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- Author or Editor: T. K. Chereskin x

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## Abstract

A systematic examination of measurement error in acoustic Doppler current profiler (ADCP) velocity estimates, in the limit of large signal-to-noise ratio, is made using a system model and sonar signal simulations coupled into an ADCP. The model is extremely successful in predicting ADCP performance. The signal simulations provide model validation. Three main sources of error are examined: frequency tracking, measurement variance (inherent variance of pulse-to-pulse incoherent volume reverberation), and measurement bias.

A theoretical lower bound on measurement variance is directly tested by coupling simulated signals into an ADCP. The observed measurement variance is approximately twice the theoretical value and varies as the inverse of the product of the pulse and averaging period (bin). Model predictions of velocity errors for back-to-back beam pairs measuring a sequence of increasing velocity-shear profiles in a medium of randomly distributed scatterers are in excellent agreement with errors measured from simulated signals coupled into an ADCP. Trade-offs between velocity error, vertical and temporal resolution, and maximum range are discussed, with specific focus on optimizing parameters available to users of commercial instruments.

For reasonable parameter choices in low velocity-shear ocean conditions, the predicted error in horizontal velocity from effects considered in this study is 1–2 cm s^{−1}. In large-shear conditions, the predicted error using the same parameters as in low shear is much worse, approximately 10 cm s^{−1}. Optimal parameter choices, however, can reduce the error in large-shear conditions to 1–4 cm s^{−1}.

## Abstract

A systematic examination of measurement error in acoustic Doppler current profiler (ADCP) velocity estimates, in the limit of large signal-to-noise ratio, is made using a system model and sonar signal simulations coupled into an ADCP. The model is extremely successful in predicting ADCP performance. The signal simulations provide model validation. Three main sources of error are examined: frequency tracking, measurement variance (inherent variance of pulse-to-pulse incoherent volume reverberation), and measurement bias.

A theoretical lower bound on measurement variance is directly tested by coupling simulated signals into an ADCP. The observed measurement variance is approximately twice the theoretical value and varies as the inverse of the product of the pulse and averaging period (bin). Model predictions of velocity errors for back-to-back beam pairs measuring a sequence of increasing velocity-shear profiles in a medium of randomly distributed scatterers are in excellent agreement with errors measured from simulated signals coupled into an ADCP. Trade-offs between velocity error, vertical and temporal resolution, and maximum range are discussed, with specific focus on optimizing parameters available to users of commercial instruments.

For reasonable parameter choices in low velocity-shear ocean conditions, the predicted error in horizontal velocity from effects considered in this study is 1–2 cm s^{−1}. In large-shear conditions, the predicted error using the same parameters as in low shear is much worse, approximately 10 cm s^{−1}. Optimal parameter choices, however, can reduce the error in large-shear conditions to 1–4 cm s^{−1}.

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## Abstract

A comparison of measured and wind-derived ageostrophic transport is presented from a zonal transect spanning the Atlantic Ocean along 11°N. The transport per unit depth shows a striking surface maximum that decays to nearly zero at a depth of approximately 100 m. We identify this flow in the upper 100 m as the Ekman transport. The sustained values of wind stress and the penetration depth of the Ekman transport reported here are considerably greater than in previous observations, which were made in conditions of light winds. The transport of 12.0 ± 5.5 × 10^{6} m^{3} s^{−1}, calculated from the difference of geostrophic shear and shear measured by an acoustic Doppler current profiler, is in good agreement with that estimated from the shipboard winds, 8.8 ± 1.9 × 10^{6} m^{3} s^{−1}, and from climatology, 13.5 ± 0.3 × 10^{6} m^{3} s^{−1}. Qualitatively, the horizontal distribution of the wind-driven flow was best predicted by the shipboard winds. The cumulative transport increased linearly over the western three-fourths of the basin, where the winds were large and spatially uniform, and remained constant over the eastern fourth where the easterly stress was uncharacteristically low. The mean depth of the Ekman transport extended below the mixed layer depth, which varied from 25 to 90 m. The profile of ageostrophic transport does not appear consonant with slablike behavior in the mixed layer, even when spatial variations in mixed layer depth are taken into account.

## Abstract

A comparison of measured and wind-derived ageostrophic transport is presented from a zonal transect spanning the Atlantic Ocean along 11°N. The transport per unit depth shows a striking surface maximum that decays to nearly zero at a depth of approximately 100 m. We identify this flow in the upper 100 m as the Ekman transport. The sustained values of wind stress and the penetration depth of the Ekman transport reported here are considerably greater than in previous observations, which were made in conditions of light winds. The transport of 12.0 ± 5.5 × 10^{6} m^{3} s^{−1}, calculated from the difference of geostrophic shear and shear measured by an acoustic Doppler current profiler, is in good agreement with that estimated from the shipboard winds, 8.8 ± 1.9 × 10^{6} m^{3} s^{−1}, and from climatology, 13.5 ± 0.3 × 10^{6} m^{3} s^{−1}. Qualitatively, the horizontal distribution of the wind-driven flow was best predicted by the shipboard winds. The cumulative transport increased linearly over the western three-fourths of the basin, where the winds were large and spatially uniform, and remained constant over the eastern fourth where the easterly stress was uncharacteristically low. The mean depth of the Ekman transport extended below the mixed layer depth, which varied from 25 to 90 m. The profile of ageostrophic transport does not appear consonant with slablike behavior in the mixed layer, even when spatial variations in mixed layer depth are taken into account.

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## Abstract

Acoustic Doppler current profiler (ADCP) velocity measurements an subject to bias due to the effect of the signal processing filters on the spectrum of the Doppler-shifted signal and on the noise. Bias will occur when the filter is not centered on the signal. Numerical models of the received signal and the processing filter used in RD Instruments profilers show that biases on the order of 10 cm s^{−1} can occur in the lower half of the current profile in regions of high current shear. Errors tend to increase with the width of the acoustic beam and with the speed of the ship, and decrease with the pulse length. These biases are identified in ADCP velocity measurements made in the high shear of the equatorial undercurrent. We suggest criteria for editing existing ADCP data to remove excessive bias, and we recommend changes in profiler parameters which should greatly reduce the bias in future datasets.

## Abstract

Acoustic Doppler current profiler (ADCP) velocity measurements an subject to bias due to the effect of the signal processing filters on the spectrum of the Doppler-shifted signal and on the noise. Bias will occur when the filter is not centered on the signal. Numerical models of the received signal and the processing filter used in RD Instruments profilers show that biases on the order of 10 cm s^{−1} can occur in the lower half of the current profile in regions of high current shear. Errors tend to increase with the width of the acoustic beam and with the speed of the ship, and decrease with the pulse length. These biases are identified in ADCP velocity measurements made in the high shear of the equatorial undercurrent. We suggest criteria for editing existing ADCP data to remove excessive bias, and we recommend changes in profiler parameters which should greatly reduce the bias in future datasets.

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## Abstract

The shape and slip of freely drifting, two-dimensional, flexible weighted drogues tethered to a surface buoy in a specified upper-ocean velocity profile are examined numerically. A simple analytic solution for a drogue in a linear shear flow, in the limit of small deviations from a straight vertical configuration, is used to identify the parameters of the problem and to predict the functional dependence of the slip and shape of the drogue on those parameters. The numerical computations, using a finite elements static equilibrium model, confirm the functional dependence predicted by the analytic solution and estimate the parametric dependences. However, a linear shear is not the “worst case” shear one needs to design for. In optimizing a drogue for linear shear, one can make use of the symmetry of the velocity profile to minimize the slip. The design problem arises from not knowing a priori the shear for which one is designing (especially since a drogue eventually moves far from its deployment site) and from asymmetric shear (i.e., the “worst case” shear is one with a bias). The final computations examine three different drogue configurations in a series of profiles that model the diurnal cycle of the mixed layer (a diurnal jet) overlying a linear shear. The best design is found to be one that maximizes the drogue over the depth interval of interest, while minimizing the drag area of the tether. The drogue length needs to be larger than the depth interval of interest to account for the rise and tilt of the drogue in shear flow, but not so large that it averages too far outside the interval. For the practical cases considered, a drogue length that was twice the averaging interval gave the best results.

## Abstract

The shape and slip of freely drifting, two-dimensional, flexible weighted drogues tethered to a surface buoy in a specified upper-ocean velocity profile are examined numerically. A simple analytic solution for a drogue in a linear shear flow, in the limit of small deviations from a straight vertical configuration, is used to identify the parameters of the problem and to predict the functional dependence of the slip and shape of the drogue on those parameters. The numerical computations, using a finite elements static equilibrium model, confirm the functional dependence predicted by the analytic solution and estimate the parametric dependences. However, a linear shear is not the “worst case” shear one needs to design for. In optimizing a drogue for linear shear, one can make use of the symmetry of the velocity profile to minimize the slip. The design problem arises from not knowing a priori the shear for which one is designing (especially since a drogue eventually moves far from its deployment site) and from asymmetric shear (i.e., the “worst case” shear is one with a bias). The final computations examine three different drogue configurations in a series of profiles that model the diurnal cycle of the mixed layer (a diurnal jet) overlying a linear shear. The best design is found to be one that maximizes the drogue over the depth interval of interest, while minimizing the drag area of the tether. The drogue length needs to be larger than the depth interval of interest to account for the rise and tilt of the drogue in shear flow, but not so large that it averages too far outside the interval. For the practical cases considered, a drogue length that was twice the averaging interval gave the best results.

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## Abstract

Depth-averaged current shears computed from shipboard acoustic Doppler current profiler (ADCP) and moored Savonius rotor and vane vector-averaging current meter (VACM) measurements are compared at 35, 62.5, 100 and 140 m depths within 7 km of each other near 0°, 140°W during a 12-day interval in November 1984. The agreement between the VACM and ADCP shears was excellent. The average root-mean-square difference of hourly shear values was small, approximately 0.21 × 10^{−2} s^{−1}, and the average correlation coefficient was 0.90. Spectral estimates were equivalent to within 95% significance level and the VACM and ADCP shears were 95% statistically coherent with zero phase difference for frequencies below 0.2 cycles per hour.

## Abstract

Depth-averaged current shears computed from shipboard acoustic Doppler current profiler (ADCP) and moored Savonius rotor and vane vector-averaging current meter (VACM) measurements are compared at 35, 62.5, 100 and 140 m depths within 7 km of each other near 0°, 140°W during a 12-day interval in November 1984. The agreement between the VACM and ADCP shears was excellent. The average root-mean-square difference of hourly shear values was small, approximately 0.21 × 10^{−2} s^{−1}, and the average correlation coefficient was 0.90. Spectral estimates were equivalent to within 95% significance level and the VACM and ADCP shears were 95% statistically coherent with zero phase difference for frequencies below 0.2 cycles per hour.

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## Abstract

Current and pressure-recording inverted echo sounders (CPIES) were deployed in an eddy-resolving local dynamics array (LDA) in the eddy-rich polar frontal zone (PFZ) in Drake Passage as part of the cDrake experiment. Methods are described for calculating barotropic and baroclinic geostrophic streamfunction and its first, second, and third derivatives by objective mapping of current, pressure, or geopotential height anomaly data from a two-dimensional array of CPIES like the cDrake LDA.

Modifications to previous methods result in improved dimensional error estimates on velocity and higher streamfunction derivatives. Simulations are used to test the reproduction of higher derivatives of streamfunction and to verify mapping error estimates. Three-day low-pass-filtered velocity in and around the cDrake LDA can be mapped with errors of 0.04 m s^{−1} at 4000 dbar, increasing to 0.13 m s^{−1} at the sea surface; these errors are small compared to typical speeds observed at these levels, 0.2 and 0.65 m s^{−1}, respectively. Errors on vorticity are 9 × 10^{−6} s^{−1} near the surface, decreasing with depth to 3 × 10^{−6} s^{−1} at 4000 dbar, whereas vorticities in the PFZ eddy field are 4 × 10^{−5} s^{−1} (surface) to 1.3 × 10^{−5} s^{−1} (4000 dbar). Vorticity gradient errors range from 4 × 10^{−10} to 2 × 10^{−10} m ^{−1} s^{−1}, just under half the size of typical PFZ vorticity gradients. Comparisons between cDrake mapped temperature and velocity fields and independent observations (moored current and temperature, lowered acoustic Doppler current profiler velocity, and satellite-derived surface currents) help validate the cDrake method and results.

## Abstract

Current and pressure-recording inverted echo sounders (CPIES) were deployed in an eddy-resolving local dynamics array (LDA) in the eddy-rich polar frontal zone (PFZ) in Drake Passage as part of the cDrake experiment. Methods are described for calculating barotropic and baroclinic geostrophic streamfunction and its first, second, and third derivatives by objective mapping of current, pressure, or geopotential height anomaly data from a two-dimensional array of CPIES like the cDrake LDA.

Modifications to previous methods result in improved dimensional error estimates on velocity and higher streamfunction derivatives. Simulations are used to test the reproduction of higher derivatives of streamfunction and to verify mapping error estimates. Three-day low-pass-filtered velocity in and around the cDrake LDA can be mapped with errors of 0.04 m s^{−1} at 4000 dbar, increasing to 0.13 m s^{−1} at the sea surface; these errors are small compared to typical speeds observed at these levels, 0.2 and 0.65 m s^{−1}, respectively. Errors on vorticity are 9 × 10^{−6} s^{−1} near the surface, decreasing with depth to 3 × 10^{−6} s^{−1} at 4000 dbar, whereas vorticities in the PFZ eddy field are 4 × 10^{−5} s^{−1} (surface) to 1.3 × 10^{−5} s^{−1} (4000 dbar). Vorticity gradient errors range from 4 × 10^{−10} to 2 × 10^{−10} m ^{−1} s^{−1}, just under half the size of typical PFZ vorticity gradients. Comparisons between cDrake mapped temperature and velocity fields and independent observations (moored current and temperature, lowered acoustic Doppler current profiler velocity, and satellite-derived surface currents) help validate the cDrake method and results.

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## Abstract

The conventional view of equatorial dynamics requires that the zonal equatorial wind stress be balanced, in the mean, by the vertical integral of “large-scale” terms, such as the zonal pressure gradient, mesoscale eddy flux, and mean advection, over the upper few hundred meters. It is usually presumed that the surface wind stress is communicated to the interior by turbulent processes. Turbulent kinetic energy dissipation rates measured at 140°W during the TROPIC HEAT I experiment and a production rate–dissipation rate balance argument have been used to calculate the zonal turbulent stress at 30 to 90 m depth. The calculated turbulent stress at 30 m depth amounts to only 20% of the wind stress and decreases exponentially with depth below 30 m. Typical large-scale estimates of the zonal pressure gradient, mesoscale eddy flux, and advection have a depth scale larger than the turbulent stress, and are inconsistent with the vertical divergence of the stress as estimated from the dissipation rate measurements. It is concluded that either 1) the measured estimates of dissipation rate are too small, 2) the actual large-scale zonal pressure gradient, mesoscale eddy flux, and advection during our observation period were highly atypical and had a very shallow depth scale, 3) some process other than the simple diffusion of momentum through shear instabilities is transporting the momentum, or 4) the assumption of a production-dissipation balance in the turbulent kinetic energy budget is incorrect. The first two possibilities are unlikely.

## Abstract

The conventional view of equatorial dynamics requires that the zonal equatorial wind stress be balanced, in the mean, by the vertical integral of “large-scale” terms, such as the zonal pressure gradient, mesoscale eddy flux, and mean advection, over the upper few hundred meters. It is usually presumed that the surface wind stress is communicated to the interior by turbulent processes. Turbulent kinetic energy dissipation rates measured at 140°W during the TROPIC HEAT I experiment and a production rate–dissipation rate balance argument have been used to calculate the zonal turbulent stress at 30 to 90 m depth. The calculated turbulent stress at 30 m depth amounts to only 20% of the wind stress and decreases exponentially with depth below 30 m. Typical large-scale estimates of the zonal pressure gradient, mesoscale eddy flux, and advection have a depth scale larger than the turbulent stress, and are inconsistent with the vertical divergence of the stress as estimated from the dissipation rate measurements. It is concluded that either 1) the measured estimates of dissipation rate are too small, 2) the actual large-scale zonal pressure gradient, mesoscale eddy flux, and advection during our observation period were highly atypical and had a very shallow depth scale, 3) some process other than the simple diffusion of momentum through shear instabilities is transporting the momentum, or 4) the assumption of a production-dissipation balance in the turbulent kinetic energy budget is incorrect. The first two possibilities are unlikely.

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## Abstract

This study discusses the upper-ocean (0–200 m) horizontal wavenumber spectra in the Drake Passage from 13 yr of shipboard ADCP measurements, altimeter data, and a high-resolution numerical simulation. At scales between 10 and 200 km, the ADCP kinetic energy spectra approximately follow a *k*
^{−3} power law. The observed flows are more energetic at the surface, but the shape of the kinetic energy spectra is independent of depth. These characteristics resemble predictions of isotropic interior quasigeostrophic turbulence. The ratio of across-track to along-track kinetic energy spectra, however, significantly departs from the expectation of isotropic interior quasigeostrophic turbulence. The inconsistency is dramatic at scales smaller than 40 km. A Helmholtz decomposition of the ADCP spectra and analyses of synthetic and numerical model data show that horizontally divergent, ageostrophic flows account for the discrepancy between the observed spectra and predictions of isotropic interior quasigeostrophic turbulence. In Drake Passage, ageostrophic motions appear to be dominated by inertia–gravity waves and account for about half of the near-surface kinetic energy at scales between 10 and 40 km. Model results indicate that ageostrophic flows imprint on the sea surface, accounting for about half of the sea surface height variance between 10 and 40 km.

## Abstract

This study discusses the upper-ocean (0–200 m) horizontal wavenumber spectra in the Drake Passage from 13 yr of shipboard ADCP measurements, altimeter data, and a high-resolution numerical simulation. At scales between 10 and 200 km, the ADCP kinetic energy spectra approximately follow a *k*
^{−3} power law. The observed flows are more energetic at the surface, but the shape of the kinetic energy spectra is independent of depth. These characteristics resemble predictions of isotropic interior quasigeostrophic turbulence. The ratio of across-track to along-track kinetic energy spectra, however, significantly departs from the expectation of isotropic interior quasigeostrophic turbulence. The inconsistency is dramatic at scales smaller than 40 km. A Helmholtz decomposition of the ADCP spectra and analyses of synthetic and numerical model data show that horizontally divergent, ageostrophic flows account for the discrepancy between the observed spectra and predictions of isotropic interior quasigeostrophic turbulence. In Drake Passage, ageostrophic motions appear to be dominated by inertia–gravity waves and account for about half of the near-surface kinetic energy at scales between 10 and 40 km. Model results indicate that ageostrophic flows imprint on the sea surface, accounting for about half of the sea surface height variance between 10 and 40 km.

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## Abstract

Kinetic energy associated with inertia–gravity waves (IGWs) and other ageostrophic phenomena often overwhelms kinetic energy due to geostrophic motions for wavelengths on the order of tens of kilometers. Understanding the dependencies of the wavelength at which balanced (geostrophic) variability ceases to be larger than unbalanced variability is important for interpreting high-resolution altimetric data. This wavelength has been termed the transition scale. This study uses acoustic Doppler current profiler (ADCP) data along with auxiliary observations and a numerical model to investigate the transition scale in the eastern tropical Pacific and the mechanisms responsible for its regional and seasonal variations. One-dimensional kinetic energy wavenumber spectra are separated into rotational and divergent components, and subsequently into vortex and wave components. The divergent motions, most likely predominantly IGWs, account for most of the energy at wavelengths less than 100 km. The observed regional and seasonal patterns in the transition scale are consistent with those from a high-resolution global simulation. Observations, however, show weaker seasonality, with only modest wintertime increases in vortex energy. The ADCP-inferred IGW wavenumber spectra suggest that waves with near-inertial frequency dominate the unbalanced variability, while in model output, internal tides strongly influence the wavenumber spectrum. The ADCP-derived transition scales from the eastern tropical Pacific are typically in the 100–200-km range.

## Abstract

Kinetic energy associated with inertia–gravity waves (IGWs) and other ageostrophic phenomena often overwhelms kinetic energy due to geostrophic motions for wavelengths on the order of tens of kilometers. Understanding the dependencies of the wavelength at which balanced (geostrophic) variability ceases to be larger than unbalanced variability is important for interpreting high-resolution altimetric data. This wavelength has been termed the transition scale. This study uses acoustic Doppler current profiler (ADCP) data along with auxiliary observations and a numerical model to investigate the transition scale in the eastern tropical Pacific and the mechanisms responsible for its regional and seasonal variations. One-dimensional kinetic energy wavenumber spectra are separated into rotational and divergent components, and subsequently into vortex and wave components. The divergent motions, most likely predominantly IGWs, account for most of the energy at wavelengths less than 100 km. The observed regional and seasonal patterns in the transition scale are consistent with those from a high-resolution global simulation. Observations, however, show weaker seasonality, with only modest wintertime increases in vortex energy. The ADCP-inferred IGW wavenumber spectra suggest that waves with near-inertial frequency dominate the unbalanced variability, while in model output, internal tides strongly influence the wavenumber spectrum. The ADCP-derived transition scales from the eastern tropical Pacific are typically in the 100–200-km range.