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  • Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81, 639640, doi:10.1002/qj.49708135027.

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  • Donelan, M. A., W. A. Drennan, and K. B. Katsaros, 1997: The air-sea momentum flux in mixed wind sea and swell conditions. J. Phys. Oceanogr., 27, 20872099, doi:10.1175/1520-0485(1997)027<2087:TASMFI>2.0.CO;2.

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  • Hara, T., and P. P. Sullivan, 2015: Wave boundary layer turbulence over surface waves in a strong forced condition. J. Phys. Oceanogr., 45, 868882, doi:10.1175/JPO-D-14-0116.1.

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  • Takagaki, N., S. Komori, N. Suzuki, K. Iwano, T. Kuramoto, S. Shimada, R. Kurose, and K. Takahashi, 2012: Strong correlation between the drag coefficient and the shape of the wind sea spectrum over a broad range of wind speeds. Geophys. Res. Lett, 39, L23604, doi:10.1029/2012GL053988.

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  • View in gallery

    (left) Schematic picture and (right) photograph of the prototype buoy.

  • View in gallery

    Schematic picture and photograph of the ocean engineering basin of the Institute of Industrial Science, University of Tokyo.

  • View in gallery

    Photograph of the location of the fixed sonic anemometer and buoy.

  • View in gallery

    One part of the time series measured by the three-axis sonic anemometer and the motion sensor in the case of the wave period of 1.1 s with no wind: (a) wind velocity (m s−1), (b) angular velocity (° s−1), and (c) acceleration (m s−2).

  • View in gallery

    Comparison between Ua (red line) and Umotion (blue line) with the no-wind case for wave periods (top to bottom) 1.1(regular waves), 1.4 (irregular waves), and 2.0 s (regular waves).

  • View in gallery

    Frequency spectra for Fig. 5.

  • View in gallery

    Transfer function—gain (top; dB) and phase (bottom; °)—for conditions with the wave period 1.1 s (regular waves) in Fig. 6.

  • View in gallery

    The quantity Umotion vs Ua in each of the three wind components with all no-wind cases.

  • View in gallery

    Comparison between Ua and Umotion with wind: Ua, (red line), Umotion (blue line), Utrue (black line), and Uc (green line) for wave period 1.1 s (regular waves) with wind speed (top) 2 and (bottom) 5 m s−1.

  • View in gallery

    As in Fig. 9, but for the frequency spectra for the x axis (main direction of the wind) in Fig. 9.

  • View in gallery

    Plot of the mean Utrue,x vs the mean Uc,x from the buoy with all wind cases.

  • View in gallery

    Relative errors of the mean Uc,x for the mean Utrue,x in Fig. 8. Intrinsic errors are shown [(mean Uc,x mean Utrue,x)/mean Utrue,x × 100 %; dashed line].

  • View in gallery

    Plot of the friction velocity from the fixed anemometer vs the motion-corrected friction velocity from the buoy with all wind cases. Error bars indicate the intrinsic errors associated with measurement from the fixed anemometer.

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Large Tank Evaluation of a GPS Wave Buoy for Wind Stress Measurements

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  • 1 Department of Mechanical Engineering, Faculty of Science and Engineering, Kindai University, Higashiosaka, Osaka, Japan
  • | 2 Department of Ocean Technology, Policy and Environment, Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba, Japan
  • | 3 Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
  • | 4 Institute of Industrial Science, University of Tokyo, Tokyo, Japan
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Abstract

There exists considerable disagreement among the observed values of the drag coefficient CD. To develop a model of CD, the wind stress generally will be calculated from the eddy correlation method. A buoy is suitable to measure the wind stress in many sea surface conditions. However, the motion correction is very difficult because the anemometer measures the wind components, including the motion of the buoy. In this study, as a first approach, the motion of a prototype buoy system with a three-axis sonic anemometer and a six-axis motion sensor installed in the small-size GPS observation buoy was investigated. The wave tank is in the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, Japan. The imposed conditions were wave periods from 1.1 to 2.5 s; wind speeds of 0, 2, and 5 m s−1; and the wave spectrum was either regular or irregular. The motion of the buoy was measured in 120 cases. For all the wave periods and without wind, the wind velocity measured by the sonic anemometer and the velocity of the anemometer motion calculated from the motion sensor data showed good agreement. Also, in the condition with wind speeds of 2 and 5 m s−1, the motion-corrected wind velocity, obtained by deducting the velocity of the anemometer motion from the wind velocity measured by the anemometer, yielded the true wind velocity with better-than-average (4.3%) accuracy. The friction velocity from corrected wind velocity components shows agreement with the friction velocity measured from a fixed sonic anemometer within expected intrinsic error. The buoy system is expected to be able to measure the wind stress in the field. The next stage is to do comprehensive field tests.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Naoya Suzuki, nsuzuki@mech.kindai.ac.jp

Abstract

There exists considerable disagreement among the observed values of the drag coefficient CD. To develop a model of CD, the wind stress generally will be calculated from the eddy correlation method. A buoy is suitable to measure the wind stress in many sea surface conditions. However, the motion correction is very difficult because the anemometer measures the wind components, including the motion of the buoy. In this study, as a first approach, the motion of a prototype buoy system with a three-axis sonic anemometer and a six-axis motion sensor installed in the small-size GPS observation buoy was investigated. The wave tank is in the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, Japan. The imposed conditions were wave periods from 1.1 to 2.5 s; wind speeds of 0, 2, and 5 m s−1; and the wave spectrum was either regular or irregular. The motion of the buoy was measured in 120 cases. For all the wave periods and without wind, the wind velocity measured by the sonic anemometer and the velocity of the anemometer motion calculated from the motion sensor data showed good agreement. Also, in the condition with wind speeds of 2 and 5 m s−1, the motion-corrected wind velocity, obtained by deducting the velocity of the anemometer motion from the wind velocity measured by the anemometer, yielded the true wind velocity with better-than-average (4.3%) accuracy. The friction velocity from corrected wind velocity components shows agreement with the friction velocity measured from a fixed sonic anemometer within expected intrinsic error. The buoy system is expected to be able to measure the wind stress in the field. The next stage is to do comprehensive field tests.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Naoya Suzuki, nsuzuki@mech.kindai.ac.jp

1. Introduction

Parameterization of the air–sea turbulent transfer of momentum, heat, CO2, and other substances is one of the most important issues for modeling of air–sea interactions. Especially, the estimation of air–sea momentum transfer is important in the generation of ocean currents and wind waves, etc. The sea surface wind stress has generally been estimated using the drag coefficient CD with the wind speed at 10 m above the sea surface U10 as follows:
e1
where ρ is the density of air and CD is generally expressed as a function only of wind speed U10 as
e2
where u* is the friction velocity of air. However, there exists considerable disagreement among the observed values of CD. Thus, many models of CD have been proposed (Charnock 1955; Smith 1980; Large and Pond 1981; Yelland and Taylor 1996; Takagaki et al. 2012). Recently, the disagreement is especially large in the context of wind-wave growth and the existence of various swells (Stewart 1974; Masuda and Kusaba 1987; Donelan et al. 1997; Drennan et al. 1999; Donelan and Dobson 2001; Garcia-Nava et al. 2009; Ocampo-Torres et al. 2011; Suzuki et al. 2002, 2014). To develop a model of CD, the wind stress generally will be calculated from the eddy correlation method, which is the direct method measuring the horizontal and vertical wind components. The direct wind stress measurement is very difficult because of the platform (observation tower, ship, buoy, etc.) motion and influence from flow distortion. On a ship, there are effects of motion and influence from wind flow. Observations on towers also are affected by wind flow. And the database of wind stress will be not able to include many sea surface conditions. A buoy is a better platform to measure the wind stress in many sea surface conditions; flow distortion is much less of a problem, though there is the effect of motion. Recently, air–sea turbulent momentum flux has been measured by many buoys designed specifically for air–sea interaction (Anctil et al. 1994; Graber et al. 2000; Drennan et al. 2014). The anemometer height of the National Data Buoy Center (NDBC) Surface Wave Dynamics Experiment (SWADE)’s 3-m discus wave directional buoy is 5.5 m above the mean sea level (Anctil et al. 1994). The Air–Sea Interaction Spar (ASIS) buoy has a total length of 11 m (Graber et al. 2000). The sizes of these buoys are very large and they cannot easily be deployed. Thus, a small buoy, which can be easily deployed, will be able to observe the wind stress in many sea surface conditions. However, wind measurements very close to and following the sea surface gain access to the turbulent stress and the wave-fluctuation stress but not the pressure stress. Hara and Sullivan (2015) show that the pressure stress is negligible above a normalized height kz of 0.3 (k is the wavenumber = 2π/wavelength). The buoy’s anemometer is 1.6 m above the water surface, so that the stress on waves shorter than 34 m (wavelength) may be estimated from the turbulent stress and wave-fluctuation stress. These wavelengths support most of the form drag and the minor (pressure stress) correction for longer waves may be obtained from Hara and Sullivan (2015). The measured wind velocity (sonic anemometer) includes the true wind velocity and the velocity of the anemometer due to the motion of the buoy. Consequently, it is necessary to eliminate the influence of the anemometer’s motion. In the ocean, the buoy’s motion has 6 degrees of freedom. But, restricting the wave directions to one direction, the buoy motion is limited to heave and pitch, and the motion correction is simpler to monitor and check. Recently, a wave directional observation buoy—the GPS wave observation buoy—has been constructed. It is small and can be easily deployed. In this study, as a first approach, we investigated the motion of the prototype buoy system, with an installed sonic anemometer and motion sensor in the GPS wave observation buoy, using a large laboratory wind-wave tank.

2. Prototype buoy system and wave tank experimentation

The six-axis motion sensor (three-axis accelerometer and three-axis gyroscope; IMU-Z Lite from ZMP Inc.) and the three-axis sonic anemometer (two horizontal components and one vertical component; WindMaster II from Prede Co. Ltd.) was installed on the buoy, in order to measure the motion of the buoy and the wind velocity components. The schematic picture of the prototype buoy system is shown in Fig. 1. The six-axis motion sensor is very small: the dimensions are 15 × 10 × 10 mm3 and the weight is 7 g. The sampling frequencies of the sonic anemometer and the six-axis motion sensor are 10 and 100 Hz, respectively. The buoy is the GPS wave observation buoy (Zeni Lite Buoy Co., Ltd.). This buoy is small: the diameter is 800 mm and the weight is 35 kg. Its measurement parameters are the significant wave height, wave height, wave period, wave direction, etc.

Fig. 1.
Fig. 1.

(left) Schematic picture and (right) photograph of the prototype buoy.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

To investigate the accuracy of the measurements of the anemometer’s motion, we used the large wave tank in the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, Japan. Figure 2 shows a schematic picture of the wave tank. The wave tank has 10-m width, 50-m length, and 5-m depth. The peak of the natural period of the buoy with the motion of water particles was about 1.2 s. Consequently, the imposed conditions were a wave period from 1.1 to 2.5 s; wind speeds of 0 (only waves), 2, and 5 m s−1; and the wave spectrum was either regular (monochromatic) or irregular. The motion of the buoy was measured in 120 cases of 180-s duration. Figure 3 shows photographs of the experimental setup. To compare the true wind velocity Utrue with the corrected wind velocity Uc obtained by deducting the velocity of the anemometer motion from the wind velocity measured by the sonic anemometer on the buoy, we installed another three-axis sonic anemometer on a fixed-mount in the wave tank as is shown in Fig. 3. The motion corrections considered the translational, rotational, and tilt terms (Anctil et al. 1994). The velocity on the x and y axes in the rotational terms was calculated from the measured angular velocity by the motion sensor times the distance from the center of rotation to the sonic anemometer, and the velocity on the z axis was calculated by the integration of the measured acceleration by the motion sensor.

Fig. 2.
Fig. 2.

Schematic picture and photograph of the ocean engineering basin of the Institute of Industrial Science, University of Tokyo.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 3.
Fig. 3.

Photograph of the location of the fixed sonic anemometer and buoy.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

3. Results

Figure 4 shows the time series of the measured data by the sonic anemometer and the motion sensor, in which the measurement conditions are a wave period of 1.1 s, a regular wave, and no wind. The measured wind velocity by the sonic anemometer Ua, the three-axis angular velocity, and three-axis acceleration by the six-axis motion sensor are shown in Figs. 4a–c for each of the three axes (x, y, z), respectively. Since there is no wind, the sonic anemometer measures the relative velocity induced by the anemometer’s motion.

Fig. 4.
Fig. 4.

One part of the time series measured by the three-axis sonic anemometer and the motion sensor in the case of the wave period of 1.1 s with no wind: (a) wind velocity (m s−1), (b) angular velocity (° s−1), and (c) acceleration (m s−2).

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

We calculated the velocity of the anemometer’s motion using data from the six-axis motion sensor: we call this the calculated wind velocity (motion sensor) Umotion. Figure 5 shows the comparison between Ua and Umotion for conditions with no wind (a wave period of 1.1 s of regular waves with no wind; a wave period of 1.4 s of irregular waves with no wind; and a wave period of 2.0 s of regular waves and wave period 1.4 s of irregular waves with no-wind). For all these cases, Ua and Umotion show good agreement with relatively small errors. In the no wind cases and for other wave periods, Ua and Umotion also show good agreement in the comparison, though there are small errors. The frequency spectra corresponding to the time series of Fig. 5 are shown in Fig. 6. The spectral peaks appear at the periods of the wave forcing. Figure 7 shows the transfer function (phase and gain) between Ua and Umotion for conditions with the wave period of 1.1 s (regular waves) and Fig. 6 is the same as Fig. 7 but with no wind. As a result, Umotion is close to 0 in the gain and phase at and near the peak frequency in Fig. 6a. However, in the low- and high-frequency bands, the gain and the phase have large positive values, which means that the sensitive motion sensor captures motion because the buoy is slowly moving but that the sonic anemometer cannot detect the small relative wind speed fluctuations at these frequencies. Where the signal-to-noise ratio is large, the transfer function shows unity gain and zero phase, attesting to the accuracy of the motion correction process. Quantities Ua and Umotion in each of the three wind components with no-wind cases are compared in Fig. 8. The root-mean-square (RMS) for the x, y, and z wind components are 0.129, 0.0638, 0.0583 m s−1, respectively. The small value of the RMS implies that the six-axis motion sensor accurately measured the pitch, roll, and heave motion of the buoy and therefore the motion of the anemometer.

Fig. 5.
Fig. 5.

Comparison between Ua (red line) and Umotion (blue line) with the no-wind case for wave periods (top to bottom) 1.1(regular waves), 1.4 (irregular waves), and 2.0 s (regular waves).

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 6.
Fig. 6.

Frequency spectra for Fig. 5.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 7.
Fig. 7.

Transfer function—gain (top; dB) and phase (bottom; °)—for conditions with the wave period 1.1 s (regular waves) in Fig. 6.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 8.
Fig. 8.

The quantity Umotion vs Ua in each of the three wind components with all no-wind cases.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Now, let us look into cases with wind. Here, the difference in the mean wind speed calculated from two sonic anemometers with only wind speed was 2.5%. Figure 9 shows the comparison between Ua and Umotion in the measurement condition of the wave period of 1.1 s with wind speeds of 2 and 5 m s−1. The quantity Uc yielded nearly the Utrue. The corresponding frequency spectra for the main direction of wind (X axis) are shown in Fig. 10. The comparison reveals that the spectra of Uc,x yield nearly the spectra of Utrue,x; hereafter, the wind velocity for the X, Y, and Z axes will appear as subscripts x, y, and z, respectively. The wind from the fan is a free jet and is not well regulated, because there are no flow conditioners to produce a homogeneous and uniform flow. Therefore, the instantaneous wind velocity can be very different at the different locations of buoy and fixed sonic anemometers. However, the mean wind velocity of the x axis showed nearly the same value between Uc,x and Utrue,x. The comparisons of the mean Utrue,x and the mean Uc,x for all cases of wind speeds are shown in Fig. 11. The mean Uc,x shows excellent agreement (RMS: 0.108 m s−1) with the mean Utrue,x, differing on average by less than 4.3%. Figure 12 shows the relative errors of the mean Uc,x from the buoy for the mean Utrue,x [(the mean Uc,x − the mean Utrue,x)/the mean Utrue,x × 100 %]. The intrinsic errors associated with the buoy measurement of mean Uz (Donelan 1990) are given by
e3
where z is the height of the anemometer above the surface and Ω is the duration of the runs (s). These intrinsic errors are indicated by the dashed line in Fig. 12. The line follows the same trend as the measured errors, but it is somewhat larger because the buoy and fixed (true) anemometers are close and their low-frequency velocity fluctuations are strongly correlated, reducing the measured “errors.” Figures 11 and 12 show that the motion corrections are accurate at least as far as the zeroth and first-order turbulent velocities are concerned.
Fig. 9.
Fig. 9.

Comparison between Ua and Umotion with wind: Ua, (red line), Umotion (blue line), Utrue (black line), and Uc (green line) for wave period 1.1 s (regular waves) with wind speed (top) 2 and (bottom) 5 m s−1.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for the frequency spectra for the x axis (main direction of the wind) in Fig. 9.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 11.
Fig. 11.

Plot of the mean Utrue,x vs the mean Uc,x from the buoy with all wind cases.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

Fig. 12.
Fig. 12.

Relative errors of the mean Uc,x for the mean Utrue,x in Fig. 8. Intrinsic errors are shown [(mean Uc,x mean Utrue,x)/mean Utrue,x × 100 %; dashed line].

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

To assess the accuracy of second-order quantities, in particular the stress, we examine the friction velocity. Figure 13 shows that the friction velocity calculated by the eddy correlation method in all cases with wind. The friction velocity from the measured wind components by the buoy shows reasonable agreement (RMS: 0.108 m s−1) with the friction velocity measured by the fixed anemometer. Both measurements are subject to the intrinsic errors associated with the estimation of second-order turbulence quantities (Donelan 1990), and the errors from the fixed sonic anemometer are indicated with error bars. When the intrinsic errors are considered, it is clear that the buoy is capable of stress measurements in the laboratory. Gill Instruments found a bug in the software for the Z-axis wind component (vertical wind component) in some version of the three-axis sonic anemometers (WindMaster). Although the small errors of our results may include the effect, it is considered to be showing good results for the motion correction. In the field, the sea surface conditions can be very much more complex. The test experimentation of motion correction of the buoy will be necessary around an observation tower in the field.

Fig. 13.
Fig. 13.

Plot of the friction velocity from the fixed anemometer vs the motion-corrected friction velocity from the buoy with all wind cases. Error bars indicate the intrinsic errors associated with measurement from the fixed anemometer.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0050.1

4. Summary

In this study, as a first approach, we investigated the motion of the prototype buoy system, with the installed three-axis sonic anemometer and the three-axis motion sensor in the small-size GPS observation buoy, using the ocean engineering basin of the Institute of Industrial Science, University of Tokyo. The imposed conditions were wave periods from 1.1 to 2.5 s; wind speeds of 0 (only wave), 2, and 5 m s−1; and the wave spectrum was either regular (monochromatic) or irregular. The motion of the buoy was measured in 120 cases of 180-s duration. The calculated wind velocity (motion sensor) Umotion shows good agreement with the measured wind velocity (sonic anemometer) Ua in no-wind cases. The RMS for the x, y, and z wind components is 0.129, 0.0638, 0.0583 m s−1, respectively. It appears that the six-axis motion sensor accurately measures the pitch, roll and heave motions of the buoy. In case of wind speeds 2 and 5 m s−1, the corrected mean wind velocity Uc,x by the motion correction also agrees well with the true mean wind velocity Utrue,x. The friction velocity calculated by the eddy correlation method using the corrected wind velocity components shows reasonable agreement with the friction velocity estimated from the fixed anemometer. It appears that the six-axis motion sensor accurately measures the motion of the buoy to the extent that stress can be measured even when the buoy is excited by mechanically generated laboratory waves. Consequently, we expect to be able to measure the wind stress in the field using this buoy system.

In future, as a second approach, we will investigate the accuracy of the motion correction in the field by mooring this buoy near an offshore observation tower.

Acknowledgments

We gratefully acknowledge Mr. Hiroshi Itakura of the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, for supporting our experimentation.

REFERENCES

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