Abstract

The wind effects on drogued and undrogued drifters are assessed using Coastal Ocean Dynamics Experiment (CODE) and Surface Velocity Program (SVP) drifter datasets and ECMWF wind products in the eastern Mediterranean. Complex and real linear regression models are used to estimate the relative slip of undrogued SVP drifters and to extract the wind-driven currents from the drifter velocities. The frequency response of the wind-driven currents is studied using cross-spectral analysis. By comparing the velocities of cotemporal and nearly collocated undrogued and drogued SVP drifters, it appears that undrogued SVP drifters have a general downwind slippage of about 1% of the wind speed. Time-lagged complex correlations and cross-spectral results show that the wind response is almost simultaneous. The velocities of SVP drifters drogued to 15 m are poorly correlated with the winds (R2 ≈ 3%): wind-driven currents have a magnitude of 0.7% of the wind speed and are 27°–42° to the right of the wind. For undrogued SVP drifters, the correlation with the winds increases to R2 ≈ 22% and the angle between winds and currents decreases to 17°–20°. The magnitude of the wind-driven currents is about 2% of the wind speed. For CODE designs, wind-driven currents are 1% of the wind speed at an angle of about 28° to the right of the wind (R2 ≈ 8%). Spectral and cospectral analyses reveal that the drifters sampled more anticyclonic than cyclonic motions. The inner coherence spectra show that wind and currents are more correlated at temporal scales spanning 3–10 days. They also confirm that the wind response is quasi-simultaneous and that currents are generally to the right of the wind.

1. Introduction

Since the advent of satellite telemetry and positioning in the late 1970s, satellite-tracked drifters have been used profusely and successfully to measure near-surface currents in all the world’s ocean basins and most semi-enclosed seas. In addition to sporadic drifter programs in coastal areas and marginal seas, mostly supporting scientific case studies, the drifter population in the World Ocean has increased and is currently maintained through international efforts coordinated by the Global Drifter Program (GDP; see Lumpkin and Pazos 2007). The quantity of surface drifters operated simultaneously worldwide at the end of 2008 was about 1200 units.

The most common drifter design used in the GDP is the Surface Velocity Program (SVP) drifter with a drogue at 15-m nominal depth (Sybrandy and Niiler 1991). For coastal and marginal sea applications, the Coastal Ocean Dynamics Experiment (CODE) drifter has been widely used to measure the currents within the top meter of the water column (Davis 1985). The near-surface currents are usually estimated from finite differences of successive positions provided by the Argo and/or the global positioning system satellite systems. All near-surface drifters are inevitably affected by surface winds and to a lesser extent by surface waves, due to the fact that some elements (mostly the antenna) are required to emerge above the sea level for data telemetry to the satellites. As a result, drifters are not perfectly Lagrangian instruments and might not follow accurately the near-surface currents. Although this effect has been minimized for the SVP and CODE models, substantial slippage of these drifters with respect to the surface currents still persists under high wind and sea conditions.

The relative motion of drifters with respect to the water has been estimated through direct slippage measurements (Kirwan et al. 1975; Geyer 1989; Niiler et al. 1995) and through statistical analyses of drifter data (Poulain et al. 1996; Pazan and Niiler 2001) to calculate corrections of the drifter-inferred velocities as a function of wind and wave characteristics. A related problem is found in the extraction of wind-driven currents from drifter data, after eventual slippage corrections to minimize direct wind effects. Statistical models used to derive wind-driven currents based on the Ekman (1905) balance have been applied on drifter data by various authors (McNally and White 1985; McNally et al. 1989; Niiler and Paduan 1995; Ralph and Niiler 1999; Rio and Hernandez 2003).

The main goal of this paper is to build on the above-mentioned studies to assess the wind-induced currents, both in terms of slippage and Ekman currents, measured by surface drifters in the eastern Mediterranean. The specific objectives are threefold. First, the effect of the winds on drogued and undrogued SVP and CODE drifters are studied using drifter datasets spanning 1995–99 and 2005–07. A simple correction for the undrogued SVP drifters is proposed so that drogued and undrogued drifter data can be combined to obtain more robust maps of mean currents and eddy variability (as done in Poulain et al. 1996). Second, complex correlations and linear regressions are used to separate the wind-driven currents from the drifter velocities. An estimation of the wind-driven currents is very useful when combining drifter, hydrographic, and satellite altimetry data to map the geostrophic currents or, in particular, to compute the mean dynamic topography (Rio and Hernandez 2003; Rio et al. 2007). Last, the subinertial response of wind-driven currents measured by the drifters is explored using cross-spectral vector analysis.

The paper is organized as follows. A brief background on the effects of wind on surface drifters is given is section 2, along with a summary of the studies on the wind-driven currents measured by drifters. The Mediterranean drifter datasets used in this study are described in section 3. The statistical methods applied to the data to estimate the wind slippage of undrogued drifters, to extract the wind-driven components from drifter velocities, and to examine their frequency dependencies are also explained. The results and their interpretation can be found in sections 4 and 5, respectively. A discussion of the results within the wider context of the Lagrangian monitoring of near-surface currents is also included in section 5.

2. Background

Two principal physical aspects determine the local wind effects on the motion of surface drifters. First, there are the effects of wind-driven Ekman currents that rotate in the water column over the vertical extent of the drifter (e.g., the top meter for the CODE drifters and down to about 15 m for the SVP drifters). Second, there is the direct action of the wind and waves on the top elements of the drifters, producing a relative motion with respect to the water called “slippage” or “leeway.”

The structure and strength of the rotating relative Ekman currents were parameterized by Ralph and Niiler (1999) as a function of wind, Coriolis parameter, and depth of the thermocline, using SVP drifters in the tropical Pacific Ocean and operational wind products. Ralph and Niiler (1999) found that in weakly stratified conditions, wind-driven currents can account for up to 50% of the variance observed in ageostrophic drifter velocities smoothed in 2° latitude × 5° longitude × 5 days bins. They tested various models expressing the wind-driven velocity as a function of the wind stress (τ), the Coriolis parameter ( f ), and the mean depth of the top of the thermocline (DT) in the following generic form:

 
formula

where the exponents a, b, and c are constants. Some of their results are summarized in Table 1. In models 1 and 2, the wind-driven current is linearly proportional to the wind stress and to the wind speed, respectively. Ralph and Niiler (1999) argued that the most generally applicable representation for the Ekman currents is proportional to the wind speed (model 2). In a recent study involving surface drifters over the World Ocean, Rio and Hernandez (2003) subtracted geostrophic velocities deduced from satellite altimetry from the drifter velocities and bandpass filtered the ageostrophic residuals between periods of 10 and 20 days where the coherence to the wind was found to be maximal. Vector regressions based on models 1 and 2 were computed in 5° latitude × 5° longitude domains using analyzed wind surface stresses from the European Centre for Medium-Range Weather Forecasts (ECMWF). The models, which can explain up to 30% of the variance in some areas, indicated that high-frequency wind-driven currents spiral to the right (left) in the Northern (Southern) Hemisphere, in qualitative agreement with Ekman theory.

Table 1.

Selected regressions results of Ralph and Niiler (1999). The coefficient of determination is denoted by R2. See the text for the symbol definitions.

Selected regressions results of Ralph and Niiler (1999). The coefficient of determination is denoted by R2. See the text for the symbol definitions.
Selected regressions results of Ralph and Niiler (1999). The coefficient of determination is denoted by R2. See the text for the symbol definitions.

It is important to note that, in addition to the direct correlation between Ekman currents and local winds, near-surface currents can be indirectly correlated to local and nonlocal winds through pressure gradient forcing [geostrophic adjustment; see Gill (1982)] and in particular via Ekman pumping processes, which are related to the wind curl (see, e.g., Weller et al. 1991). Hence, we can assume that regression models between drifter-inferred currents and local wind velocities are efficient in extracting only the Ekman currents with little contribution from the possible geostrophic wind-coherent currents at long temporal scales (>10 days; see cross spectra in Fig. 8).

Fig. 8.

Inner cross spectra of the ECMWF winds and drifter velocities (inner coherence amplitude): (left) counterclockwise and (right) clockwise.

Fig. 8.

Inner cross spectra of the ECMWF winds and drifter velocities (inner coherence amplitude): (left) counterclockwise and (right) clockwise.

Based on the above studies, we consider the simplest regression model between wind-driven currents and the local wind; that is,

 
formula

where β is a real constant, θ is an angle (positive anticlockwise), and U and W are the water and wind velocities, respectively, expressed as complex numbers (U = u1 + iu2 and W = w1 + iw2, the indices 1 and 2 corresponding to the zonal and meridional directions). Applying Eq. (2) to the velocities of the CODE (UCODE), drogued SVP (USVP), and undrogued SVP (USVPL), we obtain the following complex linear regression models:

 
formula
 
formula
 
formula

In the above equations, WCODE, WSVP, and WSVPL are the wind velocities at the drifter locations, and the complex coefficients αi and βi are to be determined by minimizing the residual error.

If we consider quasi-simultaneous and quasi-collocated velocities provided by drogued and undrogued SVP drifters, we can find the vector difference between the drifter velocities of a pair of drogued and undrogued drifters. Assuming that the drogued and undrogued drifters are advected by the same currents and are affected by the same winds, we have WSVPWSVPL and α2α3, which yield [subtracting Eq. (4) from Eq. (5)]

 
formula

for the difference between the wind-driven currents of undrogued and drogued SVP drifters. This difference is an underestimate of the slippage of undrogued SVP drifters. Poulain et al. (1996) and Pazan and Niiler (2001) used statistical models similar to Eqs. (4)(6) to assess the slippage levels of undrogued SVP drifters in the Nordic Seas and in most of the world’s oceans, respectively. They found essentially a downwind leeway of about 1% of the wind speed; that is, a 10 m s−1 wind corresponds to slippage of about 10 cm s−1. If we can assume that there is no significant veering of the slippage with respect to the wind (mostly downwind response), Eq. (6) is equivalent to the real one-dimensional regression model:

 
formula

where (USVPLUSVP)downwind is the velocity difference projected in the downwind direction and |W| is the wind speed.

3. Data and methods

a. Drifter designs

CODE drifters were developed by Davis (1985) in the early 1980s to measure the currents in the first meter under the sea surface. They were mostly used in coastal areas and in marginal seas such as the Gulf of Mexico (Ohlmann et al. 2001; Ohlmann and Niiler 2005; LaCasce and Ohlmann 2003) and the Mediterranean Sea (Poulain 1999, 2001; Poulain and Zambianchi 2007).

The CODE drifters used in this study were manufactured by Technocean (model Argodrifter). They consist of a slender, vertical, 1-m-long negatively buoyant tube with four drag-producing vanes extending radially from the tube over its entire length and four small spherical surface floats attached to the upper extremities of the vanes to provide buoyancy (Poulain 1999). Comparisons with current meter measurements (Davis 1985) and studies using dye to measure relative water movements (D. Olson 1991, personal communication) showed that the CODE drifters follow the surface currents to within 3 cm s−1, even during strong wind conditions. More recent slippage measurements (Poulain et al. 2002) with acoustic current meters positioned at the top and at the bottom of the drifter, that is, about 1 m apart along the vertical, showed that the CODE drifters follow the surface currents within 2 cm s−1 and that they move in a manner consistent with the near-surface Ekman dynamics with a velocity component perpendicular to the prevailing wind.

SVP drifters are the standard design of the GDP. They were mainly used to monitor the mixed layer circulation of the world’s oceans, but were also operated in more limited areas such as the eastern Mediterranean (Gerin et al. 2009, manuscript submitted to Ocean Sci., hereafter GOS). The SVP drifters used in this study are the mini–World Ocean Circulation Experiment (WOCE) SVP drifters (model CLEARSat-15) manufactured by Clearwater Instrumentation. They consist of a surface buoy that is tethered to a holey-sock drogue (with a diameter of about 60 cm and 5 m long), centered at a nominal depth of 15 m, that holds the drifter almost motionless with respect to the horizontal layer studied [for details on the SVP design, see Sybrandy and Niiler (1991)]. They have a drag area ratio of the drogue to the tether and surface buoy in excess of 40. The surface buoy contains the battery, antenna, temperature sensor (to measure sea surface temperature), and a microprocessor that controls the collection and the transmission of data. A tension sensor, located below the surface buoy where the drogue tether is attached, indicates the presence or absence of the drogue. Measurements of the water-following capabilities of the SVP have shown that when the drogue is attached, they follow the water to within 1 cm s−1 in 10 m s−1 winds (Niiler et al. 1995).

b. Drifter datasets in the eastern Mediterranean

The drifter data used in this study cover the eastern basin of the Mediterranean Sea (30°–40°N, 10°–36°E), including the Sicily Channel, the Ionian Sea, the Cretan Passage, and the Levantine Basin (Fig. 1). Drifter observations east of the Sicily Channel (approximately east of the transect connecting Cap Bon in Tunisia to Marsala in Sicily) and north of the Otranto Channel were excluded. The drifter observations are grouped into two datasets. The first one consists of 173 CODE drifters spanning the period 1 January 1995–31 December 1999, with maximal data densities in August 1995 and March 1998 (see data temporal distribution in Fig. 2a). These drifters were mostly deployed in the Sicily Channel (Poulain and Zambianchi 2007) and in the Adriatic Sea (Poulain 2001) and, hence, provided most of the observations in the Sicily Channel and Ionian Sea (see Fig. 1a). The total amount of data considered is about 32 drifter years.

Fig. 1.

Low-pass-filtered interpolated drifter tracks in the eastern Mediterranean: (a) CODE drifters, 1995–99; (b) SVP drogued drifters, 2005–07; and (c) SVP undrogued drifters, 2005–07.

Fig. 1.

Low-pass-filtered interpolated drifter tracks in the eastern Mediterranean: (a) CODE drifters, 1995–99; (b) SVP drogued drifters, 2005–07; and (c) SVP undrogued drifters, 2005–07.

Fig. 2.

Temporal distribution of the drifter data: (a) CODE drifters, 1995–99, and (b) SVP drifters, 2005–07.

Fig. 2.

Temporal distribution of the drifter data: (a) CODE drifters, 1995–99, and (b) SVP drifters, 2005–07.

The second dataset includes 100 SVP drifters deployed in the Sicily Channel and in the eastern Mediterranean as part of the EGYPT/EGITTO project (GOS). The dataset spans the period between 5 September 2005 and 31 October 2007 with a maximal quantity of drifters exceeding 30 units in April 2006 (Fig. 2b). The amount of drifter data available is about 30 drifter years, out of which about 60% corresponds to drogued units. The mean half and maximal lifetimes of the drogued drifters are 62 and 271 days, respectively, compared to 108 and 348 days if the drogue presence is not considered (GOS). Hence, the undrogued drifter dataset is quite substantial and, after correction for wind slippage, it increases significantly, the database used to study the circulation in the eastern Mediterranean. The spatial distributions of the drogued and undrogued drifters cover most of the eastern Mediterranean; although they are very different (see Figs. 1b and 1c). Since the majority of drifters were deployed in the Sicily Channel, southeastern Ionian Sea, Cretan Passage, and southern Levantine Basin, the drogued drifter data are more abundant in those areas. Notice that several units were deployed purposefully in anticyclonic eddies between 20° and 30°E (GOS). In contrast, when the drifters lost their drogue, they have spread around and cover more extended geographical areas of the eastern Mediterranean, excluding the Aegean Sea and the northern Levantine Basin.

c. Drifter data processing

All drifters were tracked by the Argos Data Collection and Location System installed on National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites. Drifter locations, determined from the Doppler effect on a fixed received frequency, have accuracy better than 1000 m. After data reduction and automatic–manual editing (Poulain et al. 2004), the drifter position time series were linearly interpolated at regular 2-h intervals using the kriging technique with a structure function estimated from the data themselves. The interpolated positions were then low-pass filtered with a designed filter (−3 dB at 36 h and −49 dB at 27 h) for the CODE drifters and with a Hamming filter (cutoff period at 36 h) for the SVP units, in order to remove high-frequency current components, especially the tidal and inertial currents. The low-pass time series were finally subsampled every 6 h and the velocities were computed by finite-centered differencing the 6-hourly interpolated–filtered latitude and longitude data.

d. Wind products

The ECMWF wind products were used so as to relate the drifter velocities to the local wind forcing. The 40-yr ECMWF Re-Analysis (ERA-40) wind velocities closest to the sea surface (10 m) were interpolated at the 6-hourly drifter locations for the time period spanning 1 January 1995–11 November 1999 using a simple bilinear spatial interpolation scheme. For the period spanning between 5 September 2005 and 25 June 2007, the ECMWF analysis products were interpolated at the drifter positions. All reanalysis and analysis wind time series interpolated at the drifter positions were further low-pass filtered with the same filter used for the drifter data (with a 36-h cutoff period).

e. Statistical methods

To estimate the slippage of undrogued SVP drifters, pairs of drifter observations satisfying the following conditions were sought in the EGYPT/EGITTO drifter dataset: 1) one observation is provided by a drogued SVP drifter, and the other by an undrogued SVP drifter; 2) the two observations should be simultaneous; and 3) the two drifters should be separated by less than 20 or 40 km. These distances are shorter than the main spatial scale of the eastern Mediterranean circulation [which is dominated by instability eddies ranging in size from 50 to 100 km; see GOS and Taupier-Letage (2008)] and correspond to a quantity of pairs large enough to yield robust statistical results. Figure 3 shows the locations of the pairs considered. They are mostly spread between the Sicily Channel and the southeastern Levantine basin. Complex and real linear regression models based on Eqs. (6) and (7) were applied, using the average of the ECMWF winds at the drogued and undrogued drifter positions. The goodness of the regression, or the relative variance explained by the statistical model, is expressed by the skill or the coefficient of determination (R2).

Fig. 3.

Geographical distribution of pairs of SVP drogued and undrogued observations in the eastern Mediterranean (distance: <40 km, gray; <20 km, black).

Fig. 3.

Geographical distribution of pairs of SVP drogued and undrogued observations in the eastern Mediterranean (distance: <40 km, gray; <20 km, black).

Complex linear regression models based on Eqs. (3)(5) were applied to the drifter observations and wind products in the eastern Mediterranean. In addition, complex correlation coefficients between the wind and the time-lagged drifter velocity time series were estimated following the definition of Kundu (1976). The complex correlation coefficient is a complex number whose magnitude gives the overall measure of correlation and whose phase angle gives the average angle of the drifter velocity vector with respect to the wind vector. These complex correlation results are identical to the ones obtained using linear regression models in which the offset (α) is equal to zero. In this case, the coefficient of determination (R2) is the square of the amplitude of the complex correlation coefficient.

The subinertial frequency response of wind-driven currents was explored using vector cross-spectral analysis. Rotary power spectra of drifter velocities and wind interpolated at the drifter positions were first calculated (Gonella 1972; Emery and Thomson 2001). The inner coherence amplitude and phase between the drifter velocities and the winds were estimated using the definitions of McNally et al. (1989) and Emery and Thomson (2001). The inner coherence spectrum provides an estimate of the joint variance content of the two time series for rotary components rotating in the same direction. The mean angle between the major axes of the two ellipses described by the drifter velocity and wind vectors and the mean temporal phase difference were calculated from the inner phase (McNally et al. 1989).

For all the spectral and cospectral analyses, the individual drifter time series were split into 30-day-long segments (overlapping by 50%), were subsampled at daily intervals, and were multiplied by a Kaiser window. The spectra calculated for all the segments were then block averaged. All the spectral and cospectral results span between the Nyquist period (2 days) and 30 days. Confidence intervals on the spectra were estimated using the chi-squared distribution with N degrees of freedom (Emery and Thomson 2001, 453–455), where N was taken as the number of 30-day-long segments multiplied by two. Confidence levels for the coherence were calculated using the formula of Emery and Thomson (2001, p. 488) with the same value for N.

4. Results

a. Correction of undrogued SVP drifter data

Several regression models were applied to the nearly collocated (distance <40 km) and simultaneous undrogued (USVPL) and drogued (USVP) SVP velocities (or velocity differences) as a function of wind (W) (see results in Table 2). Using 771 pairs with drifter observations separated by less than 40 km, the best regression relating USVPL to USVP and W explains about 33% of the variance. However, this model has little physical significance since it corresponds to slippage in absence of wind. Hence, the offset (α) and the slope (β) were forced to 0 and 1, respectively. Doing so, the velocity difference becomes proportional to the wind, with a slope of 0.0066 and a small veering to the right of 2°. This model explains only about 4% of the variance of the velocity difference. Since the above veering angle is small, we can assume that the response is basically downwind and a model based on Eq. (7) can be applied. It is found that the downwind slippage is 0.66% of the wind speed. The relative explained variance for this model is slightly higher (7%). The maximal distance between the drifter observations was also reduced to 20 km to compare the drogued and undrogued velocities with better collocated pairs. The quantity of pairs is obviously reduced (164) but the results are essentially the same. The downwind slippage is 0.69% of the wind speed and the model explains nearly 10% of the variance.

Table 2.

Regression models used to estimate the relative slippage of undrogued SVP drifters with respect to drogued SVP drifters. Angles in the exponential arguments are expressed as degrees in the anticlockwise direction. They should be transformed into rad to calculate the exponential. Here, N is the number of pairs and R2 is the coefficient of determination. The results for the real regression are also shown for a maximal distance of 20 km between the undrogued and drogued observations.

Regression models used to estimate the relative slippage of undrogued SVP drifters with respect to drogued SVP drifters. Angles in the exponential arguments are expressed as degrees in the anticlockwise direction. They should be transformed into rad to calculate the exponential. Here, N is the number of pairs and R2 is the coefficient of determination. The results for the real regression are also shown for a maximal distance of 20 km between the undrogued and drogued observations.
Regression models used to estimate the relative slippage of undrogued SVP drifters with respect to drogued SVP drifters. Angles in the exponential arguments are expressed as degrees in the anticlockwise direction. They should be transformed into rad to calculate the exponential. Here, N is the number of pairs and R2 is the coefficient of determination. The results for the real regression are also shown for a maximal distance of 20 km between the undrogued and drogued observations.

The scatter diagram of downwind slippage versus wind speed is depicted in Fig. 4, along with the regression lines corresponding to the models using pairs separated by less than 40 and 20 km (barely different since the models are similar). Up- or downwind slippage speeds can be as large as 50 cm s−1 for wind speeds ranging in 0–15 m s−1. Using pairs separated by <20 km yields slippage estimates ranging between −20 and +20 cm s−1. The large scatter around the regression lines is obvious, given the small variance explained by the regression models.

Fig. 4.

Scatter diagram of downwind slip vs wind speed. Circles and plus signs correspond to pairs separated by less than 20 and 40 km, respectively. Regression lines are depicted for both cases: 20 km (black dashed) and 40 km (gray solid).

Fig. 4.

Scatter diagram of downwind slip vs wind speed. Circles and plus signs correspond to pairs separated by less than 20 and 40 km, respectively. Regression lines are depicted for both cases: 20 km (black dashed) and 40 km (gray solid).

b. Wind-driven currents

The Ekman wind-driven currents were extracted from the CODE and SVP (drogued and undrogued) velocities using regression models (3)(5). In addition, the offset of the regressions (αi) were forced to zero to seek a simple linear relationship between drifter and wind velocities. The results are listed in Table 3.

Table 3.

Results of the linear regression models used to estimate wind-driven currents measured by the CODE (UCODE) and SVP drifters (drogued, USVP; undrogued, USVPL). Here, N is the number of observations and R2 is the coefficient of determination. Angles in the exponential arguments are expressed as ° in the anticlockwise direction. They should be transformed in rad to calculate the exponential.

Results of the linear regression models used to estimate wind-driven currents measured by the CODE (UCODE) and SVP drifters (drogued, USVP; undrogued, USVPL). Here, N is the number of observations and R2 is the coefficient of determination. Angles in the exponential arguments are expressed as ° in the anticlockwise direction. They should be transformed in rad to calculate the exponential.
Results of the linear regression models used to estimate wind-driven currents measured by the CODE (UCODE) and SVP drifters (drogued, USVP; undrogued, USVPL). Here, N is the number of observations and R2 is the coefficient of determination. Angles in the exponential arguments are expressed as ° in the anticlockwise direction. They should be transformed in rad to calculate the exponential.

Using about 46 000 6-hourly observations (∼32 drifter years) in the eastern Mediterranean, the wind-driven currents measured by the CODE drifters appear to be about 1% of the wind speed at an angle of 28°–30° to the right of the wind vector. Up to 8% of the CODE velocity variance can be explained by a simple linear relationship. The magnitude of the complex correlation between the drifter and wind velocities is about 28%.

The drogued SVP drifter velocities (24 812 six-hourly observations or ∼17 drifter years) are less correlated with the winds (complex correlation of about 18%). The regression models explain only 3% of the velocity variance in terms of linear wind dependence. The slope (β) is about 0.007, that is, about 0.7% of the wind. The veering angle of the drifter-inferred currents with respect to the wind ranges between 27° and 42° (to the right of the wind).

When the SVP drifters have lost their drogue (16 514 six-hourly observations or ∼11 drifter years), the correlation with the wind is much higher. Indeed, the coefficient of determination reaches 22%. The best linear model gives a slope of about 0.018 (i.e., about 2% of the wind speed) and a veering angle to the right of the wind of 17°–20°.

We can compute the complex correlation between drifter and wind velocities with a time lag to assess the possible delay of the currents with respect to the wind forcing (Fig. 5). The square of the magnitude of the complex correlation decreases for increasing time lags ranging between 0 and 3 days for all the drifter types considered. Actually, R2 decreases to values smaller than 5% in less than 2 days.

Fig. 5.

Magnitude of the square of the complex correlation (R2) between drifter and wind velocities as a function of time lag.

Fig. 5.

Magnitude of the square of the complex correlation (R2) between drifter and wind velocities as a function of time lag.

c. Spectral response of wind-driven currents

The rotary power spectra of the drifter velocities (Fig. 6) show a general decrease of energy for increasing frequency, characteristic of most geophysical flows (referred to as red spectra). The velocity variance at a period of 30 days is an order of magnitude larger than the level at 2 days. For all drifter types, the clockwise spectra appear slightly more energetic than their counterclockwise counterparts. This difference, however, becomes substantial for the drogued SVP drifters for which clockwise levels can be as much as 4 times larger than the counterclockwise values. High values are reported for periods near 3 and 6 days in particular. This result comes from the fact that some drifters were purposefully deployed in anticyclonic instability structures of the African slope current (GOS; Taupier-Letage 2008) and were trapped in them for extended periods (up to a few months). Despite this sampling bias, we can conclude that, in general, the surface currents sampled by the drifters in the eastern Mediterranean show more anticyclonic structures than cyclonic ones.

Fig. 6.

Rotary spectra of the drifter-inferred velocities: (left) counterclockwise and (right) clockwise.

Fig. 6.

Rotary spectra of the drifter-inferred velocities: (left) counterclockwise and (right) clockwise.

The ECMWF wind velocities interpolated at the drifter positions are also characterized by red spectra (Fig. 7). There is slightly more energy in the clockwise direction. The winds interpolated at the CODE drifter positions appear to have more variance for periods of 2–4 days with respect to the other drifter types. The different geographical distribution (Fig. 1) and time period (Fig. 2) of the drifter data can be the cause of this result, along with the fact that ERA-40 products were used for the CODE units and analysis winds for the other drifters.

Fig. 7.

As in Fig. 6, but for the ECMWF winds interpolated at the drifter positions.

Fig. 7.

As in Fig. 6, but for the ECMWF winds interpolated at the drifter positions.

The inner rotary coherence amplitude between the drifter and wind velocities (Fig. 8) shows results consistent with those presented in Table 3. Indeed, the maximal coherence is obtained for undrogued SVP drifters with values ranging from 12% to 28% and 8% to 28% for the counterclockwise and clockwise directions, respectively. For the CODE drifters, the coherence varies from 5% to 15%, whereas the smallest values (mostly <10%) are obtained for the drogued SVP units. For the undrogued SVP and CODE drifters, the coherence is generally maximal for periods spanning 3–10 days. This demonstrates the direct and indirect effects of the wind on the undrogued drifters at synoptic scales. In contrast, significant coherence for the drogued SVP drifters is mostly observed for long periods (>10% at scales of 10–30 days, especially for the clockwise component). We can speculate that the wind-driven currents observed by SVP drifters drogued to 15 m might have a slower response because they can include both the Ekman and geostrophic flows, the latter being indirectly related to the winds at long temporal scales in finite-size ocean basins via sea level changes and geostrophic adjustment (Gill 1982). The phase of the inner rotary coherence (Fig. 9) is generally very variable but is mainly positive; that is, the current vector is to the right of the wind. For the undrogued SVP and CODE drifters, the angle varies mostly from 5° to 15° when the coherence is maximal for periods of 3–10 days. These values are definitely less than 45°, the theoretical veering obtained for theoretical Ekman currents (Gonella 1972).

Fig. 9.

As in Fig. 8, but for inner coherence phase.

Fig. 9.

As in Fig. 8, but for inner coherence phase.

Combining the phase estimates of the counterclockwise and clockwise components (McNally et al. 1989) provides an estimate of the average spatial angle between the major axes of the two ellipses described by the drifter and wind velocity vectors. This angle appears mostly positive (to the right of the wind) and ranges from 0° to 20° (Fig. 10), in qualitative agreement with the results listed in Table 3. The undrogued SVP and CODE drifter velocities, which are mostly affected directly by the winds, have angles near 10° for periods of 2–3 days, whereas the drogued SVP drifters have angles approaching 20° at the same temporal scales. The average phase lag is also shown in Fig. 10. For all drifters, it is basically centered on zero, with some variability limited to ±10°. No significant phase lag corresponds to a zero time lag between the winds and the currents sampled by the drifters.

Fig. 10.

(left) Spatial angle and (right) temporal phase lag between the major axes of the drifter velocity and wind ellipses.

Fig. 10.

(left) Spatial angle and (right) temporal phase lag between the major axes of the drifter velocity and wind ellipses.

5. Discussion and conclusions

CODE and SVP drifter data in the eastern Mediterranean were used in concert with ECMWF wind data to study the wind effects on the drifter-inferred velocities. It was found that the difference between simultaneous and quasi-collocated drogued and undrogued SVP velocities, which is an underestimate of the slippage of the undrogued SVP drifter, amounts to about 0.7% of the wind speed and that it is essentially downwind. In other words, undrogued SVP drifters have a downwind leeway of at least 7 cm s−1 in 10 m s−1 winds. However, the regression model of downwind slippage versus wind speed explains only a maximum of about 10% of the slippage variance and the scatter of the data is large (see Fig. 4). A similar result can be obtained by considering the two regression models for USVP and USVPL [Eqs. (4) and (5)] with the numerical values of Table 3. Assuming that the same winds are blowing on the drogued and undrogued SVP drifters and that α2 = α3, we can subtract the two equations to obtain

 
formula

or the approximate relationship

 
formula

The above result is essentially identical to the findings of Poulain et al. (1996) and Pazan and Niiler (2001). The simple expression of Eq. (9) can be used to correct the velocities of undrogued SVP drifters before combining them with those of drogued SVP drifters to construct pseudo-Eulerian and Lagrangian statistics of the near-surface circulation (see GOS).

With the presence of a holey-sock drogue at 15-m nominal depth, the SVP design is a mixed layer drifter whose motion is less related to the surface winds. Indeed, the correlation with the wind velocities amounts to less than 18% (R2 ≈ 3%). This corresponds to wind-driven currents at 15 m that have a magnitude of 0.7% of the wind speed and are veered by 27°–42° to the right of the wind vector. This angle is large but still less than 45°, the theoretical value of the veering of surface Ekman currents. We can speculate that the small downwind leeway of drogued SVP drifters [0.1% of wind speed; see Niiler et al. (1995)] is partially responsible for decreasing the angle under 45°. Angle values smaller than 45° have also been estimated by Rio and Hernandez (2003) for SVP drifters in the global ocean.

In contrast, when an SVP has lost its drogue, it measures the currents at the sea surface (top 25 cm) with significant leeway. The currents measured by the undrogued SVP drifters are significantly correlated with the winds (up to 47%, R2 ≈ 22%) and the angle between the winds and currents decreases to 17°–20°, as a result of both direct (leeway) and indirect (Ekman) wind effects. The magnitude of the wind-driven currents is about 2% of the wind speed.

The CODE drifter, being more Lagrangian (less leeway) and extending deeper than the undrogued SVP design measures currents that are less influenced by the wind. In fact, the correlation and angle between the currents and winds are about 28% (R2 ≈ 8%) and 28°–30°, respectively. Winds of 10 m s−1 induce CODE wind-driven velocities of 10 cm s−1, that is, about 1% of the wind speed. These results are comparable to those of Mauri and Poulain (2004) in which CODE drifters in the Mediterranean have been correlated to the ECMWF wind products (both analysis and reanalysis).

The following formula is proposed to extract wind-driven currents from drifter data in the eastern Mediterranean before, for instance, combining them with satellite altimetry and hydrographic data (Rio et al. 2007):

 
formula

where β is 1%, 0.7%, and 2% and θ is 28°, 27°, and 17°, respectively for the CODE, drogued SVP, and undrogued SVP drifters.

Time-lagged complex correlation coefficients were also estimated with lags varying between 0 and 3 days. The maximum correlation was found for a zero time lag. Hence, we can assume that the wind response of surface drifters is quasi-simultaneous, at least with the temporal resolution of 6 h adopted in this work. Similar results were obtained by Ursella et al. (2006) and Poulain and Zambianchi (2007).

The wind effects on the CODE and SVP drifter velocities were also analyzed as a function of frequency. Rotary power spectra of the drifter velocities are generally red and indicate the predominance of anticyclonic motions sampled by the drifters. The latter result is partially due to the fact that several drifters were purposefully released in anticyclonic eddies and stayed trapped in them for some time. In general, the inner rotary spectra estimates are qualitatively compatible with the results obtained via complex correlation and regression models. For instance, the coherence between the winds and the undrogued drifter velocities is maximal at time scales between 3 and 10 days and reaches values of 29% for the undrogued SVP drifters. For the drogued SVP units, the coherence appears to increase with decreasing frequency, as already observed by Rio and Hernandez (2003) in their global analysis using ECMWF wind stress data. The inner coherence phases and spatial angles are mostly positive, in qualitative agreement with Ekman theory. The spatial angles are of the same order of magnitude as those obtained with the regression models (Table 3). The quasi-simultaneous response (i.e., in less than the sampling interval of 6 h) of the currents forced by the winds was confirmed by the cross-spectral analysis.

In summary, it was found that the correction for the slippage of undrogued SVP drifters proposed for the World Ocean can be applied to the drifter data in the Mediterranean Sea using operational ECMWF wind products. The slippage is essentially downwind and amounts to 1% of the wind speed. Note that this slippage is an order of magnitude larger than the one of drogued SVP drifters measured by Niiler et al. (1995). In addition it was found that simple regression models between drifter and operational wind velocities are efficient at extracting the currents correlated with the local winds (both slippage and Ekman currents) from drifter data. It is expected that our results in terms of amplitude factor (0.7%–2% of wind speed) and veering angle (17°–28° to the right of the wind) will be used when comparing satellite altimetry data with drifter observations in the eastern Mediterranean.

Acknowledgments

We thank all the individuals who have been involved with drifter operations in the eastern Mediterranean and those who have kindly shared their data with us. In particular, Claude Millot and Isabelle Taupier-Letage are acknowledged for making their EGYPT drifter data available. Thanks to Peter Niiler for exciting discussions about drifter leeway over the last couple of decades. They were the inspiration and motivation for this work. Acknowledgment is made for the use of ECMWF wind products in this research. We thank the anonymous reviewers for their constructive comments on the original manuscript. This work was partially supported by Grants N000140510281 and N000140610391 of the U.S. Office of Naval Research.

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Footnotes

Corresponding author address: Dr. Pierre-Marie Poulain, Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Borgo Grotta Gigante, 42/c 34010 Sgonico (Trieste) Italy. Email: ppoulain@inogs.it