expansions and solve for the uncertainty growth directly from the equations of motion. It is shown via a Lorenz model that the resulting solution can provide all the error statistics as in Monte Carlo simulation but requires much less computation. Moreover, it is shown that the functional form of the solution facilitates the uncertainty analysis. This is discussed in detail for the tangent linear case of interest to ensemble forecasting. The relevance of the uncertainty covariance result to data assimilation is also noted.

## Abstract

A time-dependent physical model whose initial condition is only approximately known can predict the evolving physical state to only within certain error bounds. In the prediction of weather, as well as its ocean counterpart, quantifying this uncertainty or the predictability is of critical importance because such quantitative knowledge is needed to provide limits on the forecast accuracy. Monte Carlo simulation, the accepted standard for uncertainty determination, is impractical to apply to the atmospheric and ocean models, particularly in an operational setting, because of these models’ high degrees of freedom and computational demands. Instead, methods developed in the literature have relied on a limited ensemble of simulations, selected from initial errors that are likely to have grown the most at the forecast time. In this paper, the authors present an alternative approach, the polynomial chaos method, to the quantification of the growth of uncertainty. The method seeks to express the initial errors in functional form in terms of stochastic basis expansions and solve for the uncertainty growth directly from the equations of motion. It is shown via a Lorenz model that the resulting solution can provide all the error statistics as in Monte Carlo simulation but requires much less computation. Moreover, it is shown that the functional form of the solution facilitates the uncertainty analysis. This is discussed in detail for the tangent linear case of interest to ensemble forecasting. The relevance of the uncertainty covariance result to data assimilation is also noted.

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## Abstract

Acoustic Doppler profiler measurements of inertial waves embedded within the high shell region of a cold core ring in the Sargasso Sea are described. By repeatedly traversing the same point from different directions, a sampling pattern resembling an asterisk was obtained. The data reveal the presence of two different wave signals which are advected through the test region: a strong, monochromatic, downgoing wave, and a less well defined ensemble of mostly downgoing waves. Calculations of the phase of the vertical shear and coherence in the vertical and horizontal planes establishes the horizontal and vertical wavenumbers. These are 33 m and 11.8 km, respectively, and the wave propagates in a nearly cross-stream direction. The weaker ensemble of waves advected through the test region later in the experiment has similar dominant scales: ∼30 m in the vertical and a horizontal wavelength in the range 11.6–30.0 km. For all of these waves, the ratio of vertical to horizontal wavelength is small and the intrinsic frequency is 1.09*f*, so that the waves are of near-inertial frequency. By examining individual terms in the near-inertial ray equations, it is seen that the horizontal crosscurrent variations cause the horizontal wavenumber to be rotated so as to propagate perpendicular to the current. Consideration of the full ray equations for all internal wave frequencies in a barotropic current shows a filtering effect that also preserves waves propagating across the current. Both of these results are consistent with the observation that the waves are propagating nearly cross stream.

## Abstract

Acoustic Doppler profiler measurements of inertial waves embedded within the high shell region of a cold core ring in the Sargasso Sea are described. By repeatedly traversing the same point from different directions, a sampling pattern resembling an asterisk was obtained. The data reveal the presence of two different wave signals which are advected through the test region: a strong, monochromatic, downgoing wave, and a less well defined ensemble of mostly downgoing waves. Calculations of the phase of the vertical shear and coherence in the vertical and horizontal planes establishes the horizontal and vertical wavenumbers. These are 33 m and 11.8 km, respectively, and the wave propagates in a nearly cross-stream direction. The weaker ensemble of waves advected through the test region later in the experiment has similar dominant scales: ∼30 m in the vertical and a horizontal wavelength in the range 11.6–30.0 km. For all of these waves, the ratio of vertical to horizontal wavelength is small and the intrinsic frequency is 1.09*f*, so that the waves are of near-inertial frequency. By examining individual terms in the near-inertial ray equations, it is seen that the horizontal crosscurrent variations cause the horizontal wavenumber to be rotated so as to propagate perpendicular to the current. Consideration of the full ray equations for all internal wave frequencies in a barotropic current shows a filtering effect that also preserves waves propagating across the current. Both of these results are consistent with the observation that the waves are propagating nearly cross stream.

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## Abstract

This work examines the presence of internal-inertial waves in a front in the North Atlantic subtropical convergence zone. Results of Doppler shear profiler and towed thermistor chain surveys are displayed to document the position and magnitude of the front. Objective maps of the total measured velocity are computed and subtracted from the observed velocity fields. The remaining wave signal is processed to yield horizontal (towed) and vertical (dropped) kinetic energy spectra across the front. From these, rotary spectra are also computed along the line of tow and in the vertical to determine the horizontal and vertical anisotropy. It is found that several nearly monochromatic waves are propagating northward and southward from the front with horizontal length scales of ∼32–50 km. It was also discovered that the region of anticyclonic frontal vorticity exhibits an excess of downgoing energy at the longest vertical wavelength thus sampled (∼50 m), while the region of cyclonic vorticity possesses more upgoing than downgoing energy at the same wavelengths. Vertical and horizontal spectra variances of the total kinetic energy within the region of the front am each enhanced by a factor of about five over the variances outside the front. These results are discussed in the light of recent work by Kunze.

## Abstract

This work examines the presence of internal-inertial waves in a front in the North Atlantic subtropical convergence zone. Results of Doppler shear profiler and towed thermistor chain surveys are displayed to document the position and magnitude of the front. Objective maps of the total measured velocity are computed and subtracted from the observed velocity fields. The remaining wave signal is processed to yield horizontal (towed) and vertical (dropped) kinetic energy spectra across the front. From these, rotary spectra are also computed along the line of tow and in the vertical to determine the horizontal and vertical anisotropy. It is found that several nearly monochromatic waves are propagating northward and southward from the front with horizontal length scales of ∼32–50 km. It was also discovered that the region of anticyclonic frontal vorticity exhibits an excess of downgoing energy at the longest vertical wavelength thus sampled (∼50 m), while the region of cyclonic vorticity possesses more upgoing than downgoing energy at the same wavelengths. Vertical and horizontal spectra variances of the total kinetic energy within the region of the front am each enhanced by a factor of about five over the variances outside the front. These results are discussed in the light of recent work by Kunze.

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## Abstract

The seven intensive hydrographic surveys of temperature, salinity and oxygen of the POLYMODE local Dynamics Experiment (LDE) (15 May–15 July 1978) were carded out in a 200 km-wide octagonal region centered at 31°05′N, 69°30′W; this location was within the southern portion of the Gulf Stream Recirculation. The vertical structure of the mean and standard deviations of water properties and physical parameters for the experiment are presented. Comparisons of LDE and climatological statistics at 31°N, 70°W showed that the profiles of mean quantities were not markedly different; however, LDE eddy potential energy in the water column above 2000 m was roughly one-half to one-third the long-term climatological values. There were peaks in variability of salinity on potential density surfaces in the 18°C-water, the midthermocline (850 db) and the lower thermocline (1400 db). The 18°C-peak was associated with a marked bimodal salinity distribution, the midthermocline peak with extreme outliers (positive and negative) on the frequency distribution and the lower thermocline with a positively skewed frequency distribution indicating Mediterranean Sea Water influence. Peaks in oxygen variability were observed at the same levels as for salinity. Examples of small anomalous water masses (outliers) are shown in vertical and horizontal sections. The dynamical fields (pressure of density surfaces, dynamic height) were highly anisotropic with the preferred orientation being in the NE/SW direction. There was evidence of northwest translation of dynamical features at a speed of 4 km d^{−1}; the long horizontal scale of the dynamical features (ridges and troughs or elongated eddies) were not resolved by the experiment. Measurements adjacent to the LDE region indicate that the scale in the NE/SW direction was in excess of 400 km. The last four surveys showed the development of a very strong baroclinic feature (velocity shear > 50 cm s^{−1} between 700 and 1500 db). This jetlike structure, which extended across the survey region, had a gradient (NW/SE direction) with a horizontal able of 100 km. Because of the development of the Strong flow during the period of hydrographic surveys, the results are not typical of the whole period of the experiment; mooring measurements showed that two such events occurred in a 15-month period. There are three major differences between MODE and LDE results: the eddy potential and eddy kinetic energy was 3 to 4 times higher in the LDE; the LDE dynamic height fields were more anisotropic; and them were a number of intense small-scale (horizontal and vertical) property anomalies observed in the LDE that did not have a counterpart in MODE.

## Abstract

The seven intensive hydrographic surveys of temperature, salinity and oxygen of the POLYMODE local Dynamics Experiment (LDE) (15 May–15 July 1978) were carded out in a 200 km-wide octagonal region centered at 31°05′N, 69°30′W; this location was within the southern portion of the Gulf Stream Recirculation. The vertical structure of the mean and standard deviations of water properties and physical parameters for the experiment are presented. Comparisons of LDE and climatological statistics at 31°N, 70°W showed that the profiles of mean quantities were not markedly different; however, LDE eddy potential energy in the water column above 2000 m was roughly one-half to one-third the long-term climatological values. There were peaks in variability of salinity on potential density surfaces in the 18°C-water, the midthermocline (850 db) and the lower thermocline (1400 db). The 18°C-peak was associated with a marked bimodal salinity distribution, the midthermocline peak with extreme outliers (positive and negative) on the frequency distribution and the lower thermocline with a positively skewed frequency distribution indicating Mediterranean Sea Water influence. Peaks in oxygen variability were observed at the same levels as for salinity. Examples of small anomalous water masses (outliers) are shown in vertical and horizontal sections. The dynamical fields (pressure of density surfaces, dynamic height) were highly anisotropic with the preferred orientation being in the NE/SW direction. There was evidence of northwest translation of dynamical features at a speed of 4 km d^{−1}; the long horizontal scale of the dynamical features (ridges and troughs or elongated eddies) were not resolved by the experiment. Measurements adjacent to the LDE region indicate that the scale in the NE/SW direction was in excess of 400 km. The last four surveys showed the development of a very strong baroclinic feature (velocity shear > 50 cm s^{−1} between 700 and 1500 db). This jetlike structure, which extended across the survey region, had a gradient (NW/SE direction) with a horizontal able of 100 km. Because of the development of the Strong flow during the period of hydrographic surveys, the results are not typical of the whole period of the experiment; mooring measurements showed that two such events occurred in a 15-month period. There are three major differences between MODE and LDE results: the eddy potential and eddy kinetic energy was 3 to 4 times higher in the LDE; the LDE dynamic height fields were more anisotropic; and them were a number of intense small-scale (horizontal and vertical) property anomalies observed in the LDE that did not have a counterpart in MODE.

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## Abstract

Dynamical properties examined in this paper are the dynamic height and the pressure on an isopycnal. Scalars are the salinity and the oxygen concentration on an isopycnal. The sea surface temperature and salinity are also examined. These properties are obtained from the spatially uniform and densely sampled hydrographic surveys conducted during a two-month period of the POLYMODE Local Dynamics Experiment in 1978 near 31°N, 69.5°W. The spatial maps of the dynamic height and the pressure of an isopycnal show that the baroclinic current in this area sometimes intensifies to a jetlike flow and at other times has the shape of elongated eddies. The current flows primarily in the NE–SW direction. Westward propagation occurs but varies in time and with depth. Eddies that transport water properties are also observed in this area. The salinity and the oxygen on an isopycnal are found to be correlated with itself and with each other from the surface to the 18°C water layer, within a 200-db range in the thermocline and an ∼400-db range centered near 1500 db. There are periods during which the salinity and the oxygen as well as the sea surface properties are correlated with the near-surface current structure; the correlation is not found at deeper depths. These scalar properties, which are interpreted as tracers, are more vigorously “stirred” in and above the thermocline than below, where the motion is more waveline. The net movement of water mass indicated by these tracers is due west through most of the water column during the period of the experiment.

## Abstract

Dynamical properties examined in this paper are the dynamic height and the pressure on an isopycnal. Scalars are the salinity and the oxygen concentration on an isopycnal. The sea surface temperature and salinity are also examined. These properties are obtained from the spatially uniform and densely sampled hydrographic surveys conducted during a two-month period of the POLYMODE Local Dynamics Experiment in 1978 near 31°N, 69.5°W. The spatial maps of the dynamic height and the pressure of an isopycnal show that the baroclinic current in this area sometimes intensifies to a jetlike flow and at other times has the shape of elongated eddies. The current flows primarily in the NE–SW direction. Westward propagation occurs but varies in time and with depth. Eddies that transport water properties are also observed in this area. The salinity and the oxygen on an isopycnal are found to be correlated with itself and with each other from the surface to the 18°C water layer, within a 200-db range in the thermocline and an ∼400-db range centered near 1500 db. There are periods during which the salinity and the oxygen as well as the sea surface properties are correlated with the near-surface current structure; the correlation is not found at deeper depths. These scalar properties, which are interpreted as tracers, are more vigorously “stirred” in and above the thermocline than below, where the motion is more waveline. The net movement of water mass indicated by these tracers is due west through most of the water column during the period of the experiment.

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## Abstract

Ten anomalous water parcels were detected in the water column of a western Atlantic oceanographic section (0–5550 m; 70°W; 23–33°N). The parcels had extreme properties lying either two standard deviations from historical mean values, or estimated origins lying 2000 km from the oceanographic section. Detection, structure, and origin of the parcels were determined from analyses on isobaric and isopycnal surfaces using eight kinds of measurements temperature, salinity, oxygen, light scattering, silicate, phosphate, nitrate, and tritium.

The parcels originated from seven of the major water masses comprising the North Atlantic Ocean. As observed along the oceanographic section the parcels had the following average (range) characteristics vertical pressure extent = 650 db (100–150 db); horizontal extent = 130 km (30–260 km); and distance to origin = 2300 km (400–5200 km). A population density equaling approximately one parcel per 100 km was obtained as the number of parcels (10) divided by the length of the cruise track (1080 km). This density suggests that 10^{3}–10^{4} parcels may populate the North Atlantic Ocean. The population appears to be sufficiently large that geographic distributions of anomalous water parcels may eventually reveal general circulatory patterns.

## Abstract

Ten anomalous water parcels were detected in the water column of a western Atlantic oceanographic section (0–5550 m; 70°W; 23–33°N). The parcels had extreme properties lying either two standard deviations from historical mean values, or estimated origins lying 2000 km from the oceanographic section. Detection, structure, and origin of the parcels were determined from analyses on isobaric and isopycnal surfaces using eight kinds of measurements temperature, salinity, oxygen, light scattering, silicate, phosphate, nitrate, and tritium.

The parcels originated from seven of the major water masses comprising the North Atlantic Ocean. As observed along the oceanographic section the parcels had the following average (range) characteristics vertical pressure extent = 650 db (100–150 db); horizontal extent = 130 km (30–260 km); and distance to origin = 2300 km (400–5200 km). A population density equaling approximately one parcel per 100 km was obtained as the number of parcels (10) divided by the length of the cruise track (1080 km). This density suggests that 10^{3}–10^{4} parcels may populate the North Atlantic Ocean. The population appears to be sufficiently large that geographic distributions of anomalous water parcels may eventually reveal general circulatory patterns.