# Measurement Characteristics of Near-Surface Currents from Ultra-Thin Drifters, Drogued Drifters, and HF Radar

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Drifters

^{®}network at 5-min intervals.

#### 2.2. HF Radar

#### 2.3. Analysis of Drifter Velocity

**U**and φ are the speed and course over ground (COG, clockwise from north, not to be confused with expressing angle in the typical mathematical sense of anti-clockwise from the positive x direction) of either 10-cm or CODE drifters, and

**U**and φ

_{5}_{5}are the speed and COG of the co-located 5-cm drifter. A scaled velocity of (u

_{r}Orange Beachv

_{r}) = (0,1) indicates that the velocity of the drifter being compared is identical to the 5-cm drifter velocity. Non-zero values of u

_{r}indicate the COG of the drifter being compared is rotated relative to the 5-cm drifter COG. This quantity is only considered for co-located pairs of drifters where the speed of the 5-cm drifter exceeds 0.2 m/s to prevent dividing by small values.

#### 2.4. Analysis of Stokes Drift

_{c}is 3.05 rad/s. Consequences of computing the Stokes drift from the directional wave spectra versus the bulk wave characteristics more commonly obtained from buoy measurements are discussed in [18]. The Stokes velocity has a vertical profile of

**U**(z) averaged over the drifter profile or drogue depth (4 cm for the 5-cm drifters, or 55–146 cm for CODE drifters). In the analysis presented here, the vertical decay profile is computed for each directional and frequency bin of the wave spectrum.

_{s}## 3. Results

#### 3.1. Drifter Trajectories and Velocity

#### 3.2. Stokes Drift

_{s}is the significant wave height and k is the wavenumber associated with the dominant wave period, rapidly increases from 0.03 to >0.15 (Figure 5). As shown by Banner et al. [23], wave breaking begins to occur for ε > 0.05. Although wave breaking does not affect the vertically integrated Lagrangian momentum due to wave motions, it does result in a change in the Stokes drift profile [24]. Essentially, wave breaking mixes momentum from the surface to the ocean’s interior breaking down the classic depth profile for Stokes drift. This explains why, during wave breaking conditions, the forward speed of the CODE drifters more closely matches the 5-cm drifters, and adding a Stokes drift velocity to the CODE drifter velocity results in a much higher speed than the 5-cm drifters.

## 4. Discussion and Conclusions

^{−1}. This is much less than the difference between the ultra-thin drifter speeds and the CODE-style drifter and HF radar speeds analyzed here. This supports that the strongest shear occurs much closer to the surface than 0.4 m, as would be expected from the theoretical exponential decay profile of Stokes drift velocity (Equation (2)).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Map of the deployment region and drifter tracks for the first sixteen days of the experiment. Drifters were deployed at four drop points in a triangular pattern as described in Section 2.1, with each triangle centered at the black dots in the plot. The 5-cm drifter trajectories are shown in red, 10-cm drifters in pink, and the CODE-style drifters in green. The location of National Data Buoy Center (NDBC) buoy 42012 (cyan dot) is shown along with the HF radar antennae locations (yellow dots). The inset shows the drifter trajectories over their first three days.

**Figure 3.**Time series of percent of drifters transmitting their position at least once every 30 min. Green = 5-cm drifters, Red = 10-cm drifters, and Blue = CODE-style drifters.

**Figure 4.**Histogram (bin size of two days) of the number of co-located bin-averaged drifter velocity data points (with at least fifteen 5-min velocity measurements) and HF radar velocity measurements. Blue = 5-cm drifters, Green = 10-cm drifters, and Blue = CODE-style drifters.

**Figure 5.**(

**a**) Hourly wind vectors and speed measured at NDBC Buoy 42012 (Figure 1) during the first sixteen days of the field experiment (commencing on 24 January 2017 18UTC). Vector color indicates the magnitude (m/s). (

**b**) Hourly significant wave height (m) and wave steepaness (computed as in Equation (4)) measured at NDBC Buoy 42012. (

**c**) Surface Stokes drift velocity (vectors) and magnitude (black curve and vector color, m/s) computed from hourly directional wave spectra measurements at NDBC Buoy 42012.

**Figure 6.**The 10-cm drifter (

**a**); and CODE-style drifter (

**b**) velocity relative to co-located 5-cm drifter velocity (u

_{r}, v

_{r}), as calculated by Equation (1). The red dots are centroids of the scatter points and the red ellipses represent the standard deviations of the scatter points. Listed on each plot are the number of co-located observations (N), the angle clockwise from vector (0,1) to the centroid (mean), and the magnitude of the mean with 95% confidence interval.

**Figure 7.**HF radar velocity relative to binned 5-cm (

**a**), 10-cm (

**b**) and CODE-style (

**c**) drifter velocity (u

_{r}, v

_{r}), as calculated by Equation (1). The red dots are centroids of the scatter points and the red ellipses represent the standard deviations of the scatter points. Listed on each plot are the number of co-located observations (N), the angle clockwise from vector (0,1) to the centroid (mean), and the magnitude of the mean with 95% confidence interval.

**Figure 8.**Mean magnitude of the HF radar velocity relative to binned 5-cm, 10-cm, and CODE-style drifter velocity as calculated by Equation (1). Error bars represent the 95% confidence interval of the estimate of the mean.

**Figure 9.**(

**a**) CODE drifter velocity relative to co-located 5-cm drifter velocity (u

_{r}, v

_{r}), as calculated by Equation (1), but using a distance threshold of 4000 m for co-located drifter pairs. (

**b**) Same as (

**a**), except surface Stokes velocity computed by Equation (2) has been added to the CODE drifter velocity. (

**c**) Same as (

**b**), except the differential velocity of Stokes drift of the surface 4 cm over that averaged between 55 and 146 cm (the CODE drifter drogue depth) has been added to the CODE drifter velocity. The red dots are centroids of the scatter points and the red ellipses represent the standard deviations of the scatter points. Listed on each plot are the number of co-located observations (N), the angle clockwise from vector (0,1) to the centroid (mean), and the magnitude of the mean with 95% confidence interval.

**Figure 10.**Time series of mean speed of all 5-cm drifters (thick black line) and CODE-style drifters (thin black line) for the first three days of the field experiment. The gray line is the mean of the magnitude of CODE drifter velocity plus the surface Stokes drift velocity. Black plus symbols near the bottom indicate times of co-located drifter velocity observations plotted in Figure 9, and the number of each co-located pair of observations in each cluster is indicated.

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**MDPI and ACS Style**

Morey, S.L.; Wienders, N.; Dukhovskoy, D.S.; Bourassa, M.A.
Measurement Characteristics of Near-Surface Currents from Ultra-Thin Drifters, Drogued Drifters, and HF Radar. *Remote Sens.* **2018**, *10*, 1633.
https://doi.org/10.3390/rs10101633

**AMA Style**

Morey SL, Wienders N, Dukhovskoy DS, Bourassa MA.
Measurement Characteristics of Near-Surface Currents from Ultra-Thin Drifters, Drogued Drifters, and HF Radar. *Remote Sensing*. 2018; 10(10):1633.
https://doi.org/10.3390/rs10101633

**Chicago/Turabian Style**

Morey, Steven L., Nicolas Wienders, Dmitry S. Dukhovskoy, and Mark A. Bourassa.
2018. "Measurement Characteristics of Near-Surface Currents from Ultra-Thin Drifters, Drogued Drifters, and HF Radar" *Remote Sensing* 10, no. 10: 1633.
https://doi.org/10.3390/rs10101633