# Search Results

## Abstract

Pressure gradient measurements on a subsurface Lagrangian float are used to measure the spectrum of surface waves for 100 days of measurements at Ocean Weather Station *Papa*. Along Lagrangian trajectories of surface waves, the pressure is constant and the vertical pressure gradient fluctuations equal the Eulerian fluctuations at the mean float depth to second order in wave height. Measurement of the pressure difference between the top and the bottom of the float can thus be used to measure the waves. Corrections for the wave decay with depth, for the vertical motion of the float, for the finite sampling interval, and for the sampling noise (among others) are necessary to obtain accurate results. With these corrections, scalar spectra accurately match those from a nearby Waverider buoy for significant wave heights greater than about 3 m. For smaller wave heights, noise in the pressure measurements biases the float spectral measurements. Significant wave height is measured with an rms error of 0.37 m over the measured range of 1–9 m. This demonstrates that Lagrangian floats accurately follow the Lagrangian trajectories of surface waves. More detailed and quieter measurements of float motion could likely measure directional wave spectra from below the surface. Similar methods could be used to infer surface wave properties from other subsurface vehicles.

## Abstract

Pressure gradient measurements on a subsurface Lagrangian float are used to measure the spectrum of surface waves for 100 days of measurements at Ocean Weather Station *Papa*. Along Lagrangian trajectories of surface waves, the pressure is constant and the vertical pressure gradient fluctuations equal the Eulerian fluctuations at the mean float depth to second order in wave height. Measurement of the pressure difference between the top and the bottom of the float can thus be used to measure the waves. Corrections for the wave decay with depth, for the vertical motion of the float, for the finite sampling interval, and for the sampling noise (among others) are necessary to obtain accurate results. With these corrections, scalar spectra accurately match those from a nearby Waverider buoy for significant wave heights greater than about 3 m. For smaller wave heights, noise in the pressure measurements biases the float spectral measurements. Significant wave height is measured with an rms error of 0.37 m over the measured range of 1–9 m. This demonstrates that Lagrangian floats accurately follow the Lagrangian trajectories of surface waves. More detailed and quieter measurements of float motion could likely measure directional wave spectra from below the surface. Similar methods could be used to infer surface wave properties from other subsurface vehicles.

## Abstract

The ability of neutrally buoyant, high-drag floats to measure the air–sea heat flux from within the turbulent oceanic boundary layer is investigated using float data from four different winter and fall float deployments. Two flux estimates can be made: *Q*
_{0A
} measures the vertical advection of heat, and *Q*
_{0D
} integrates the Lagrangian heating rate. Because the floats are only imperfectly Lagrangian, a key issue is diagnosing the ability of a given set of float data to make accurate flux measurements. A variety of diagnostics are explored and evaluated. Here *Q*
_{0A
} and *Q*
_{0D
} are compared to heat flux measurements computed using bulk formulas and shipboard measurements for one 2-week cruise. Quality controlled float-based fluxes agree with bulk fluxes to within 10 W m^{−2} for both positive and negative values. The differences are well within the expected statistical errors in the float measurements and the bias errors of the bulk measurements.

## Abstract

The ability of neutrally buoyant, high-drag floats to measure the air–sea heat flux from within the turbulent oceanic boundary layer is investigated using float data from four different winter and fall float deployments. Two flux estimates can be made: *Q*
_{0A
} measures the vertical advection of heat, and *Q*
_{0D
} integrates the Lagrangian heating rate. Because the floats are only imperfectly Lagrangian, a key issue is diagnosing the ability of a given set of float data to make accurate flux measurements. A variety of diagnostics are explored and evaluated. Here *Q*
_{0A
} and *Q*
_{0D
} are compared to heat flux measurements computed using bulk formulas and shipboard measurements for one 2-week cruise. Quality controlled float-based fluxes agree with bulk fluxes to within 10 W m^{−2} for both positive and negative values. The differences are well within the expected statistical errors in the float measurements and the bias errors of the bulk measurements.

## Abstract

A truly Lagrangian float would follow all three components of oceanic velocity on all timescales. Progress toward this goal is reviewed by analyzing the performance of nearly Lagrangian floats deployed in a variety of oceanic flows. Two new float types, described in this paper, are autonomous with durations of months, can alternate between Lagrangian and profiling modes, relay data via satellite, and can carry a variety of sensors. A novel hull design is light, strong, and has a compressibility close to that of seawater.

The key to making floats accurately Lagrangian is an improved understanding of the factors that control float buoyancy and motion. Several insights are presented here. Anodized aluminum gains weight in seawater due to reactions between its surface and seawater. At low pressure the buoyancy of floats with O-ring seals varies as if attached bubbles of air were being compressed. The volume of “air” decays exponentially with a decay scale of a few days from 10 to 30 cc at deployment to an asymptotic value that depends on pressure. The drag of floats moving slowly through a stratified ocean is dominated by internal wave generation and is thus linear, not quadratic. Internal wave drag acting on an isopycnal-seeking float will cause the float to be Lagrangian for frequencies greater than about *N*/30, where *N* is the buoyancy frequency.

These floats have proven most useful in measuring the turbulence in ocean boundary layers and other regions of strong turbulence where the ability of the floats to be Lagrangian on short timescales matches the short timescale of the processes and where the size of the turbulent eddies exceeds the size of the float. On longer timescales, the floats successfully operate as isopycnal followers. Because truly Lagrangian floats are highly sensitive to minor perturbations, extension of the frequency band over which the floats are Lagrangian will require careful control of float buoyancy and thus a detailed understanding of the float's equation of state.

## Abstract

A truly Lagrangian float would follow all three components of oceanic velocity on all timescales. Progress toward this goal is reviewed by analyzing the performance of nearly Lagrangian floats deployed in a variety of oceanic flows. Two new float types, described in this paper, are autonomous with durations of months, can alternate between Lagrangian and profiling modes, relay data via satellite, and can carry a variety of sensors. A novel hull design is light, strong, and has a compressibility close to that of seawater.

The key to making floats accurately Lagrangian is an improved understanding of the factors that control float buoyancy and motion. Several insights are presented here. Anodized aluminum gains weight in seawater due to reactions between its surface and seawater. At low pressure the buoyancy of floats with O-ring seals varies as if attached bubbles of air were being compressed. The volume of “air” decays exponentially with a decay scale of a few days from 10 to 30 cc at deployment to an asymptotic value that depends on pressure. The drag of floats moving slowly through a stratified ocean is dominated by internal wave generation and is thus linear, not quadratic. Internal wave drag acting on an isopycnal-seeking float will cause the float to be Lagrangian for frequencies greater than about *N*/30, where *N* is the buoyancy frequency.

These floats have proven most useful in measuring the turbulence in ocean boundary layers and other regions of strong turbulence where the ability of the floats to be Lagrangian on short timescales matches the short timescale of the processes and where the size of the turbulent eddies exceeds the size of the float. On longer timescales, the floats successfully operate as isopycnal followers. Because truly Lagrangian floats are highly sensitive to minor perturbations, extension of the frequency band over which the floats are Lagrangian will require careful control of float buoyancy and thus a detailed understanding of the float's equation of state.

## Abstract

Rain in tropical cyclones is studied using eight time series of underwater ambient sound at 40–50 kHz with wind speeds up to 45 m s^{−1} beneath three tropical cyclones. At tropical cyclone wind speeds, rain- and wind-generated sound levels are comparable, and therefore rain cannot be detected by sound level alone. A rain detection algorithm that is based on the variations of 5–30-kHz sound levels with periods longer than 20 s and shorter than 30 min is proposed. Faster fluctuations (<20 s) are primarily due to wave breaking, and slower ones (>30 min) are due to overall wind variations. Higher-frequency sound (>30 kHz) is strongly attenuated by bubble clouds. This approach is supported by observations that, for wind speeds < 40 m s^{−1}, the variation in sound level is much larger than that expected from observed wind variations and is roughly comparable to that expected from rain variations. The hydrophone results are consistent with rain estimates by the Tropical Rainfall Measuring Mission (TRMM) satellite and with Stepped-Frequency Microwave Radiometer (SFMR) and radar estimates by surveillance flights. The observations indicate that the rain-generated sound fluctuations have broadband acoustic spectra centered around 10 kHz. Acoustically detected rain events usually last for a few minutes. The data used in this study are insufficient to produce useful estimation of rain rate from ambient sound because of limited quantity and accuracy of the validation data. The frequency dependence of sound variations suggests that quantitative rainfall algorithms from ambient sound may be developed using multiple sound frequencies.

### Significance Statement

Rain is an indispensable process in forecasting the intensity and path of tropical cyclones. However, its role in the air–sea interaction is still poorly understood, and its parameterization in numerical models is still in development. In this work, we analyzed sound measurements made by hydrophones on board Lagrangian floats beneath tropical cyclones. We find that wind, rain, and breaking waves each have distinctive signatures in underwater ambient sound. We suggest that the air–sea dynamic processes in tropical cyclones can be explored by listening to ambient sound using hydrophones beneath the sea surface.

## Abstract

Rain in tropical cyclones is studied using eight time series of underwater ambient sound at 40–50 kHz with wind speeds up to 45 m s^{−1} beneath three tropical cyclones. At tropical cyclone wind speeds, rain- and wind-generated sound levels are comparable, and therefore rain cannot be detected by sound level alone. A rain detection algorithm that is based on the variations of 5–30-kHz sound levels with periods longer than 20 s and shorter than 30 min is proposed. Faster fluctuations (<20 s) are primarily due to wave breaking, and slower ones (>30 min) are due to overall wind variations. Higher-frequency sound (>30 kHz) is strongly attenuated by bubble clouds. This approach is supported by observations that, for wind speeds < 40 m s^{−1}, the variation in sound level is much larger than that expected from observed wind variations and is roughly comparable to that expected from rain variations. The hydrophone results are consistent with rain estimates by the Tropical Rainfall Measuring Mission (TRMM) satellite and with Stepped-Frequency Microwave Radiometer (SFMR) and radar estimates by surveillance flights. The observations indicate that the rain-generated sound fluctuations have broadband acoustic spectra centered around 10 kHz. Acoustically detected rain events usually last for a few minutes. The data used in this study are insufficient to produce useful estimation of rain rate from ambient sound because of limited quantity and accuracy of the validation data. The frequency dependence of sound variations suggests that quantitative rainfall algorithms from ambient sound may be developed using multiple sound frequencies.

### Significance Statement

Rain is an indispensable process in forecasting the intensity and path of tropical cyclones. However, its role in the air–sea interaction is still poorly understood, and its parameterization in numerical models is still in development. In this work, we analyzed sound measurements made by hydrophones on board Lagrangian floats beneath tropical cyclones. We find that wind, rain, and breaking waves each have distinctive signatures in underwater ambient sound. We suggest that the air–sea dynamic processes in tropical cyclones can be explored by listening to ambient sound using hydrophones beneath the sea surface.

## Abstract

The calibration accuracy and stability of three Aanderaa 3835 optodes and three Sea-Bird Electronics SBE-43 oxygen sensors were evaluated over four years using in situ and laboratory calibrations. The sensors were mostly in storage, being in the ocean for typically only a few weeks per year and operated for only a few days per year. Both sensors measure partial pressure of oxygen, or equivalently saturation at standard pressure; results are expressed in this variable. It is assumed that sensor drift occurs in the oxygen sensitivity of the sensors, not the temperature compensation; this is well justified for the SBE-43 based on multiple calibrations. Neither sensor had significant long-term drift in output when sampling anoxic water. Sensor output at 100% saturation differed from the factory calibrations by up to ±6% (averaging −2.3% ± 3%) for the SBE-43 and up to −12.6% for the optodes. The optode output at 100% saturation is well described by a single decaying exponential with a decay constant of approximately 2 yr and an amplitude of 28%. The mechanism of this drift is unknown but is not primarily due to sensor operation. It may be different from that experienced by sensors continuously deployed in the ocean. Thus, although the optodes in this study did not have a stable calibration, their drift was stable and, once calibrated, allowed optode and SBE-43 pairs mounted on the same autonomous floats to be calibrated to an accuracy of ±0.4% over a 4-yr period.

## Abstract

The calibration accuracy and stability of three Aanderaa 3835 optodes and three Sea-Bird Electronics SBE-43 oxygen sensors were evaluated over four years using in situ and laboratory calibrations. The sensors were mostly in storage, being in the ocean for typically only a few weeks per year and operated for only a few days per year. Both sensors measure partial pressure of oxygen, or equivalently saturation at standard pressure; results are expressed in this variable. It is assumed that sensor drift occurs in the oxygen sensitivity of the sensors, not the temperature compensation; this is well justified for the SBE-43 based on multiple calibrations. Neither sensor had significant long-term drift in output when sampling anoxic water. Sensor output at 100% saturation differed from the factory calibrations by up to ±6% (averaging −2.3% ± 3%) for the SBE-43 and up to −12.6% for the optodes. The optode output at 100% saturation is well described by a single decaying exponential with a decay constant of approximately 2 yr and an amplitude of 28%. The mechanism of this drift is unknown but is not primarily due to sensor operation. It may be different from that experienced by sensors continuously deployed in the ocean. Thus, although the optodes in this study did not have a stable calibration, their drift was stable and, once calibrated, allowed optode and SBE-43 pairs mounted on the same autonomous floats to be calibrated to an accuracy of ±0.4% over a 4-yr period.

## Abstract

The effects of upward buoyancy on the accuracy with which Lagrangian floats can measure the Eulerian mean variance 〈*ww*〉*
_{E}
* and skewness

*S*of vertical fluid velocity

_{w}^{E}*w*in the wind-driven upper-ocean boundary layer is investigated using both simulated floats in large-eddy simulation (LES) models and two float datasets. Nearly neutrally buoyant floats are repeatedly advected by the turbulent velocities across the boundary layer. Their vertical position

*Z*is determined from pressure measurements; their

*W*variance 〈

*WW*〉

*and skewness*

_{F}*S*are determined from the time series of float

_{W}^{E}*W*=

*dZ*/

*dt*. If the float buoyancy is small, then the simulated floats measure the Eulerian velocity accurately; that is,

*δW*

^{2}= 〈

*WW*〉

*− 〈*

_{F}*ww*〉

*and*

_{E}*δS*=

_{W}*S*−

_{W}^{F}*S*are small compared to 〈

_{w}^{E}*ww*〉

*and*

_{E}*S*respectively. If the floats are buoyant, and thus have an upward vertical velocity

_{w}^{E}*W*

_{bias}relative to the water, then

*δW*

^{2}and

*δS*can become significant. Buoyancy causes the floats to oversample both shallow depths and strong vertical velocities, leading to positive values of

_{W}*δW*

^{2}and negative values of

*δS*. The skewness

_{W}*S*

_{ Z′}

*of depth measures the degree to which shallow depths are oversampled; it is shown to be a good predictor of*

^{F}*W*

_{bias}/〈

*WW*〉

_{ F }

^{1/2},

*δW*

^{2}/〈

*WW*〉, and

_{F}*δS*/

_{W}*S*over a wide range of float buoyancies and boundary layer forcings. Float data collected during two deployments confirm these results, but averaging times of several float days are typically required to obtain stable statistics. Significant differences in the magnitude of the effect may occur between datasets from different ocean forcing regimes and float designs. Other measures of float buoyancy are also useful predictors. These results can be used to correct existing float measurements of 〈

_{W}^{F}*ww*〉

*for the effects of buoyancy and also can be used as a means to operationally assess and control float buoyancy.*

_{E}## Abstract

The effects of upward buoyancy on the accuracy with which Lagrangian floats can measure the Eulerian mean variance 〈*ww*〉*
_{E}
* and skewness

*S*of vertical fluid velocity

_{w}^{E}*w*in the wind-driven upper-ocean boundary layer is investigated using both simulated floats in large-eddy simulation (LES) models and two float datasets. Nearly neutrally buoyant floats are repeatedly advected by the turbulent velocities across the boundary layer. Their vertical position

*Z*is determined from pressure measurements; their

*W*variance 〈

*WW*〉

*and skewness*

_{F}*S*are determined from the time series of float

_{W}^{E}*W*=

*dZ*/

*dt*. If the float buoyancy is small, then the simulated floats measure the Eulerian velocity accurately; that is,

*δW*

^{2}= 〈

*WW*〉

*− 〈*

_{F}*ww*〉

*and*

_{E}*δS*=

_{W}*S*−

_{W}^{F}*S*are small compared to 〈

_{w}^{E}*ww*〉

*and*

_{E}*S*respectively. If the floats are buoyant, and thus have an upward vertical velocity

_{w}^{E}*W*

_{bias}relative to the water, then

*δW*

^{2}and

*δS*can become significant. Buoyancy causes the floats to oversample both shallow depths and strong vertical velocities, leading to positive values of

_{W}*δW*

^{2}and negative values of

*δS*. The skewness

_{W}*S*

_{ Z′}

*of depth measures the degree to which shallow depths are oversampled; it is shown to be a good predictor of*

^{F}*W*

_{bias}/〈

*WW*〉

_{ F }

^{1/2},

*δW*

^{2}/〈

*WW*〉, and

_{F}*δS*/

_{W}*S*over a wide range of float buoyancies and boundary layer forcings. Float data collected during two deployments confirm these results, but averaging times of several float days are typically required to obtain stable statistics. Significant differences in the magnitude of the effect may occur between datasets from different ocean forcing regimes and float designs. Other measures of float buoyancy are also useful predictors. These results can be used to correct existing float measurements of 〈

_{W}^{F}*ww*〉

*for the effects of buoyancy and also can be used as a means to operationally assess and control float buoyancy.*

_{E}## Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy *ɛ* from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of *ɛ* varied from 10^{−8} to 10^{−3} W kg^{−1}. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to *ɛ*. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements *ɛ*
_{float} were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate *ɛ*
_{ADV} was computed from the level of this spectrum. These two independent estimates, *ɛ*
_{ADV} and *ɛ*
_{float}, were highly correlated. The ratio *ɛ*
_{float}/*ɛ*
_{ADV} deviated from one by less than a factor of 2 over the five decades of *ɛ* measured. This analysis confirms that *ɛ* can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of *ɛ*
_{float} > 10^{−8} W kg^{−1}.

## Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy *ɛ* from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of *ɛ* varied from 10^{−8} to 10^{−3} W kg^{−1}. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to *ɛ*. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements *ɛ*
_{float} were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate *ɛ*
_{ADV} was computed from the level of this spectrum. These two independent estimates, *ɛ*
_{ADV} and *ɛ*
_{float}, were highly correlated. The ratio *ɛ*
_{float}/*ɛ*
_{ADV} deviated from one by less than a factor of 2 over the five decades of *ɛ* measured. This analysis confirms that *ɛ* can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of *ɛ*
_{float} > 10^{−8} W kg^{−1}.

## Abstract

This paper describes the instrumentation and techniques for long-term targeted observation of the centimeter-scale velocity structure within the oceanic surface boundary layer, made possible by the recent developments in capabilities of autonomous platforms and self-contained pulse-coherent acoustic Doppler current profilers (ADCPs). Particular attention is paid to the algorithms of ambiguity resolution (“unwrapping”) of pulse-coherent Doppler velocity measurements. The techniques are demonstrated using the new Nortek Signature1000 ADCP mounted on a Lagrangian float, a combination shown to be capable of observing ocean turbulence in a number of recent studies. Statistical uncertainty of the measured velocities in relation to the ADCP setup is also evaluated. Described techniques and analyses should be broadly applicable to other autonomous and towed applications of pulse-coherent ADCPs.

## Abstract

This paper describes the instrumentation and techniques for long-term targeted observation of the centimeter-scale velocity structure within the oceanic surface boundary layer, made possible by the recent developments in capabilities of autonomous platforms and self-contained pulse-coherent acoustic Doppler current profilers (ADCPs). Particular attention is paid to the algorithms of ambiguity resolution (“unwrapping”) of pulse-coherent Doppler velocity measurements. The techniques are demonstrated using the new Nortek Signature1000 ADCP mounted on a Lagrangian float, a combination shown to be capable of observing ocean turbulence in a number of recent studies. Statistical uncertainty of the measured velocities in relation to the ADCP setup is also evaluated. Described techniques and analyses should be broadly applicable to other autonomous and towed applications of pulse-coherent ADCPs.

## Abstract

The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin– Helmholtz (K–H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K–H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time-and volume-averaged vertical advective flux can be estimated to only 20% accuracy. Despite the relatively low Reynolds number of the flow, *R*
_{
λ
} ≈ 100, the dissipation rates of energy ɛ and density variance *χ* are correlated with the spectral levels of transverse velocity and density in an inertial subrange, as expected for high-Reynolds-number turbulence. The Kolmogorov constants are consistent with previous studies. This suggests that these inertial dissipation methods are the most promising techniques for making useful measurements of diapycnal mixing rates from practical Lagrangian floats because they converge rapidly and have a clear theoretical basis.

## Abstract

The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin– Helmholtz (K–H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K–H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time-and volume-averaged vertical advective flux can be estimated to only 20% accuracy. Despite the relatively low Reynolds number of the flow, *R*
_{
λ
} ≈ 100, the dissipation rates of energy ɛ and density variance *χ* are correlated with the spectral levels of transverse velocity and density in an inertial subrange, as expected for high-Reynolds-number turbulence. The Kolmogorov constants are consistent with previous studies. This suggests that these inertial dissipation methods are the most promising techniques for making useful measurements of diapycnal mixing rates from practical Lagrangian floats because they converge rapidly and have a clear theoretical basis.

## Abstract

Seven subsurface Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats measured the voltage induced by the motional induction of seawater under Typhoon Fanapi in 2010. Measurements were processed to estimate high-frequency oceanic velocity variance *f*
_{
p
} and significant wave height *H*
_{
s
} are estimated by a nonlinear least squares fitting to *H*
_{
s
} is further corrected for the effects of float rotation, Earth’s geomagnetic field inclination, and surface wave propagation direction. The *f*
_{
p
} is 0.08–0.10 Hz, with the maximum *f*
_{
p
} of 0.10 Hz in the rear-left quadrant of Fanapi, which is ~0.02 Hz higher than in the rear-right quadrant. The *H*
_{
s
} is 6–12 m, with the maximum in the rear sector of Fanapi. Comparing the estimated *f*
_{
p
} and *H*
_{
s
} with those assuming a single dominant surface wave yields differences of more than 0.02 Hz and 4 m, respectively. The surface waves under Fanapi simulated in the WAVEWATCH III (ww3) model are used to assess and compare to float estimates. Differences in the surface wave spectra of JONSWAP and ww3 yield uncertainties of <5% outside Fanapi’s eyewall and >10% within the eyewall. The estimated *f*
_{
p
} is 10% less than the simulated *H*
_{
s
} and simulated

## Abstract

Seven subsurface Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats measured the voltage induced by the motional induction of seawater under Typhoon Fanapi in 2010. Measurements were processed to estimate high-frequency oceanic velocity variance *f*
_{
p
} and significant wave height *H*
_{
s
} are estimated by a nonlinear least squares fitting to *H*
_{
s
} is further corrected for the effects of float rotation, Earth’s geomagnetic field inclination, and surface wave propagation direction. The *f*
_{
p
} is 0.08–0.10 Hz, with the maximum *f*
_{
p
} of 0.10 Hz in the rear-left quadrant of Fanapi, which is ~0.02 Hz higher than in the rear-right quadrant. The *H*
_{
s
} is 6–12 m, with the maximum in the rear sector of Fanapi. Comparing the estimated *f*
_{
p
} and *H*
_{
s
} with those assuming a single dominant surface wave yields differences of more than 0.02 Hz and 4 m, respectively. The surface waves under Fanapi simulated in the WAVEWATCH III (ww3) model are used to assess and compare to float estimates. Differences in the surface wave spectra of JONSWAP and ww3 yield uncertainties of <5% outside Fanapi’s eyewall and >10% within the eyewall. The estimated *f*
_{
p
} is 10% less than the simulated *H*
_{
s
} and simulated