## 1. Introduction

In recent years a great deal of attention has been directed toward air–sea interaction as scientists have begun to study environmental issues by properly treating the ocean and atmosphere as a coupled system. This approach has resulted in a number of air–sea interaction studies, which have united scientists from a variety of disciplines. These studies have also forced researchers to address the problems associated with making high-resolution measurements of turbulence statistics at sea. The problems largely arise from three sources: platform motion, flow distortion, and environmental factors unique to the ocean.

Some of the environmental factors that prove troublesome include the contamination of temperature probes by sea spray (Friehe et al. 1975; Larsen et al. 1993) and mechanical failure induced by a combination of corrosion, wave stress, and unavoidable neglect due to infrequent maintenance. Many of these problems have been overcome by the use of the latest generation of sonic anemometers–thermometers. However, sea-spray contamination of fast-response humidity sensors still plagues marine meteorologists. Dual-wavelength infrared hygrometers have shown some promise in combating this problem in recent field experiments. Unfortunately, these devices often present additional problems (e.g., Fairall and Young 1991), which make the development of a reliable fast-response humidity sensors one of the greatest challenges in marine instrumentation.

Attempts have been made to combat the problems of platform motion and flow distortion by choosing indirect measurement techniques that are less sensitive to their contaminating effects. An example of an indirect measurement is the use of the inertial-dissipation method to infer meteorological fluxes from spectral estimates in the inertial subrange (Fairall and Larsen 1986; Fairall et al. 1990). This method is commonly used on research vessels because the inertial subrange estimates are generally uncontaminated by wave-induced motion. The method has also been shown by Edson et al. (1991) to be less sensitive to flow distortion because it is based on autovariance statistics rather than covariances (see also Anderson 1993; Yelland et al. 1994).

Unfortunately, the inherent limitations of less direct methods can lead to unsatisfactory flux estimates depending on the project’s research objectives. For example, the bulk aerodynamic (e.g., Liu et al. 1979; Large and Pond 1981, 1982; Fairall et al. 1996) and inertial dissipation methods have a disadvantage in that they provide only an estimate of the magnitude of the flux. One can assume that the stress is directed along the streamwise velocity component, but recent studies have shown that this is not necessarily the case and that the difference between the two vectors may be an important indicator of larger-scale forcing (Geernaert 1988). Additionally, recent studies by Davidson et al. (1991), Geernaert et al. (1993), and Rieder et al. (1994) have shown that sea-state parameters such as swell and gradients in the surface currents can also influence the direction of the stress vector. Therefore, it is necessary to compute the vector stress using the eddy correlation technique if the objective of the experiment is to understand directional processes.

Second, both indirect methods must rely on additional parameterizations to account for the interaction between the wave field and the surface fluxes. These parameterizations are presently poorly understood and vary widely depending on the oceanic conditions (e.g., open ocean versus coastal zones), such that direct estimates of the fluxes are necessary if we hope to improve these methods. Since these interactions include those associated with surface slicks, wave–current interactions, and temperature stratification, directional stress estimates must be combined with directional wave spectra, current measurements, oceanic and atmospheric stratification parameters, and surfactant concentrations to examine the functional relationship between the wind forcing and wave state. This is clearly a difficult task but one that will become less daunting with the data collected during several field experiments, one of which is briefly discussed in section 6.

Direct covariance (or eddy correlation) measurements generally require an experimental setup around a platform that removes or minimizes the aforementioned effects. One such experimental design is the use of a fixed structure (such as a shallow-water tower) to eliminate platform motion. The sensors are then mounted on low profile masts or booms to move them away from the distorted flow near the platform. This approach was used during the Humidity Exchange over the Sea Main Experiment (HEXMAX), where eddy correlation (or direct covariance) flux estimates were made on a boom extending 17 m upwind of a research platform (Oost et al. 1994). The obvious disadvantage to this approach is that these fixed platforms are relatively scarce and are generally limited to shallow water, and it is often difficult to reduce the flow distortion to satisfactory levels.

Still another approach is to start with a low profile platform, moored buoy (e.g., Dugan et al. 1991; Anctil et al. 1994), or mast, and then correct for platform motion by carefully measuring this motion relative to some reference frame. The systems required to make these measurements generally use a combination of radial and linear accelerometers, compasses, and gyros. These sensors can either be mounted on a stabilized subplatform that has sufficiently slow response to motion or they can be strapped down to the main platform. Signals from both these types of systems are processed in various ways to ultimately produce an estimate of the platform’s velocity at the measurement location. Further processing of these signals can be used to estimate the position of the platform relative to the sea surface.

This paper describes our recent efforts to directly measure turbulent fluxes and statistics at sea from mobile platforms using the latter approach. In sections 2–5 we examine the methods used to compute the mean and turbulent meteorological statistics from moving platforms at sea. This involves a detailed description of the methods for obtaining the necessary correction terms using either a strapped-down or gyro-stabilized system. In section 6 we provide a discussion of the results obtained from two strapped-down systems deployed during the High Resolution experiment (Herr et al. 1991). This section describes the system components in some detail and gives examples of the velocity measurements before and after correction to illustrate the effects of motion contamination. The section concludes with a comparison of the eddy correlation derived fluxes with bulk aerodynamic derived estimates.

## 2. Direct covariance flux systems

*τ*

*ρ*

**i**

*u*

*w*

**j**

*υ*

*w*

*ρ*is the density of air, the brackets denote a time average, and

*u*′,

*υ*′, and

*w*′ are the longitudinal, lateral, and vertical velocity fluctuations about their means. In (1), −〈

*u*′

*w*′〉 represents the longitudinal (along wind) component of the stress, and −〈

*υ*′

*w*′〉 is the lateral component.

*c*

_{p}is the specific heat of air at constant pressure,

*L*

_{e}is the latent heat of evaporation of water, and

*θ*′ and

*q*′ denote fluctuations in potential temperature and specific humidity, respectively. These fluxes can then be combined with estimates of the surface stress to compute atmospheric stability parameters.

The obvious problem that arises when estimating these fluxes from a moving platform is that part of the fluctuating velocity is due to platform motion. This motion contamination must therefore be removed before we can compute the fluxes. The contamination arises from three sources: 1) instantaneous tilt of the anemometer due to the pitch, roll, and heading variations of the platform; 2) angular velocities at the anemometer due to rotation of the platform about its local coordinate system axes; and 3) translational velocities of the platform with respect to a fixed frame of reference (Hare et al. 1992).

**V**

_{true}

**T**

**V**

_{obs}

**Ω**

**T**

**M**

**V**

_{CM}

**V**

_{true}is the desired wind velocity vector in the reference coordinate system,

**V**

_{obs}is the measured wind velocity vector in the platform frame of reference,

**T**

**Ω**is the angular velocity vector of the platform coordinate system,

**M**is the position vector of the wind sensor with respect to the center of gravity, and

**V**

_{CM}is the translational velocity vector at the center of motion of the platform with respect to a fixed coordinate system.

**V**

_{true}

**T**

**V**

_{obs}

**Ω**

**T**

**M**

**S**

**V**

_{mot}

**S**is the vector distance from the motion system to the center of motion of the platform and

**V**

_{mot}now includes the additional translational velocities. Fortunately,

**M**−

**S**is just the position vector of the wind sensor with respect to the motion package. Therefore, one does not need to know the exact location of the center of motion, which is often difficult to identify.

## 3. Angles and angular rates

To use (5), we need three angular variables describing the platform’s orientation in the fixed frame and the angular velocity vector describing the time rate of change of its orientation. Several different angular coordinate systems are available (Goldstein 1965), but roll *ϕ,* pitch *θ,* and yaw Ψ are most often used because they are the variables output from common doubly gimbaled gyro-stabilized systems. In the sections that follow, we will describe two common approaches to compute these variables from moving platforms.

### a. Gyro-stabilized systems

*x, y, z*) coordinate system with

*x*positive forward (to bow),

*y*positive to port,

*z*positive upward, Ψ positive for the ship’s bow yawed clockwise from north,

*ϕ*positive for the port side rolled up, and

*θ*positive for the bow pitched down. Note that

*ϕ*and

*θ*are right-handed rotations, but to conform to the normal convention for heading, we have used a left-handed definition for Ψ. This definition allows us to directly use the platform’s compass in the transformation matrix.

Equation (6) represents the coordinate system transform for a combination of the three separate rotations of the platform coordinate frame about the three axes of our frame of reference (i.e., the earth). Note that this total coordinate transformation matrix is dependent on the order of the three separate rotations. However, for small roll and pitch angles such as those encountered on a large research vessel or discus buoy in the ocean environment (perhaps ±10°), the error due to the order of rotation is negligible. On smaller vessels such as the towed catamaran described in section 6, the errors associated with the order of rotation are minimized by the 3, 2, 1 rotation used in (6). Additionally, these errors remain small simply because the catamaran cannot be operated in high sea states, such that the angles rarely exceed ±10°.

### b. Strapped-down systems

**Ω**

**T**

**Ω**

_{obs}

**U**

_{true}

**T**

**U**

_{obs}

**Ω**

_{obs}

**R**

**V**

_{mot}

**R**is the position vector of the wind sensor with respect to the motion package.

*ϕ, θ,*and Ψ from the strapped-down angular rate sensors. The general approach is to use (6) and (7) in (9) to obtain an expression for the time derivative of these angles in terms of the measured angular rates given by

*ϕ*and

*θ*as one stepped through the measurements. In practice, problems often arise with this approach due to the drift found in angular rate sensors. Therefore, the angles are generally found by high-pass filtering the angles that are computed by integration of (12) or (13) and then adding these results to low-pass filtered reference angles. This is the approach taken by Fairall et al. (1997) and Thwaites et al. (1995).

### c. Complementary filtering

**X**= (

*x, y, z*), and

*g*is the gravitational acceleration.

The second term on the right-hand side of (14) represents the tilt-induced acceleration. These tilt-induced accelerations will eventually have to be removed before we integrate our accelerometers to compute the platform velocities as described in section 4. However, we can use these measured accelerations and angular rates to approximate the desired angles using complementary filtering.

*ϕ, θ,*and Ψ by applying filters to our signals to obtain

*s*represents the differentiation operator such that

*ϕ̇*

_{obs}=

*sϕ*

_{obs},

*τ*is a time constant, Ψ

_{slow}represents the compass output, and we have again assumed that these angles are small in (15) and (16). The first term on the right-hand side is the low-frequency tilt reference from the accelerometers as follows from (14). The second term on the right-hand side represents a high-pass filter [i.e.,

*τs*/(

*τs*+ 1)] that integrates the angular rate sensors to provide the wave-induced angular motions. By filtering the signals in this way we do not introduce any time delays, that is, the process is an all-pass filter that removes the unwanted drift in the rate gyros while retaining the low-frequency tilt reference.

*ϕ, θ,*and Ψ. Alternatively, we have computed the angles using a digital filter on the time series such that

*t*is the time step between samples,

*τ*

_{c}is the filter time constant given by

*ω*

_{c}is the prewarped frequency

The choice of the time constant *τ* is dependent on how the platform responds to the wave field. During the High Resolution Main Experiment, our spectra showed that the peak in the accelerometer spectra generally occurred around *f*_{n} = 0.2–0.25 Hz, that is, the platforms were responding strongly to 4–5-s waves. Since the accelerometers are sensing both platform and tilt-induced accelerations about this maximum, it is necessary to use a much longer time constant to obtain the low-frequency tilts. In practice, we have found that a value of *τ* equal to 5/(2*πf*_{m}) provides a smooth transition between the spectral components as shown in Fig. 1.

## 4. Translational velocities

Historically, instruments that measure absolute velocities have not been available (differential GPS may soon change this). As a result, velocities are usually computed by integrating measurements of platform acceleration after removal of the tilt-induced components discussed in section 3c. The removal of all traces of the tilt-induced components in our measured accelerations is a difficult task. Additionally, ship maneuvers require accurate measurements of the low-frequency translational velocity that can be difficult to obtain from the integrated accelerations. Therefore, we again rely on filtering to provide us with the high- and low-frequency translational velocity components.

**V**

_{mot}

**V**

_{lp}

**V**

_{hp}

**T**

*ϕ, θ, ψ*), subtracting the gravity vector, high-pass filtering and integrating the remainder, and then high-pass filtering the resultant velocities,

**g**= (0, 0, −

*g*). The same expression applies for the gyro-stabilized velocities except that the gyro-stabilized accelerometers need only be rotated to account for any change in heading before subtraction of gravity. This high-passed component represents the wave-induced motions of the anemometer where we typically use a time constant of 2 min for the filter.

The low-pass components are computed only for the horizontal velocities (i.e., we assume the platform does not leave the ocean surface) using either GPS or a current meter that measures the platform speed relative to water. The combination of the high-pass and low-pass signals results in a value of **V**_{mot} that describes the mean velocity platform relative to earth (measured with a GPS system) or relative to water (measured with a current meter) plus the fluctuating velocity components computed from our accelerometers. The method used to compute the low-frequency component depends on whether we are using real-time or postprocessing of the data as described below.

## 5. Data processing

For real-time processing we use simple exponential time filters and compute fluxes in 10-min blocks. These simple filters introduce a time lag that must be taken into account before the high-pass platform velocities are added to transformed velocities in (10). The mean translational motion of the platform is computed over the 10-min period and then added to the otherwise corrected velocities at the end of the averaging period (i.e., the low-pass time constant is 10 min). The averages, variances, and covariances are then computed and displayed at the end of each averaging period. This allows us to check the system performance during the cruise.

A flowchart for the postprocessing procedure is given in Fig. 2, which is intended to summarize the process described above. In this procedure we first remove any mean in our angular rate time series when the angles are found from complementary filtering. This step helps offset the gentle roll-off of our first-order Butterworth filters and gives us more flexibility in choosing the cutoff frequency 1/*τ.* We then use time-symmetric high-pass filters to avoid time lags in our translational velocities and apply the low-pass filtered GPS or current meter data at every time step. In this instance, the low-pass time constant is chosen to compliment the high-pass filter.

**U**

^{water}

_{true}

**T**

**U**

_{obs}

**Ω**

_{obs}

**R**

**V**

_{hp}

**T**

**V**

_{o}

**V**

_{o}is the platform velocity relative to water and Lp represents a low-pass filter operator. Equation (25) provides us with the relative velocity used in our bulk flux algorithm. The GPS system is used to directly compute the north and west components of the ship speed relative to earth. These are then used to compute the north and west components of the wind velocity relative to earth:

**U**

^{earth}

_{true}

**T**

**U**

_{obs}

**Ω**

_{obs}

**R**

**V**

_{hp}

**V**

_{GPS}

The velocities in these two coordinates systems are generally rotated into the streamwise wind (i.e., *V***W**

Finally, it is worth noting that our stress values tend to be invalidated by drastic platform maneuvers, which add low-frequency noise to the flux cospectra. In fact, our real-time stress estimates tend to be invalidated by even modest platform maneuvers because the low-pass filter in the real-time processing is essentially a 10-min block average. Therefore, the preferred mode of operation is to take measurements under way at a constant speed and heading whenever possible. In postprocessing the data, however, our algorithms are able to correct for heading changes. The data given in section 6 are taken from the postprocessed flux estimates, where the mean relative wind direction was limited to ±90° from the bow.

## 6. Discussion of results

In the discussion that follows, we will focus on measurements made using the WHOI flux system during the High Resolution and Marine Boundary Layers (MBLs) experiments. Results from the system deployed by NOAA’s Environmental Technology Laboratory can be found in Fairall et al. (1997). The High Resolution program is an Office of Naval Research (ONR)-sponsored Accelerated Research Initiative that was designed to investigate surface signatures in radar backscatter measurements in and around the Gulf Stream. This region was selected because the gradients associated with sea surface temperature and current fronts often give rise to roughness contrasts that cause the features seen in remotely sensed images. In these regions it is especially important to compute the fluxes in a frame of reference moving with the ocean surface. This is because the momentum flux, at least in a bulk sense, is proportional to the relative difference between the wind and current velocities.

The MBL experiment was another ONR-sponsored research program that took place off the California coast. The experiment was conducted from research vessels, an aircraft, and the research platform *FLIP.* The R/P *FLIP* is a 110-m-long spar buoy that provides a relatively stable platform for ocean-going research (particularly when compared with research vessels). The meteorological measurements made aboard the *FLIP* used a low profile mast erected off its port boom. Comparisons between the *FLIP* data and flux estimates taken aboard the research vessel are used to investigate the influence of flow distortion on our measurements.

### a. The WHOI direct covariance flux system

The WHOI Direct Covariance Flux System (DCFS) has been deployed in two recent field experiments on three platforms. Two ship-based systems have been on bow masts aboard the R/V *Columbus Iselin* during the High Resolution Main Experiment and from the R/V *Wecoma* during the MBL experiment. Additionally, a DCFS was deployed aboard the laser slope gauge, acoustic Doppler current profiler, Attitude measurement unit, sonic anemometer (*LADAS*) catamaran that was towed from the R/V *Columbus Iselin,* as shown in Fig. 3. The *LADAS* has been developed to allow us to study a wide range of microscale and mesoscale processes within the oceanic and atmospheric boundary layers by integrating several systems on a single platform. The catamaran is remotely “flown” outside of the wake of the research vessel, with power and signals going to and from the vessel by way of the towing cable. The platform is designed to collocate the probes as much as possible so as to study cause and effect on very fine spatial and temporal scales, while making the platform itself much less obtrusive to the environment than previous ocean-going platforms. The catamaran has additional advantages over buoys in that it is highly mobile and is not limited by power consumption restraints.

The 1993 High Resolution Main Experiment was conducted off Cape Hatteras in and around the Gulf Stream. The primary objective of these experiments was to examine the relationship between microwave remote sensing, meteorological forcing, and oceanic surface processes. In this regard, the scientific team instrumenting the R/P *LADAS* was most interested in making accurate measurements of the meteorological forcing through wind stress and the short-wave component of the wave spectrum, which is the primary source for microwave backscatter from the ocean surface. The system used to measure the short-wave spectra is described in detail by Bock and Hara (1995).

The meteorological package aboard all three platforms consisted of a Solent three-axis sonic anemometer–thermometer and a Väisälä relative humidity–temperature sensor with a radiation shield. The sonic anemometer and Väisälä units were deployed 5.6, 11.5, and 11.3 m above the mean sea surface on the R/P *LADAS,* R/V *Iselin,* and R/V *Wecoma,* respectively. The ship-based systems also included an Ophir infrared hygrometer in order to make direct estimates of the latent heat flux, as shown in Fig. 4.

The R/P *LADAS* used a Honeywell MK 50 Attitude Measurement Unit (AMU) to provide the three axes angular rates and linear accelerations needed to correct the various measurement systems onboard. The AMU is strapped down near the center of mass of the catamaran, which was 5.3 m away from the sonic sampling volume. The R/P *LADAS* computed the mean velocity relative to water using a SimTronix UCM 40 three-axis current meter provided by Johns Hopkins Applied Physics Laboratory. The current meter also contained a compass to provide heading and a temperature probe for the near sea surface temperature. The current meter was deployed approximately 1 m forward and between the catamaran’s pontoons at a depth of 1 m.

The ship-based DCFS used the three-axis accelerometers and rate sensors provided by a Systron Donner MotionPAK. The MotionPAK was mounted directly beneath the sonic anemometer package, which decreased the distance between the sensors and the sonic sampling volume to |**R**| ≈ 1 m in (10), as shown in Fig. 4. The R/V *Iselin* used the ship’s gyrocompass to obtain heading, while the R/V *Wecoma* system incorporated a Precision Navigation compass. A hull-mounted ADCP provided the relative velocity for both ships using the uppermost bins of the ADCP data. A temperature probe was dragged off the side of the ships to provide the DCFS with a continuous record of near-surface temperature.

### b. Platform contamination

A segment of a uncorrected sonic vertical velocity time series taken from the R/V *Iselin* is shown in Fig. 5 along with the computed velocity correction. Obviously most of the fluctuating signal seen by the anemometer in this time series is platform motion. This figure also indicated that a mean vertical velocity remains even after correction. The residual tilt varies from approximately 3° to 5° for relative wind directions from 0° (i.e., toward the bow) to ±90° (from port or starboard). The residual tilt on the R/P *LADAS* is always less than 1° for the relative wind directions used in this analysis. We believe that the larger residual tilt is due to flow distortion by the vessel’s superstructure and provide evidence for this in section 5d.

The corresponding vertical velocity spectra are shown in Fig. 6, where the motion is apparent as a spike at about 0.25 Hz in the uncorrected spectrum. This figure shows that this spike is effectively removed after the correction procedure has been applied. The low-frequency changes in the velocity spectra are due to the instantaneous tilt corrections, which add components of the other two velocity measurements, as well as the low-frequency translational motion of the platform (only the mean was removed from the uncorrected time series).

The effect of motion contamination in our flux estimates can be examined in detail using the cospectral equivalent of (1). The cospectral estimates of the stress components are shown in Figs. 7 and 8. The uncorrected components are clearly contaminated by a spike in the cospectra occurring at the frequency *f*_{m}. This spike dominates the signal and results in a positive values of the longitudinal momentum fluxes when we integrate under the curve. However, when we remove the platform contamination from our signals we obtain cospectra that agree well with empirical predictions. An example of this is shown in Fig. 9 where we have plotted the corrected a *uw* cospectrum versus the empirical formula determined by Kaimal et al. (1972).

### c. Flux comparisons

*u*

*u*

*w*

^{2}

*υ*

*w*

^{2}

^{1/4}

*LADAS,*while Figs. 12 and 13 give the same comparisons for the R/V

*Iselin.*Clearly, the agreement between the two methods is dramatically improved through correction, where the platform motion tends to cause an increase in the correlation between the signals that leads to an overestimation of the flux. There is very good agreement between the direct covariance and bulk estimates from the R/P

*LADAS.*However, there appears to be some additional scatter and bias in the R/V

*Iselin*comparison.

This bias is also evident in the comparison of the direct-covariance stress components computed from the R/P *LADAS* and R/V *Iselin.* These fluxes were computed by averaging together three 10-min estimates. We expect our 10-min averages to miss some of the turbulent flux that would result in an underestimation of the flux, particularly for the measurements under the low winds from the R/P *LADAS.* However, Mahrt et al. (1996) have shown that averaging together our 10-min fluxes reduces the random error in our estimates, which more than offsets the slight loss of covariance under most wind conditions.

Figures 14 and 15 compare all the 30-min averaged flux estimates where there was at least 20 min of overlap. As one would expect, the comparisons show that the lateral components are smaller in magnitude than the longitudinal components except perhaps at low wind speeds. However, the absolute values of the R/V *Iselin* fluxes are generally larger than the R/P *LADAS,* and a correlation between the lateral component of the flux is not readily apparent. While some of the discrepancy could be caused by the underestimation of the fluxes from the R/P *LADAS* at low wind speeds, we believe that we have additional evidence that points to flow distortion as the primary cause for the disagreement.

### d. Flow distortion

Because of its size, the catamaran is a much better wave follower than the ship. This causes the magnitude of the motion correction required for the R/P *LADAS* to be larger than the correction required for the R/V *Iselin.* Therefore, the reduced scatter and better agreement found in Fig. 11 versus Fig. 13 (as well as the smaller residual tilt) lead us to believe that most of the difference between the various flux comparisons is due to the effects of flow distortion on our ship-based measurements. This flow distortion is expected to influence both the mean flow and the turbulence. A comparison of the wind speeds relative to the ocean surface is shown in Fig. 16, where the *LADAS* winds have been brought up to 11.5 m using the friction velocity and stability corrections obtained from the bulk algorithm. While this comparison exhibits some enhanced scatter at low wind speeds, any systematic difference between these velocity measurements is not readily apparent. As such, our suggestion that flow distortion causes the differences seen in the above figures remains speculative.

Fortunately, the MBL experiment provided us with the opportunity to compare our ship-based DCFS with the flux measurements made aboard the R/P *FLIP.* During the MBL experiment, the R/P *FLIP* was moored 40 km off the Monterey coast. A heavily instrumented 15-m mast was deployed at the end of the port boom by the first author and colleagues at the University of California, Irvine. This instrumentation was used to measure the momentum flux at three levels above the ocean surface. The velocity measurements from the *FLIP* also require motion correction before the fluxes were computed. However, because the corrections are typically an order of magnitude smaller than the ship-based system, we believe that this comparison provides a more quantitative evaluation of the DCFS.

Time series of the longitudinal component of the momentum flux measured at 8.7 m (dotted line) and 13.8 m (dashed line) aboard the R/P *FLIP* and at 11.3 m aboard the R/V *Wecoma* are shown in Fig. 17. This figure shows all of the flux estimates made when the ship was within 50 km of *FLIP* for relative wind directions between −120° and +120° of the bow. The time series shows that the fluxes follow each other very closely over the course of several frontal passages. However, this also indicates that the magnitude of the momentum fluxes from the ship are often higher than the R/P *FLIP.*

A direct comparison of these estimates is shown in Figs. 18 and 19, where the ship fluxes have been reduced by 15% in Fig. 19. The percentage was chosen based on a least squares fit to the data that gave a slope of 0.99 and intercept of −0.004. Correction of the R/V *Iselin* data by this same amount is shown in Fig. 20. The improved agreement in this figure provides further evidence, though indirect, that the bias is mainly due to flow distortion rather than inadequate motion correction.

We also attempted to quantify this increase as a function of relative wind direction. Unfortunately, there is not enough data to present a functional dependence of this increase on relative wind direction. However, it was clear that the magnitude of the required correction dramatically increased for directions beyond ±130° of the bow. This is why we limited our comparisons to ±120 in the comparisons shown in the above figures.

We believe that we have removed most of the bias in our flux estimates, reducing the flux by 15% and limiting our relative direction to within ±120° of the bow. The scatter that remains in these figures is a combination of naturally occurring spatial variability and any remaining flow distortion or incomplete motion correction. The rms difference divided by the mean of these points gives an uncertainty of approximately 18% in Fig. 19. A comparison of the momentum flux estimates measured on *FLIP* at two different heights is shown in Fig. 21. If we assume that the differences between these two heights are due primarily to atmospheric variability, then at least 9% (as calculated above) of the *Wecoma* versus *FLIP* difference is due to this variability. In fact, it is very likely that more of the difference is due to horizontal variability, particularly because the surface temperature field was very inhomogeneous in the coastal ocean off Monterey.

Perhaps the most interesting comparison between the R/V *Wecoma* and R/P *FLIP* is shown in Fig. 22. Our previous comparisons have shown that the lateral component of the momentum stress is generally small enough so that it is difficult to distinguish between the signal and noise. However, in Fig. 22 we find strong evidence of a meteorological event that causes a noticeable lateral component in both the R/P *FLIP* and R/V *Wecoma* time series. During this period the ship was cruising toward the platform at approximately 2 kt. Rawinsonde launched from the ship indicated large wind shear in the upper boundary layer indicative of strongly baroclinic conditions. A frontal passage coinciding with the oscillation in the stress vector seen in this figure passed the platforms at different times as the ship steamed toward the R/P *FLIP.* We postulate that the decrease in the separation between the two platforms is responsible for the decreasing phase lag evident in the time series.

## 7. Conclusions

This paper has shown that the flux systems deployed in a number of recent over-sea field programs are capable of accurately measuring a direct estimate of the flux after removing the contamination in the signal due to platform motion and flow distortion. The ability to make these estimates from a research vessel is very advantageous since the mobility of a ship makes it a very effective platform for open-ocean measurements. Additionally, deployment from a ship allows us to make flux measurements under much worse conditions than possible with the catamaran.

The comparisons shown in this paper indicate that the flow distortion causes an increase in the measured covariance of approximately 15% (or about 8% for the friction velocity). Though substantial, this correction is of a similar magnitude to the corrections for platform distortion applied to the HEXMAX dataset (Oost et al. 1994). Our evidence suggests that this correction is appropriate for the commonly used class of research vessels represented by the R/Vs *Wecoma* and *Iselin.* There is some evidence that this correction is a function of the direction of the relative wind vector. However, we do not have enough data processed from the R/P *FLIP* to make any definitive conclusions at this time.

Finally, some caution must be exercised when using ship-based measurements in studies examining the directional properties of marine surface layer turbulence (e.g., investigations of the influence of misaligned wind and waves on the stress vector). This caution is necessary because of the magnitude of the flow distortion and motion contamination relative to the magnitude of the lateral component of the flux. However, it appears that the fluxes can be used in case studies of directional processes under conditions where the cross-stream component of the vector stress is comparable with the along-wind component, as shown in Fig. 22. Additionally, many problems associated with flow distortion can be circumvented through use of smaller coastal vessels, low-profile towed vehicles, and moored platforms such as the R/P *LADAS,* surface buoys (e.g., Anctil et al. 1994), and the R/P *FLIP.* In fact, the time series showing the lateral component of the stress vector points out one advantage of having both mobile and moored platforms in studies investigating air–sea interactions.

## Acknowledgments

The authors would like to thank Erik Bock and Fredrik Thwaites for their helpful discussions during the construction of both the system and processing algorithms, and Ditmar Bock for his suggestions on the use of complementary filtering. The engineering, technical, and scientific contributions of Nick Witzell, David Schroeder, Steve Murphy, Robert Handy, and John Boutillette at WHOI and Dave Gregg, Scott Abbott, Jesse Leach, Cat Russell, and Norbert Szczepczynski at NOAA/ETL are also acknowledged. The first author would like to thank Judy White for her assistance in preparing the manuscript. Special thanks go to Scott Miller and Carl Friehe of UC-Irvine for their help in collecting and processing the R/P *FLIP* data. The High Resolution and MBL components of this research has been supported by the Office of Naval Research (Grants N00014-92-J-1585, N00014-93-1-0274, and N00014-96-1-0012). Partial support for the NOAA/ETL component has been provided by the DOE Atmospheric Radiation Measurement program and the U.S. National Oceanic and Atmospheric Administration Climate and Global Change Program.

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A flowchart of the method used to postprocess the data. Spinup represents the time given to the complementary filters to provide the proper angles, while *t*_{max} represents the record length.

Citation: Journal of Atmospheric and Oceanic Technology 15, 2; 10.1175/1520-0426(1998)015<0547:DCFEFM>2.0.CO;2

A flowchart of the method used to postprocess the data. Spinup represents the time given to the complementary filters to provide the proper angles, while *t*_{max} represents the record length.

Citation: Journal of Atmospheric and Oceanic Technology 15, 2; 10.1175/1520-0426(1998)015<0547:DCFEFM>2.0.CO;2

A flowchart of the method used to postprocess the data. Spinup represents the time given to the complementary filters to provide the proper angles, while *t*_{max} represents the record length.

Citation: Journal of Atmospheric and Oceanic Technology 15, 2; 10.1175/1520-0426(1998)015<0547:DCFEFM>2.0.CO;2

The R/P *LADAS* catamaran. The sonic anemometer is mounted on the mast above the starboard pontoon. The Honeywell AMU was located in one of the splash-proof containers near the center of the catamaran.

The R/P *LADAS* catamaran. The sonic anemometer is mounted on the mast above the starboard pontoon. The Honeywell AMU was located in one of the splash-proof containers near the center of the catamaran.

The R/P *LADAS* catamaran. The sonic anemometer is mounted on the mast above the starboard pontoon. The Honeywell AMU was located in one of the splash-proof containers near the center of the catamaran.

The Direct Covariance Flux System used aboard the R/Vs *Iselin* and *Wecoma.* The anemometer is mounted directly above the metal canister that houses the MotionPAK AMU sensors. The sensor mounted horizontally below the canister is an Ophir infrared hygrometer. The antenna for the GPS receiver integrated into the system is visible on the horizontal crosspiece.

The Direct Covariance Flux System used aboard the R/Vs *Iselin* and *Wecoma.* The anemometer is mounted directly above the metal canister that houses the MotionPAK AMU sensors. The sensor mounted horizontally below the canister is an Ophir infrared hygrometer. The antenna for the GPS receiver integrated into the system is visible on the horizontal crosspiece.

The Direct Covariance Flux System used aboard the R/Vs *Iselin* and *Wecoma.* The anemometer is mounted directly above the metal canister that houses the MotionPAK AMU sensors. The sensor mounted horizontally below the canister is an Ophir infrared hygrometer. The antenna for the GPS receiver integrated into the system is visible on the horizontal crosspiece.

The top panel shows a time series of the measured sonic vertical velocity (solid line) with the high-passed vertical velocity correction *W*_{hp}(*t*). The bottom panel shows the true vertical velocity computed from Eq. (10).

The top panel shows a time series of the measured sonic vertical velocity (solid line) with the high-passed vertical velocity correction *W*_{hp}(*t*). The bottom panel shows the true vertical velocity computed from Eq. (10).

The top panel shows a time series of the measured sonic vertical velocity (solid line) with the high-passed vertical velocity correction *W*_{hp}(*t*). The bottom panel shows the true vertical velocity computed from Eq. (10).

The measured (broken line) and corrected (solid line) vertical velocity power spectra. The spectra are computed from the average of three 3-min time series within a 10-min record. The straight line in the figure represents the expected −2/3 slope in the inertial subrange.

The measured (broken line) and corrected (solid line) vertical velocity power spectra. The spectra are computed from the average of three 3-min time series within a 10-min record. The straight line in the figure represents the expected −2/3 slope in the inertial subrange.

The measured (broken line) and corrected (solid line) vertical velocity power spectra. The spectra are computed from the average of three 3-min time series within a 10-min record. The straight line in the figure represents the expected −2/3 slope in the inertial subrange.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the longitudinal component of the momentum flux.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the longitudinal component of the momentum flux.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the longitudinal component of the momentum flux.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the lateral component of the momentum flux.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the lateral component of the momentum flux.

The uncorrected (broken line) and corrected (solid line) covariance spectra for the lateral component of the momentum flux.

The corrected (solid line) covariance spectra for the longitudinal component of the momentum flux plotted with a parameterization of this component (dotted line) reported in Kaimal et al. (1972).

The corrected (solid line) covariance spectra for the longitudinal component of the momentum flux plotted with a parameterization of this component (dotted line) reported in Kaimal et al. (1972).

The corrected (solid line) covariance spectra for the longitudinal component of the momentum flux plotted with a parameterization of this component (dotted line) reported in Kaimal et al. (1972).

A comparison of the uncorrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the uncorrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the uncorrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/P *LADAS* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the uncorrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the uncorrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the uncorrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of the corrected friction velocity estimates from the R/V *Iselin* computed from Eq. (27) vs our bulk aerodynamic estimates. The fluxes represent 30-min averages computed from three 10-min estimates.

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of measurements of the lateral component 〈*υ*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of measurements of the lateral component 〈*υ*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of measurements of the lateral component 〈*υ*′*w*′〉 of the momentum flux taken from the R/V *Iselin* and R/P *LADAS.* The data represent 30-min averages where there is at least 20 min of overlap between the estimates.

A comparison of our relative wind speed measurements taken from the R/V *Iselin* and R/P *LADAS.* The R/P *LADAS* measurements have been adjusted to the height of the R/V *Iselin* measurements using the friction velocity and stability corrections computed using the bulk aerodynamic method of Fairall et al. (1996).

A comparison of our relative wind speed measurements taken from the R/V *Iselin* and R/P *LADAS.* The R/P *LADAS* measurements have been adjusted to the height of the R/V *Iselin* measurements using the friction velocity and stability corrections computed using the bulk aerodynamic method of Fairall et al. (1996).

A comparison of our relative wind speed measurements taken from the R/V *Iselin* and R/P *LADAS.* The R/P *LADAS* measurements have been adjusted to the height of the R/V *Iselin* measurements using the friction velocity and stability corrections computed using the bulk aerodynamic method of Fairall et al. (1996).

A time series of the longitudinal component 〈*u*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

A time series of the longitudinal component 〈*u*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

A time series of the longitudinal component 〈*u*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Wecoma* and R/P *FLIP.* The data represent 30-min averages computed when the R/V *Wecoma* was within 50 km of the R/P *FLIP.*

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Wecoma* and R/P *FLIP.* The data represent 30-min averages computed when the R/V *Wecoma* was within 50 km of the R/P *FLIP.*

A comparison of measurements of the longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/V *Wecoma* and R/P *FLIP.* The data represent 30-min averages computed when the R/V *Wecoma* was within 50 km of the R/P *FLIP.*

As in Fig. 18 except that the R/V *Wecoma* estimates have been reduced by 15%.

As in Fig. 18 except that the R/V *Wecoma* estimates have been reduced by 15%.

As in Fig. 18 except that the R/V *Wecoma* estimates have been reduced by 15%.

As in Fig. 14 except that the R/V *Iselin* estimates have been reduced by 15%.

As in Fig. 14 except that the R/V *Iselin* estimates have been reduced by 15%.

As in Fig. 14 except that the R/V *Iselin* estimates have been reduced by 15%.

A comparison of measurements of 30-min averaged longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/P *FLIP* at 8.7 and 13.8 m.

A comparison of measurements of 30-min averaged longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/P *FLIP* at 8.7 and 13.8 m.

A comparison of measurements of 30-min averaged longitudinal component 〈*u*′*w*′〉 of the momentum flux taken from the R/P *FLIP* at 8.7 and 13.8 m.

A time series of the lateral component 〈*υ*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

A time series of the lateral component 〈*υ*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

A time series of the lateral component 〈*υ*′*w*′〉 of the momentum flux measured aboard the R/P *FLIP* and R/V *Wecoma* during a 3-day period in May 1995. The dotted and dashed lines represent measurements taken at 8.7 and 13.8 m aboard the R/P *FLIP,* respectively. The solid line represents the R/V *Wecoma* data.

^{}

* WHOI Contribution Number 9126.