ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus GmbHGöttingen, Germany10.5194/acp-15-10619-2015Motion-correlated flow distortion and wave-induced biases in air–sea flux measurements from shipsPrytherchJ.j.prytherch@leeds.ac.ukhttps://orcid.org/0000-0003-1209-289XYellandM. J.BrooksI. M.https://orcid.org/0000-0002-5051-1322TupmanD. J.PascalR. W.MoatB. I.https://orcid.org/0000-0001-8676-7779NorrisS. J.School of Earth and Environment, University of Leeds, Leeds, UKNational Oceanography Centre, Southampton, UKnow at: Centre for Applied Geosciences, University of Tübingen, GermanyJ. Prytherch (j.prytherch@leeds.ac.uk)25September20151518106191062917April201510June20153September20158September2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/15/10619/2015/acp-15-10619-2015.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/15/10619/2015/acp-15-10619-2015.pdf
Direct measurements of the turbulent air–sea fluxes of momentum, heat,
moisture and gases are often made using sensors mounted on ships. Ship-based
turbulent wind measurements are corrected for platform motion using well
established techniques, but biases at scales associated with wave and
platform motion are often still apparent in the flux measurements. It has
been uncertain whether this signal is due to time-varying distortion of the
air flow over the platform or to wind–wave interactions impacting the
turbulence. Methods for removing such motion-scale biases from scalar
measurements have previously been published but their application to
momentum flux measurements remains controversial. Here we show that the
measured motion-scale bias has a dependence on the horizontal ship velocity
and that a correction for it reduces the dependence of the measured momentum
flux on the orientation of the ship to the wind. We conclude that the bias
is due to experimental error and that time-varying motion-dependent flow
distortion is the likely source.
Introduction
Obtaining direct eddy covariance estimates of turbulent air–sea fluxes from
ship-mounted sensors is extremely challenging. Measurements of the turbulent
wind components must be corrected for the effects of platform motion and
changing orientation (Edson et al., 1998; Schulze et al., 2005; Brooks,
2008; Miller et al., 2008). The ship also acts as an obstacle to the air
flow forcing it to lift and change speed; this results in both the measured
mean wind being biased (accelerated/decelerated) relative to the upstream
flow and the effective measurement height being lower than the instrument
height. This can significantly bias estimates of the 10 m neutral wind speed
(U10n) and the surface exchange coefficients (Yelland et al., 1998).
Computational fluid dynamics (CFD) modelling studies of the flow distortion
have been used to determine corrections for these mean flow distortion
effects for a number of different research vessels (Yelland et al., 1998,
2002; Dupuis et al., 2003; Popinet et al., 2004; Moat et al., 2005;
O'Sullivan et al., 2013, 2015) and also generic corrections for commercial
vessels that report meteorological measurements (Moat et al., 2006a, b).
The modelled corrections show a strong dependence on the relative wind
direction (Yelland et al., 2002; Dupuis et al., 2003) and a much weaker
dependence on wind speed, but in general they have been determined only for ships
with zero pitch and roll angles. Weill et al. (2003) and Brut et al. (2005)
reported on experiments with a 1/60 scale physical model of the RV La Thalassa to
investigate the effect of pitch and roll angles on the mean flow distortion.
They found the tilt of the mean streamline to vary by more than 1∘
and the mean wind speed by up to 12 % for pitch angles between ±10∘; these effects were asymmetric about zero pitch. Roll angle
had only a small impact on the measured wind speed, about 1 % for roll of
up to 10∘, but this was examined for bow-on flows only and a
larger impact might be expected for flows with a significant beam-on
component. Comparison of in situ measurements from sonic anemometers, the
physical model tests and CFD modelling also revealed that the foremast
itself, along with the instruments and electronics enclosures mounted on it,
had a significant impact on flow distortion at the location of the sonic
anemometer.
The studies of flow distortion cited above addressed only the mean flow for
a fixed orientation of the ship with respect to the mean streamline; to the
best of our knowledge no studies have investigated the effect of
time-varying flow distortion as ship attitude changes. That the time-varying
flow distortion has an impact can, however, be inferred from reported biases
of ship-based eddy covariance measurements. Edson et al. (1998) compared
eddy covariance estimates of the kinematic wind stress from two ships with
those from a small catamaran and from the stable research platform FLIP.
They found that the ship-based estimates were on average 15 % higher than
those from FLIP and the catamaran. They argued that the difference resulted
from flow distortion over the ship rather than from inadequate motion
correction because the catamaran experienced more severe platform motion.
Pedreros et al. (2003) similarly found momentum flux estimates from a ship
to be 18 % higher than estimates from a nearby air–sea interaction spar
buoy. Evidence of such biases, ascribed to flow distortion, led to the
exclusion of ship-based direct flux measurements from the most recent update
of the COARE bulk air–sea flux algorithm (v3.5; Edson et al., 2013).
Features in cospectra that manifest as significant deviations from the
expected spectral form (e.g. Kaimal et al., 1972) at frequencies associated
with waves and platform motion have been reported in observations of
momentum fluxes measured from FLIP (Miller et al., 2008) and from fixed
platforms (Deleonibus, 1971) and towers (Drennan et al., 1999). A decrease
in the magnitude of the feature with height led Miller et al. (2008) to
ascribe its source to interactions between the waves and atmospheric
turbulence. The authors also note that the anemometers used were not
co-mounted with inertial motion units and their tilt from horizontal was
determined using the planar fit method; errors in the determined tilt or in
estimation of anemometer and inertial motion unit alignment could also
contribute to the observed features via incomplete correction for platform
motion (Brooks, 2008; Landwehr et al., 2015). Edson et al. (2013) analysed
wind profile measurements from three field campaigns and found little
evidence of wave influence on winds at heights above 4 m in sea conditions
with cp/U10n<2.5, where cp is the wave phase
speed. In general, reported motion-scale signals in the turbulence have been
observed in measurements made either at heights below 10 m (Deleonibus,
1971; Miller et al., 2008) or in conditions of fast, high swell where
cp/U10n≈2 and Hsswell≫Hswind, and Hsswell and Hswind are the significant wave heights of the
swell and wind–wave components of the wave field respectively (Drennan et
al., 1999). Recent results from large eddy simulations over moving wave
fields also suggest that, in developing sea conditions, waves are not
expected to significantly influence turbulent winds at heights of more than
about 10 m (Sullivan et al., 2014). In summary, the wave field is only
expected to influence the turbulent winds near the surface or in conditions
where swell dominates the wave field.
High-frequency gas concentration measurements for studies of air–sea
exchange have been shown to suffer significant motion-correlated biases
resulting from the hydrostatic pressure change with vertical displacement
(Miller et al., 2010) and potentially from mechanical sensitivities of the
sensors themselves (McGillis et al., 2001; Yelland et al., 2009; Miller et
al., 2010). These biases cause distortions of the cospectra between the
vertical wind component and gas concentration (Edson et al., 2011) apparent
in the cospectra at frequencies associated with the platform motion, and
several recent studies have applied motion decorrelation algorithms to
remove this signal (Miller et al., 2010; Edson et al., 2011; Blomquist et
al., 2014).
Such an approach can also correct the apparent motion-scale bias in the
momentum flux but is controversial since, as discussed above, there are
circumstances in which a real wave-correlated signal may be expected in the
turbulence measurements. Here we present measurements which demonstrate a
significant motion-scale feature in momentum flux measurements from a
research ship. We show the impact of applying a simple regression procedure
to remove the bias and provide evidence that suggests the source of the
bias is time-varying flow distortion correlated with ship motion and
attitude.
Data
The measurements were made on the RRS James Clark Ross as part of the Waves, Aerosol and Gas
Exchange Study (WAGES), a programme of near-continuous measurements using
the autonomous AutoFlux system (Yelland et al., 2009). Turbulent wind
components were measured by a Gill R3 sonic anemometer installed above the
forward, starboard corner of the ship's foremast platform (Fig. 1). The
measurement volume was approximately 16.5 m above sea level. Platform motion
was measured with a Systron Donner MotionPak Mk II, mounted rigidly at the
base of the anemometer and sampled synchronously with it. Wave field
measurements were made using a WAVEX X-band radar installed above the bridge
top. The WAVEX system obtains directional wave spectra and mean wave
parameters every 5 min.
Locations of the flux instrumentation on the RRS James Clark Ross. The sonic
anemometer is 2.0 m above the starboard forward corner of the platform. Note
that the forecastle crane is generally stowed close to the deck while the
ship is underway or on station.
The fast-response instrumentation operated at 20 Hz, and flux estimates were
calculated over 30 min periods. The raw wind and motion measurements were
first despiked and the wind components corrected for platform motion using
the complementary filtering approach of Edson et al. (1998). The motion
correction algorithm set out in Edson et al. (1998) and as usually applied
corrects the measured horizontal winds for low-frequency horizontal motions
(ship's underway velocity) in the earth frame. This neglects the aliasing of
the ship's horizontal speed into the vertical imposed by the non-horizontal
mean streamline at the point of measurement due to flow distortion over the
ship. The true vertical wind speed, wtrue, is determined from the
measured, motion-corrected vertical wind, wrel, and the horizontal true
and relative winds (Utrue and Urel) as
wtrue=wrel-wrel‾×1-Utrue‾/Urel‾,
where an overbar indicates a time average (Tupman, 2013). The derivation of Eq. (1)
and the impact of applying this correction are described in Appendix A.
This correction addresses the same source of measurement error as that
recently described by Landwehr et al. (2015), who address it by applying
corrections for the ship's low-frequency horizontal velocity after rotating
the ship-relative winds (corrected for high-frequency motions) into the
reference frame of the mean streamline for each flux averaging period.
Frequency-weighted inverted and normalised momentum flux cospectra (a)
and normalised ogives (b), shown relative to
non-dimensionalised frequency using measurement height z and mean relative wind speed
Urel. Also shown are frequency-weighted, inverted and normalised cospectra
calculated prior to motion correcting the turbulent velocity components,
which results in a large upwards flux signal at the motion scale (c).
Results shown are an average of 131 30 min duration measurements at mean
wind speeds 10ms-1<U10n<14ms-1. EC
indicates the cospectra after removing platform motion following Edson et
al. (1998) and shows the residual signal at scales typical of the wave
field. The interpolation across the wave scales has been applied between
frequencies of 0.04 and 0.4 Hz. The motion-scale correction (MSC) can either
be applied as per Eq. (2) (MSC), with Eq. (2) applied to both the along and
vertical wind components (MSCuw), or as described by Edson et al. (2011) (MSCf). Normalisation of the five different sets of results is
by u∗ with MSC applied as per Eq. (2). Note that the MSCf line
overlies the MSC line at all frequencies, and the interpolated, MSCuw
and EC lines overlie at frequencies away from the motion-scale.
After motion correction, each 30 min record is rotated into a reference
frame aligned with the mean streamline, wind components were linearly
detrended and eddy covariance momentum fluxes calculated. CFD modelling of
the air flow over the James Clark Ross was initially undertaken by Yelland
et al. (2002) but only for flow on to the bow; we have extended the CFD
study for a much wider range of relative wind directions and the results
were used to determine direction-dependent corrections to the mean
(30 min averaged) relative wind speed and measurement height. The new CFD
study is documented in Moat and Yelland (2015) and the primary results
reproduced here in Appendix B. The modelled wind speed bias at the sensor
location varied between -0.9 and 8.4 % for wind directions between
20∘ to port of the bow and 120∘ to starboard, and the
height by which the flow was raised varied between 1.3 and 3.2 m. Wind
directions beyond 20∘ to port of the bow were affected by
small-scale obstructions on the foremast platform that are not included in
the CFD model; these wind directions are thus excluded from the following
analysis. After applying the corrections, the measured winds were corrected
to 10 m height and neutral stability using the Businger–Dyer relationships
(Businger, 1988) and the 10 m neutral drag coefficient, CD10n, was
calculated from U10n and the momentum flux estimates.
The measurements used here were obtained between 9 January and 16 August 2013
in locations throughout the North and South Atlantic, the Southern
Ocean and the Arctic Ocean, at latitudes ranging from 62∘ S to
75∘ N. After excluding measurement periods when the ship was
within sea ice, there were 2920 individual flux estimates available for
analysis. Flux estimates were then rejected from the analysis where there
was excessive ship manoeuvring, where flux quality control criteria were
failed (Foken and Wichura, 1996; Vickers and Mahrt, 1997) and when the air
temperature was less than 2 ∘C when ice build-up may affect the
sensors. Of the remaining 1054 flux estimates, 80 were removed as outliers
(CD10n>5×10-3). Unless otherwise indicated,
mean relative wind direction limits of 20∘ to port and
50∘ to starboard of the bow were applied, a condition met by 499
flux estimates. Of the removed outliers, 38 lay within acceptable relative
wind direction limits; of these, 6 were at winds speeds of 6 ms-1 or
greater.
Drag coefficients bin-averaged by wind speed, relative to
U10n (n=499). Four versions of the measurements are shown: without correction for wave-scale
bias (EC); with correction applied to the vertical velocity only (MSC);
correction applied to both vertical and horizontal velocity components (MSCuw);
and correction via a simple interpolation across the wave-scale portion of the
cospectra (interpolated). The bulk COARE 3.0 and 3.5 results are calculated without
dependence on wave field or radiation.
Removal of the ship motion-scale signal
Momentum flux cospectra and ogives for U10n between 10 and 14 ms-1,
normalised (by f/u∗2 and 1/u∗2
respectively, where f is frequency` and u∗ is the friction velocity)
and averaged, are shown in Fig. 2. The cospectra and ogives differ from the
typical forms obtained from experiments over land (e.g. Kaimal et al., 1972)
at frequencies between approximately 0.06 and 0.25 Hz (0.09 and 0.37 in the
non-dimensionalised frequency shown in Fig. 2), where a significant
anomalous signal is present. These are frequencies associated with surface
waves and with the platform motion that results; hence we term the
cospectral signal at these frequencies the motion-scale signal.
At wind speeds above 7 ms-1, the CD10n measurements are biased high
compared with previous results (Fig. 3). The bias relative to the eddy-covariance-based parameterisation of Smith (1980) increases with wind speed
from approximately 20 % at 8 ms-1 to 60 % at 20 ms-1. Note
that the Smith (1980) parameterisation was derived from eddy covariance
measurements made from a slim floating tower moored so as to minimise
platform motion and induce minimal flow distortion. The bias is smaller
when compared to the COARE 3.0 (Fairall et al., 2003) or COARE 3.5 (Edson et
al., 2013) bulk algorithms.
The motion-scale signal can be removed from the vertical wind component to
obtain a corrected vertical wind, wMSC, via a simple regression method:
wMSC′=wtrue′-α1accz′-α2velz′,
where accz and velz are the platform's vertical acceleration and
velocity, measured at the base of the sonic anemometer, and primes denote
fluctuations determined from Reynolds' decomposition. The coefficients
α1 and α2 are determined here by regression for
each 30 min flux measurement period. This algorithm, which we term the
motion-scale correction (MSC), is based on the regression corrections of
Yelland et al. (2009) and Miller et al. (2010). It is also similar to the
motion decorrelation algorithm given in a spectral formulation by Edson et
al. (2011), originally utilised to remove motion biases from CO2 flux
cospectra, and here termed the MSCf. The MSCf algorithm
coefficients are defined as the ratio of covariances of vertical wind and
platform motion to variances of platform motion. The MSC and MSCf
methods give almost identical results (Fig. 2).
Applying the MSC algorithm removes the motion-scale signal (Fig. 2) and
results in a 20 to 30 % decrease in CD10n for wind speeds above 7 ms-1
and absolute values similar to those of COARE 3.0 or 3.5 (Fig. 3).
The signal removed is similar in size and of the same sign as the biases in
ship-based momentum flux measurements reported by Edson et al. (1998) and
Dupuis et al. (2003).
Applying the MSC to the along-wind component as well as the vertical
component makes an insignificant (≪1 %) additional
difference to the measured flux (shown as MSCuw in Figs. 2 and 3).
Interpolating the measured cospectra across the motion-scale frequencies
gives similar results to the MSC algorithm under most conditions (shown as
“interpolated” in Figs. 2 and 3: Prytherch, 2011; Tupman, 2013). However,
interpolation requires selection of appropriate frequencies to interpolate
between, in this case, 0.04 and 0.4 Hz (0.06 and 0.59 in the
non-dimensionalised frequency shown in Fig. 2), and is not dependent on a
physical variable related to the presumed source of the error (platform
motion-dependent flow distortion). For these reasons, correction using the
MSC algorithm is preferable.
Discussion
Following application of the MSC the cospectral shape matches the Kaimal
form expected. This suggests that the motion-scale bias is being effectively
removed.
The MSC also results in drag coefficients that lie within the range of
previous parameterisations. At the highest wind speeds (over 15 ms-1)
the parameterisations begin to diverge significantly and the WAGES
CD10n are larger than those given by Smith (1980) and lie between those
of COARE 3.0 and 3.5. It should be noted that COARE 3.0 and 3.5 are both
defined using wind speeds in the frame of reference of the surface currents
(see Appendix in Edson et al., 2013) rather than in the earth frame of
reference as used by Smith (1980). Surface current measurements were not
available for the WAGES data. For surface currents aligned with the
prevailing wind direction, adopting a surface current frame of reference
would lead to a small apparent increase in the drag coefficients presented
here.
While several previous studies have ascribed a high bias in drag coefficient
estimates from ships to flow distortion (Edson et al., 1998, 2013; Pedreros
et al., 2003), they have not examined the effect in detail. Inaccurate tilt
estimation, a related source of error, may also contribute to this bias,
particularly at low wind speeds (Landwehr et al., 2015). Few other studies
have discussed such biases at all, and it seems likely that the severity of
any motion-correlated bias is highly dependent on individual platforms and
instrument installations in the same manner as the mean flow distortion. The
bias is potentially worse here than in many other studies; the sonic
anemometer is mounted lower on the foremast than would be ideal because the
long-term measurement programme made it necessary to be able to service the
instruments easily and without access to a crane. There are also a greater
number of small-scale obstructions such as searchlights near to the
measurement point than would be the case on lattice-style masts often
deployed on dedicated flux measurement campaigns. Because the measurements
are continuous and autonomous, a large fraction of our data is also obtained
with the ship underway. In contrast, dedicated eddy covariance studies of
air–sea exchange would usually focus almost exclusively on measurements made
on station when ship motion is substantially less than when underway.
Finally it is possible that such biases are present in some fraction of the
measurements of many studies but are excluded from final analysis by
quality control procedures without a close examination of the bias being
made. Many studies with modest data volumes have quality controlled the
individual flux estimates via a visual inspection of the ogive curves,
rejecting those that do not closely match the expected form (e.g. Fairall et
al., 1997; Norris et al., 2012).
As discussed in Sect. 1 above, there is evidence from previous studies that
the influence of the wave field on the turbulent winds should be small, at
heights above some limit which is assumed to be related to the wave
properties: values between 4 and 10 m have been cited (Miller et al.,
2008;
Sullivan et al., 2014). The Sullivan et al. (2014) results correspond to a
height of the order of 1.5 times the significant wave height. Real wave effects are
thus expected to be negligible for typical measurement heights of ship-based
sensors (15–20 m) under most conditions. Below we provide more direct
evidence that the wave-scale signal seen in the WAGES data is due, in large
part at least, to the effects of flow distortion over a moving platform.
(a) Time series (60 s) of vertical platform displacement,
velocity and acceleration, platform pitch and tilt from horizontal of the
streamwise airflow measured by the AutoFlux anemometer. The tilt has been
smoothed with a 40-sample moving average. The measurements are sampled from
a period (23 April 2013, 21:00–21:30 UTC) with near bow-on winds and mean
U10n of 15.2 ms-1. (b) Variation of the tilt of streamwise
airflow from horizontal, relative to the vertical platform displacement,
velocity, acceleration and platform pitch each normalised by their measured
range. Tilt averages were made over the 30 min period that the
measurements in (a) were sampled from.
Motion dependence of the streamline
The angle to the horizontal of the airflow measured at the sonic anemometer
site was found to be dependent on the vertical motion of the ship (Fig. 4).
Perturbations in the tilt of the streamline are approximately in phase with
accz, out of phase with the vertical displacement and pitch, and lead
velz by about 90∘. There are multiple processes that may affect
the streamline orientation as the ship moves over the waves:
Vertical displacement of the ship changes the vertical extent of the
obstacle that the ship presents to the flow and the relative height
of the measurement volume with respect to that of the bow above the water line.
The ship's pitch similarly changes both the effective size of the obstacle
presented to the flow and the relative location of the sonic anemometer within the distorted flow above the bow.
Vertical motion of the ship will force the overlying air to move.
In the example here for 15 ms-1, bow-on winds, the airflow tilt varies
by about ±3∘ around a mean of approximately 10∘.
The various parameters shown in Fig. 4a are all inter-dependent, but
streamline tilt showed slightly more consistent trends with the velocity and
acceleration parameters than with displacement or pitch, suggesting that
“pumping” of the air above the moving deck may be the dominant effect.
Comparison of averaged spectra. In all panels two sets of averaged
data are compared: periods when the ship was stationary (Vship<1ms-1, 21 periods) and periods when the ship was steaming
(Vship>5ms-1, 20 periods); the individual spectra
are shown as pale lines for reference. For all measurements, U10n was
between 10 and 12 ms-1. (a) Spectral density of non-directional wave
heights from WAVEX with frequency shifted to the reference frame of the
moving ship; (b) spectral density of platform vertical velocity as measured
on the foremast; (c) frequency-weighted inverted cospectral density for the
momentum flux (positive upwards) – turbulent velocity components are motion
corrected, but the MSC correction is not applied. The dashed vertical lines
indicate the peak frequency of the wave spectrum; dotted vertical lines
indicate the peak frequency of the momentum flux cospectra in (c). Note that
the axis limits are set very close to the scale of the ship motion to allow
details to be seen clearly.
Characteristic frequencies of spectral features
For a platform moving through a wave field aligned with the direction of
travel, it would be expected that the frequency of ship motion forced by the
waves would differ from that for a ship on station with no mean horizontal
velocity. The change could be of either sign depending on the ratio of
wavelength to the length of the ship, with an increase in frequency for
wavelengths much longer than the ship. The measured frequency of atmospheric
turbulent structures would also be shifted to higher frequencies relative to
those measured when on station. The nature of the frequency shift should
differ for turbulent air motions, which advect with the wind and have a
ship-relative velocity equal to the sum of wind and ship speeds, and
wave-correlated features in the turbulence field, which are phase-locked to
the surface waves (Sullivan et al., 2000, 2008, 2014), and will have a
ship-relative velocity of the sum of wave-phase and ship speeds. A signal
due to real wind–wave interaction should thus appear at a different
frequency to that from a ship-motion-induced measurement bias.
Figure 5 shows a comparison of the power spectral density of platform
vertical velocity (Svelz, Fig. 5b) and frequency weighted cospectral
densities for the streamwise momentum flux (normalised by u∗) both
for periods during which the ship was on station (Vship<1ms-1, where Vship is the speed of the ship) and when underway
(Vship>5ms-1). The cospectra are shown after
applying the standard motion correction to the measured turbulent velocity
components but without applying the MSC correction. Also shown are the
spectral densities of the surface wave field (Fig. 5a). The wave radar
provides wave spectra in the earth frame, corrected for ship speed; in order
to compare these directly with the measured turbulence and ship-motion
spectra when underway, we need to transform them into a reference frame
moving with the ship. This is achieved by plotting against a modified
frequency, fm=f0(cp+Vship)/cp, where fm is
the frequency that would be measured in the ship reference frame and
f0 is the true frequency in the earth frame. The periods chosen all have
bow-on winds, wind speeds of between 10 and 12 ms-1 and similar sea
states: the (true) mean peaks of the mean WAVEX-derived non-directional wave
spectra (Szwave) are 0.120 and 0.110 Hz, and mean significant wave
heights are 4.73 and 3.51 m for the stationary and underway periods
respectively.
For the on-station measurements, the peak in the momentum flux cospectra (no
MSC, Fig. 5c) is at 0.113 Hz, which matches that of the peak in ship
vertical velocity (Fig. 5b) and is at slightly lower frequency than the peak
in the ship-frame surface wave spectra (0.120 Hz, Fig. 5a). For the underway
cases the peak in the ship-frame wave spectra is shifted to higher frequency
(0.163 Hz) compared to the true spectra. The peak in the ship motion
spectrum (0.148 Hz) is again lower than that of the wave spectrum and by a
larger margin than for the on-station case. The peak in the momentum flux
cospectrum at 0.153 Hz is much closer to that of the ship motion than that
of the wave spectrum.
The correspondence of the peak in momentum flux cospectra with that of the
ship motion rather than that of the wave field suggests that the residual
signal after motion correction is an artefact of motion-correlated flow
distortion rather than a result of a real wave-correlated signal in the
turbulence.
(a) Measurements either without correction for wave-scale bias
(EC) or with correction applied to the vertical velocity only (MSC) for
wind speeds 7ms-1<U10n<16ms-1 (n=335) and relative wind directions between -20 and
+50∘ (where a wind on the bow is at 0∘). Lines are
linear fits to the measurements. (b) variation of the difference between
measured drag coefficients and the linear fits against relative wind
direction for the same wind speed criteria (n=663). Both panels also
show measurements (with and without MSC) which have not had CFD-derived
corrections to mean wind speed and height applied. Note that CFD corrections
were only applied for the shaded range.
Directional dependence of drag coefficient bias
Mean flow distortion is strongly dependent on relative wind direction
(Yelland et al., 1998), even for a motionless ship with zero pitch and roll
angles. The dependence of the calculated drag coefficients on relative wind
direction before and after applying the MSC algorithm is shown in Fig. 6.
First, a linear fit was made between the drag coefficient and wind speed
data obtained for wind directions between -20 and +50∘ of the bow.
Then the drag coefficient anomalies (individual minus fit) were calculated
and averaged into 10∘ relative wind direction bins, and the
results were plotted against relative wind direction. It can be seen that
prior to applying the MSC algorithm, the drag coefficient anomalies have a
significant dependence on relative wind direction and that application of
the algorithm significantly reduces this dependence. For completeness the
results are also shown without first applying the direction-dependent
CFD-derived correction to the mean 30 min averaged wind speed; this
also reduces the dependence of the drag coefficient on relative wind
direction.
Application of the MSC and the mean CFD correction does not completely
remove all dependence of the drag coefficient on relative wind direction.
This suggests that one or both corrections may need refinement. In the case
of the MSC algorithm, the effect of the roll of the ship is likely to become
significant when the wind direction is beam-on rather than bow-on. In the
case of the CFD correction to the mean wind speed, the model of the ship
geometry may have to be refined to take into account local flow distortion
caused by small objects mounted on the foremast, close to the anemometer.
These are areas for future investigation.
Conclusions
Methods for removal of motion-correlated signals from fast-response gas
measurements made onboard moving platforms have become more commonly applied
in recent years; however, these techniques remain controversial when applied
to fast-response winds for the purpose of momentum flux calculation. The
results here demonstrate these methods and their impact on ship-based
momentum flux measurements where a significant motion-correlated bias is
present in the motion-corrected cospectra. The motion-correlated signals are
shown to be dependent on platform velocity relative to the wave field. In
addition, the dependence of the flux on wind direction relative to the ship
is reduced after applying the correction methods. These results suggest that
the motion-correlated signal is due to the effects of time-varying flow
distortion. Further investigation is required to resolve the details of the
physical processes involved.
The recent revision of the COARE bulk flux algorithm (COARE 3.5, Edson et
al., 2013) is determined only from data from platforms other than ships
(buoys, towers, FLIP). These data all require motion correction, and Bigorre
et al. (2013) report biases of a few percent in mean wind speed due to flow
distortion around one of the buoys used to collect data at high wind speed,
but these platforms generally do not suffer such significant flow distortion
problems as ships.
For many applications, ship-based measurements are the only option; for
example, direct eddy covariance measurements of gas transfer require
instrumentation that can only realistically be operated on a ship. A means
of effectively dealing with biases induced by flow distortion around a
moving platform is thus essential. The methods demonstrated above provide a
successful correction; after its application the shape of the cospectra
matches the Kaimal form expected and our drag coefficient results lie within
the range of recent leading parameterisations.
Underway vertical wind speed
The motion correction algorithm of Edson et al. (1998) calculates a total
platform velocity in the earth frame as the sum of high-pass filtered
wave-induced motions, obtained from the integration of accelerometers, and
low-pass filtered velocities (the platform's underway motion). The latter are
applied only in the horizontal since the mean vertical velocity is 0 by
definition. The corrected winds in the earth frame are obtained as the
vector sum of measured and platform velocities. This neglects the impact of
flow distortion on the measured winds (Fig. A1). At the point of measurement
on the foremast of a ship, the mean flow is forced to lift, resulting in a
streamline tilted upwards from the horizontal. The measured along-streamline
wind depends upon ship velocity as well as earth-relative wind. Since the
streamline is tilted, a fraction of the ship velocity affects the measured
vertical as well as the horizontal winds in the earth frame and must be
corrected.
When conditions are stationary (an implicit assumption for direct flux
measurement) the measured, motion-corrected vertical wind, wrel, can be
corrected for the horizontal platform mean velocity to obtain the true
vertical wind speed wtrue. The ratio of the mean true to mean relative
vertical winds is equal to the ratio of the mean true to mean relative
horizontal winds, i.e.
Utrue‾Urel‾=wtrue‾wrel‾
(Fig. A1). Then, as
wtrue=wrel-wrel‾-wtrue‾,wtrue can be determined via Eq. (1),
wtrue=wrel-wrel‾×1-Utrue‾/Urel‾.
Note that this affects the mean vertical wind only and not the high-frequency
perturbations; however, failure to account for the impact of flow distortion
on the vertical wind measurements would result in the streamline orientation
being incorrectly calculated and both u′ and w′ values being biased after
rotation into the streamline-oriented reference frame in which the fluxes
are calculated. We also note that at low wind speeds (∼<5ms-1), the determination of the reference frame for a
particular measurement interval may be biased by offsets in the vertical
wind speed, leading to errors in the tilt calculation (Wilczak et al., 2001;
Landwehr et al., 2015).
Schematic of the impact of ship horizontal velocity on
non-horizontal airflow. The measured horizontal (Urel) and vertical
(wrel) wind components must both be corrected for ship velocity to
obtain the true wind components. Not correcting the measured vertical wind
will result in an incorrect determination of the tilt angle of the flow from
horizontal.
Wind speed-averaged drag coefficients, relative to U10n. Two
sets of measurements are compared: where the ship was deemed stationary
(Vship<1ms-1, n=233) and where the ship was
underway (Vship>5ms-1, n=182). The measurements
are shown with (“corr”) and without the vertical wind speed corrected as per
Eq. (1).
The effectiveness of this correction is demonstrated through comparison of
drag coefficients from periods when the ship was stationary (Vship<1ms-1)
and underway (Vship>5ms-1).
Prior to correction, measurements from the underway ship are biased high
relative to the stationary measurements (Fig. A2). Following correction, the
stationary and underway measurements are in very good agreement for all but
the very lowest wind speeds. Furthermore, for stationary periods (where the
effect is small), the corrected and uncorrected results are also in good
agreement.
CFD corrections for flow distortion
The relative wind-direction-dependent CFD corrections for the mean flow
distortion over the ship are given in Table B1. These are strictly valid
only for the location of our sonic anemometer (1.24 m to starboard,
16.5 m
above the waterline and 5.0 m aft of the bow) but should be broadly
representative for nearby locations and indicative of the directionally
dependent flow distortion that might be expected on any similar installation
on other ships.
Variation of wind speed bias and vertical flow displacement with
relative wind direction, determined at the location of the AutoFlux
anemometer (height above sea level, z, 16.5 m). The wind speed bias and
Δz are relative to a free stream location 2 s upstream of the
anemometer site (after Yelland et al., 2002). A negative relative wind
direction indicates a flow over the port side. Further details are given in
Moat and Yelland (2015).
WAGES was funded by the Natural Environment Research Council (grant numbers
NE/G00353X/1 and NE/G003696/1). We would like to thank the two captains and
crews of the RRS James Clark Ross and the ship logistics support staff at the British Antarctic
Survey for their help throughout the project. We would also like to
acknowledge helpful and ongoing technical discussions with S. Landwehr and
B. Ward (University of Galway) that have contributed to this research.
Edited by: R. MacKenzie
ReferencesBigorre, S. P., Weller, R. A., Edson, J. B., and Ware, J. D.: A Surface
Mooring for Air–Sea Interaction Research in the Gulf Stream. Part II:
Analysis of the Observations and Their Accuracies, J. Atmos. Oceanic
Technol., 30, 450–469. 10.1175/JTECH-D-12-00078.1,
2013.Blomquist, B. W., Huebert, B. J., Fairall, C. W., Bariteau, L., Edson, J. B., Hare, J. E.,
and McGillis, W. R.: Advances in air-sea CO2 flux measurement by eddy
correlation, Bound.-Lay. Meteorol., 152, 245–276, 10.1007/s10546-014-9926-2, 2014.Brooks, I. M.: Spatially Distributed Measurements of Platform Motion for the
Correction of Ship-Based Turbulent Fluxes, J. Atmos. Ocean. Tech., 25,
2007–2017, 10.1175/2008JTECHA1086.1, 2008.Brut, A., Butet, A., Durand, P., Caniaux, G., and Planton, S.: Air–sea
exchanges in the equatorial area from the EQUALANT99 dataset: Bulk
parameterizations of turbulent fluxes corrected for airflow distortion, Q.
J. Roy. Meteorol. Soc., 131, 2497–2538, 10.1256/qj.03.185, 2005.Businger, J. A.: A note on the Businger–Dyer profiles, Bound.-Lay.
Meteorol., 42, 145–151, 10.1007/978-94-009-2935-7_11,
1988.Deleonibus, P.: Momentum flux and wave spectra observations from an ocean
tower, J. Geophys. Res., 76, 6506–6527, 10.1029/JC076i027p06506, 1971.Drennan, W., Kahma, K., and Donelan, M.: On momentum flux and velocity
spectra over waves, Bound.-Lay. Meteorol., 92, 489–515,
10.1023/A:1002054820455, 1999.Dupuis, H., Geurin, D., Hauser, D., Weill, A., Nacass, P., Drennan, W. M.,
Cloche, S., and Graber, H. C.: Impact of flow distortion corrections on
turbulent fluxes estimated by the inertial dissipation method during the
FETCH experiment on R/V L'Atalante, J. Geophys. Res., 108, 8064,
10.1029/2001JC001075, 2003.Edson, J. B., Hinton, A. A., Prada, K. E., Hare, J. E., and Fairall, C. W.:
Direct covariance flux estimates from mobile platforms at sea, J. Atmos.
Ocean. Tech., 15, 547–562, 10.1175/1520-0426(1998)015<0547:DCFEFM>2.0.CO;2, 1998.Edson, J. B., Fairall, C. W., Bariteau, L., Zappa, C. J.,
Cifuentes-Lorenzen, A., McGillis, W. R., Pezoa, S., Hare, J. E., and Helmig,
D.: Direct covariance measurement of CO2 gas transfer velocity during
the 2008 Southern Ocean Gas Exchange Experiment: Wind speed dependency, J.
Geophys. Res., 116, C00F10, 10.1029/2011JC007022, 2011.Edson, J. B., Venkata Jampana, V., Weller, R. A., Bigorre, S. P.,
Plueddemann, A. J., Fairall, C. W., Miller, S. D., Mahrt, L., Vickers, D.,
and Hersbach, H.: On the exchange of momentum over the open ocean, J. Phys.
Oceanogr., 43, 1589–1610, 10.1175/JPO-D-12-0173.1, 2013.Fairall, C. W., White, A. B., Edson, J. B., and Hare, J. E.: Integrated
shipboard measurements of the marine boundary layer, J. Atmos. Ocean. Tech.,
14, 338–359, 10.1175/1520-0426(1997)014<0338:ISMOTM>2.0.CO;2, 1997.Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A., and Edson, J.
B.: Bulk parameterization of air–sea fluxes: Updates and verification for
the COARE algorithm, J. Climate, 16, 571–591, 10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2, 2003.Foken, T. and Wichura, B.: Tools for quality assessment of surface-based
flux measurements 1, Agr. For. Meteorol., 78, 83–105,
10.1016/0168-1923(95)02248-1, 1996.Kaimal, J. C., Izumi, Y. J., Wyngaard, C., and Cote, R.: Spectral
characteristics of surface-layer turbulence, Q. J. Roy. Meteorol. Soc., 98, 563–589, 10.1002/qj.49709841707, 1972.Landwehr, S., O'Sullivan, N., and Ward, B.: Direct Flux Measurements from
Mobile Platforms at Sea: Motion and Air-Flow Distortion Corrections
Revisited, J. Atmos. Ocean. Tech., 32, 1163–1178,
10.1175/JTECH-D-14-00137.1, 2015.McGillis, W. R., Edson, J. B., Hare, J. E., and Fairall, C. W.: Direct
covariance air-sea CO2 fluxes, J. Geophys. Res.-Oceans, 106,
16729–16745, 10.1029/2000JC000506, 2001.Miller, S. D., Hristov, T. S., Edson, J. B., and Friehe, C. A.: Platform
motion effects on measurements of turbulence and air–sea exchange over the
open ocean, J. Atmos. Ocean. Tech., 25, 1683–1694,
10.1175/2008JTECHO547.1, 2008.Miller, S. D., Marandino, C., and Saltzman, E. S.: Ship-based measurement of
air–sea CO2 exchange by eddy covariance, J. Geophys. Res.-Atmos., 115,
D02304, 10.1029/2009JD012193, 2010.Moat, B. I. and Yelland, M. J.: Airflow distortion at instrument sites on
the RRS James Clark Ross during the WAGES project. National Oceanography
Centre, Southampton, UK Internal Document No. 12, available at:
http://eprints.soton.ac.uk/373216/, last access: 16 January 2015.Moat, B. I., Yelland, M. J., Pascal, R. W., and Molland, A. F.: An overview
of the airflow distortion at anemometer sites on ships, Int. J. Climatol.,
25, 997–1006, 10.1002/joc.1177, 2005.Moat, B. I., Yelland, M. J., and Molland, A. F.: Quantifying the airflow
distortion over merchant ships. Part II: application of the model results,
J. Atmos. Ocean. Tech., 23, 351–360, 10.1175/JTECH1859.1, 2006a.Moat, B. I., Yelland, M. J., Pascal, R. W., and Molland, A. F.: Quantifying
the airflow distortion over merchant ships. Part I: validation of a CFD
model, J. Atmos. Ocean. Tech., 23, 341–350, 10.1175/JTECH1858.1,
2006b.Norris, S. J., Brooks, I. M., Hill, M. K., Brooks, B. J., Smith, M. H., and
Sproson, D. A. J.: Eddy Covariance Measurements of the Sea Spray Aerosol
Flux over the Open Ocean, J. Geophys. Res., 117, D07210,
10.1029/2011JD016549, 2012.O'Sullivan, N., Landwehr, S., and Ward, B.: Mapping flow distortion on
oceanographic platforms using computational fluid dynamics, Ocean Sci., 9, 855–866, 10.5194/os-9-855-2013, 2013.O'Sullivan, N., Landwehr, S., and Ward, B.: Air-flow distortion and wave
interactions: An experimental and numerical comparison, Methods Oceanogr.,
12, 1–17, 10.1016/j.mio.2015.03.001, 2015.Pedreros, R., Dardier, G., Dupuis, H., Graber, H. C., Drennan, W. M., Weill,
A., Geurin, C., and Nacass, P.: Momentum and heat fluxes via the eddy
correlation method on the R/V L'Atalante and an ASIS buoy, J. Geophys. Res.,
108, C11, 10.1029/2002JC001449, 2003.Popinet, S., Smith, M., and Stevens, C.: Experimental and numerical study of
turbulence characteristics of airflow around a research vessel, J. Atmos.
Ocean. Tech., 21, 1575–1589, 10.1175/1520-0426(2004)021<1575:EANSOT>2.0.CO;2, 2004.Prytherch, J.: Measurement and parameterisation of the air-sea CO2 flux
in high winds, PhD thesis, University of Southampton, 2011.Schulze, E. W., Sanderson, B. G., and Bradley, E. F.: Motion correction for
shipborne turbulence sensors, J. Atmos. Ocean. Tech., 22, 44–69,
10.1175/JTECH-1685.1, 2005.Smith, S.: Wind stress and heat flux over the ocean in gale force winds, J.
Phys. Oceanogr., 10, 709–726, 10.1175/1520-0485(1980)010<0709:WSAHFO>2.0.CO;2, 1980.Sullivan, P. P., McWilliams, J. C., and Moeng, C.-H.: Simulation of
turbulent flow over idealized water waves, J. Fluid. Mech., 404, 47–85,
10.1017/S0022112099006965, 2000.Sullivan, P. P., Edson, J. B., Hristov, T., and McWilliams, J. C.:
Large-eddy simulations and observations of atmospheric marine boundary
layers above non-equilibrium surface waves, J. Atmos. Sci., 65, 1225–1245,
10.1175/2007JAS2427.1, 2008.Sullivan, P. P., McWilliams, J. C., and Patton, E. G.: Large-Eddy Simulation
of Marine Atmospheric Boundary Layers above a Spectrum of Moving Waves, J.
Atmos. Sci., 71, 4001–4027, 10.1175/JAS-D-14-0095.1, 2014.
Tupman, D. J.: Air-sea flux measurements over the Southern Ocean, PhD thesis,
University of Leeds, 2013.Vickers, D. and Mahrt, L.: Quality control and flux sampling problems for
tower and aircraft data, J. Atmos. Ocean. Tech., 14, 512–526,
10.1175/1520-0426(1997)014<0512:QCAFSP>2.0.CO;2,
1997.Weill, A., Eymard, L., Caniaux, G., Hauser, D., Planton, S., Dupuis, H.,
Brut, A., Guerin, C., Nacass, P., Butet, A., Cloché, S., Perderos, R.,
Durand, P., Bourras, D., Giordani, H., Lachaud, G., and Bouhours. G.: Toward
a Better Determination of Turbulent Air–Sea Fluxes from Several
Experiments, J. Climate, 16, 600–618,
10.1175/1520-0442(2003)016<0600:TABDOT>2.0.CO;2,
2003.Wilczak, J., Oncley, S., and Stage, S.: Sonic anemometer tilt correction
algorithms, Bound.-Lay. Meteorol., 99, 127–150,
10.1023/A:1018966204465, 2001.Yelland, M. J., Moat, B. I., Taylor, P. K., Pascal, R. W., Hutchings, J., and
Cornell, V. C.: Wind stress measurements from the open ocean corrected for
airflow distortion by the ship, J. Atmos. Ocean. Tech., 28, 1511–1526,
10.1175/1520-0485(1998)028<1511:WSMFTO>2.0.CO;2,
1998.Yelland, M. J., Moat, B. I., Pascal, R. W., and Berry, D. I.: CFD model
estimates of the airflow distortion over research ships and the impact on
momentum flux measurements, J. Atmos. Ocean. Tech., 19, 1477–1499,
10.1175/1520-0426(2002)019<1477:CMEOTA>2.0.CO;2,
2002.Yelland, M., Pascal, R., Taylor, P., and Moat, B.: AutoFlux: an autonomous
system for the direct measurement of the air-sea fluxes of CO2, heat
and momentum. J. Operation. Oceanogr., 2, 15–23,
10.1080/1755876X.2009.11020105, 2009.