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Title
Author(s)
Lower-atmosphere upper-ocean interactions: the influences of
breaking waves
Scanlon, Brian
Publication
Date
2015-10-29
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Lower-Atmosphere
Upper-Ocean Interactions:
The Influences of Breaking
Waves
A Dissertation Submitted in Accordance with the
Requirements for the Degree of Doctor of Philosophy
in the College of Science
by
Brian Scanlon
School of Physics
National University of Ireland, Galway
Supervisor: Dr. Brian Ward
October 2015
Abstract
Wave breaking at the ocean surface is an important process for air-sea
exchange. Whitecaps are visual sea surface signatures of breaking waves.
By measuring the fractional coverage of whitecaps on the sea surface, it is
possible to quantify wave breaking. This thesis comprises of three distinctive
pieces of research. I compare model simulations of sea surface temperature
to high resolution observations for three unique cases. The model runs
over a daily cycle using a 1-dimensional 2nd moment closure turbulence
scheme with the inclusion of a wave breaking model. The comparisons reveal
poor performance when the wave breaking model is included. Subsequently,
attempts to improve on our understanding of wave breaking were made. I
developed a technique for estimating whitecap coverage estimates of both
actively breaking (stage A) waves, and maturing (stage B) foam. The Spatial
Separation of Whitecap Pixels (SSWP) allows for accurate distinguishing
of stage A and stage B whitecap regions by manually evaluating the pixel
intensity, location (with respect to the crest of the wave), texture and shape of
a given whitecap region. Finally, measured WA and overall whitecap coverage
(WT = WA + WB ) for the North Atlantic dataset were then compared with
modeled estimates of whitecap coverage, derived using a semi empirical
formula and various wave-field model parameters. High resolution model
estimates of the wave-field are provided by the European Center for Medium
Range Weather Forecasting (ECMWF) Wave Model (WAM). Results reveal
good performance between WA and modeled generated WT for specific tuning
values, which are provided.
i
Acknowledgments
I would firstly like to thank my supervisor, Brian Ward, for all his support
and guidance over the course of this work. I am immensely grateful for all
his patience and dedication to improving my work. He went well beyond
the call of duty helping me on my journey to becoming a respected scientific
researcher. I would also like to thank my fellow students for their company
and support, Sebastian Landwehr, Joao de Almeida, Graigory Sutherland,
Niall O Sullivan, Anneke ten Doeschate, Leonie Esters and post docs Adrian
Callaghan, Danielle Wain, Ciaran Kennedy, Chiara Uglietti, and Kieran
Walesby. I would like to thank my fellow coauthors Brian Ward, Gary Wick,
Adrian Callaghan, Øyvind Breivik, Jean Bidlot and Peter Janssen for their
patience, support and opportunities. I am very grateful to Peter Minnett
who provided the M-AERI data for the study outlined in section 3.1. I
would like to thank the captains and crew of the R/V Knorr, during the
North Atlantic Ocean cruise in 2011, and the R/V Tangaroa, during the
Southern Ocean cruise in 2012.
This research is supported by the Research Council of Norway (Grant
207541: OILWAVE), and the EU FP7 project CARBOCHANGE under
grant agreement no. 264879, and by the College of Science (Fellowship).
Dissemination of part of the research through international conferences were
financially supported by the Marine Institute under the Marine Research
Sub-program funded by the Irish Government and the Smartbay Ireland
Postgraduate scheme via the PRTLI Partnership, by the College of Science
travel fellowship, and by European Cooperation in Science and Technology
(COST).
ii
1 Introduction
As 71% of the Earth’s surface is covered in water, it is beneficial to improve
on our understandings of air–sea interaction. Physical processes that occur in,
and interact between, the upper ocean and lower atmosphere, are currently
poorly accounted for. In this study, we concern ourselves with the process
of wave breaking which can promote the air–sea transfers of gas, heat and
momentum, and the production of marine aerosols and ocean turbulence.
1.1 Importance of wave breaking
Wave breaking acts as a mechanism of energy transfer from the wave-field
to the upper ocean (Cardone, 1969). Turbulent kinetic energy (TKE) is
dissipated from the waves and injected into the upper few metres of the ocean
(Melville, 1996) due to wave breaking (Craig and Banner , 1994; Kantha
and Clayson, 2004; Hwang and Sletten, 2008; Breivik et al., 2015). Previous
studies that attempted to parameterize upper ocean mixing (Osborn, 1980;
Agrawal et al., 1992; Terray et al., 1996; Sutherland et al., 2013) have
demonstrated the complexity involved when quantifyting TKE injection due
to wave breaking. As a result, parameterizations of upper ocean mixing
1
Introduction
tend to mix weakly or too strong when compared to observations. On a
global scale, this poor representation of upper ocean mixing poses as a
significant weakness to ocean-only models and ocean-atmosphere coupled
forecast systems (Fan and Griffies, 2014; Breivik et al., 2015), whereby the
modeled mixed layer depth (MLD) is commonly underestimated which leads
to the modeled sea surface temperature (SST) being overestimated. Such
SST and MLD biases serve to upset delicate feedbacks in the climate system
(Sheldon and Czaja, 2014).
Wave breaking enhances air–sea transfer of gas (Asher and Wanninkhof , 1998;
Woolf , 1997) and heat (Andreas and Monahan, 2000) both by disrupting the
water surface microlayer and by promoting eddy diffusion through forming
of temporary low impedance vents in the upper water column (Monahan
and Spillane, 1984). Despite 40 years of active research attempting to
parameterize gas transfer (Liss and Slater , 1974; Monahan and Spillane,
1984; Wanninkhof and McGillis, 1999; Asher et al., 2002; Wanninkhof et al.,
2009; Bell et al., 2013), the scientific community still demands globally
representative parameterizations of air-sea gas exchange for more accuracte
predictions of our climate.
Figure 1.1: Schematic illustrating the evolution of a typical breaking wave:
a spilling wave crest (I), bubble plume formation (II), evolution
into stage-B whitecap (III), and decay of the whitecap (IV),
(Scanlon and Ward , 2013).
Breaking waves trap and entrain air into the upper ocean (Fig. 1.1). This
2
Introduction
process of air entrainment forms plumes of bubbles which are injected to
depths below the surface on the order of metres. Once the bubbles reach
the maximum depth, they rise to the surface, horizontally diverge from one
another and decay via bubble bursting. This mechanism of bubble bursting is
responsible for the production of film and jet droplets which are transported
into the upper atmosphere where they play an influential role as sea salt
aerosols (SSA) (Monahan, 1986; Andreas et al., 1995; Lewis and Schwartz ,
2004; O’Dowd and de Leeuw , 2007; de Leeuw et al., 2011). The presence
of SSA in the atmosphere contribute significantly to the Earth’s radiation
budget (Andreas and Edgar , 1998), cloud formation (O’Dowd et al., 1999)
and ocean-atmosphere transport of organics (Blanchard , 1963).
Sea foam coverage on the sea surface generated via wave breaking serves to
increase the ocean albedo (Koepke, 1984; Frouin et al., 1996; Gordon, 1997)
and thus exerts a strong influence on the global radiation budget (Frouin
et al., 2001).
For these reasons, we must acknowledge that wave breaking plays a vital
role in upper-ocean lower-atmosphere interactions. Thus it is of importance
to achieve suitable quantification of wave breaking.
1.2 Quantification of wave breaking
The spatial and temporal evolutions of air entrainment due to breaking
waves can be monitored by appealing to their surface signature whitecap
manifestations (Monahan and Lu, 1990). Previous studies have attempted
to quantify wave breaking by estimating the sea surface area covered in
3
Introduction
102
WT Monahan (1971)
WT [OLS] Monahan and OMuir.(1980)
WA Bondur and Sharkov (1982)
WB Bondur and Sharkov (1982)
WT Monahan and OMuir. (1986)
100
WA [∆T=0] Monahan and Woolf (1989)
WT [all] Hanson and Philips (1999)
W (%)
WA Asher and Wann.(1998)
WA Asher et al.(2002)
WT Stramska and Pet. (2003)
WT Lafon et al. (2004)
-2
10
WT Lafon et al. (2007)
WT [pure wind] Sugihara et al (2007)
WT [mixed seas] Sugihara et al (2007)
W10 Salisbury et al (2013)
W37 Salisbury et al (2013)
10-4
W37 Pandey and Kahar (1982)
WA Reising et al. (2002)
WT Callaghan et al. (2008)
5
10
15
20
25
U10N (m s−1 )
Figure 1.2: Summary of published parameterizations of whitecap coverage
(W ) with neutral wind speed (U10N ) over the past 45 years.
whitecaps using imaging techniques (Blanchard , 1963; Monahan, 1971; Toba
and Chaen, 1973; Ross and Cardone, 1974; Monahan and O’Muircheartaigh,
1986; Asher and Wanninkhof , 1998; Hanson and Phillips, 1999; Stramska
and Petelski, 2003; Lafon et al., 2004, 2007; Sugihara et al., 2007; Callaghan
et al., 2008a; Goddjin-Murphy et al., 2011), satellite sensing (Monahan et al.,
1981; Pandey and Kahar , 1982; Koepke, 1986; Anguelova and Webster , 2006;
Salisbury et al., 2013) and acoustics (Thorpe, 1982; Monahan and Lu, 1990;
Ding and Farmer , 1994).
While the community agrees that the extent of whitecap coverage W can be
represented by a power-law of wind speed, there exists significant differences
between various whitecap coverage parameterizations published over the past
45 years (see Figure (1.2) or Anguelova and Webster , 2006; Goddjin-Murphy
et al., 2011). A plethora of theories arose which attempted to account
for these differences. Such theories hypothesized the differences between
4
Introduction
results of previous studies arose due to variations of (1) methodologies
used, (2) convergence of whitecap observations, (3) quality control, and (4)
natural variation of environmental conditions. These sources of variation
are explained below:
1. Variations in methodology: Over 45 years, significant improvement
in technology has made available to researchers cost effective high
resolution imaging systems, data storage solutions and image processing software. The first extensive dataset of W were achieved from
photography (Monahan, 1969), which involved the dissection and
weighing of whitecap regions. More recently, the implementation of
digital imaging techniques were employed (Monahan, 1993; Sugihara
et al., 2007; Callaghan and White, 2009) using both manual and automated image processing techniques. An alternative methodology
for obtaining whitecap parameterizations involves satellite sensing of
microwave emissivity of the sea surface. Such remote sensing inherits
large uncertainties and noise compared to studies involving in-situ
observations. This highlights the importance of minimizing systematic
and human (subjective) error when conducting future studies. For
further information, please see (Anguelova and Webster , 2006).
2. Convergence of whitecap observations: As observations of W are considered to be independent of time, it is vital that a sufficient number of
wave breaking events are sampled such that a population-representative
estimate of W is obtained. This highlights the importance of adopting appropriate sampling sizes, intervals and rates when conducting
future studies. Please refer to Callaghan and White (2009) for further
information on the convergence of whitecap observations.
5
Introduction
3. Quality control: Measurements of whitecaps can contain significant
sources of contamination such as imagery containing sun glint, humaninduced whitecaps (such as bow breakers and wakes due to ship)
and seagulls. Various studies employ manually controlled quality
checks during data processing stages which requires large amounts
of dedication, effort and time. Studies choosing to approach data
processing autonomously without manual quality control checks can
incur significant uncertainties for W observations (Scanlon and Ward ,
2013).
4. Natural variation of environmental conditions: For any given wind
speed, whitecap coverage has been observed to correlate for variations
of wave-field development (Callaghan et al., 2008b; Goddjin-Murphy
et al., 2011), SST (Monahan and O’Muircheartaigh, 1986; Bortkovski ,
1987; Bortkovski and Novak , 1993; Callaghan et al., 2014) sea – air
temperature (atmospheric stability) (Thorpe, 1982; Monahan and
O’Muircheartaigh, 1986; Monahan and Woolf , 1989; Monahan and Lu,
1990), salinity (Monahan and Zietlow , 1969), fetch (Nordberg et al.,
1971), latitude (Monahan et al., 2015) and surfactants (Callaghan
et al., 2012, 2013).
To address the variable lifetimes of whitecaps (Callaghan et al., 2012), few
studies (Bondur and Sharkov , 1982; Monahan and Woolf , 1989; Monahan
and Lu, 1990; Asher and Wanninkhof , 1998; Reising et al., 2002; Bobak
et al., 2011) have attempted to separate whitecap coverage into two stages
of evolution; actively breaking waves (stage A) and maturing foam (stage
B), following the definitions in Monahan and Lu (1990). In doing this,
quantifications of the coverage of stage A (WA ) provide a suitable proxy for
6
Introduction
dynamical air–sea processes such as air transfer (Asher and Wanninkhof ,
1998) and wave energy dissipation (Scanlon et al., 2015). Quantifications
of stage B coverage (WB ) provide a suitable proxy for the area of whitecaps undergoing bubble bursting processes and thus the generation of SSA
(Monahan, 1986).
1.3 Objectives of this presented study
A number of objectives arise following a review of published literature related
to wave breaking, whitecap coverage and air–sea interactions.
1. Evaluate state-of-the-art upper ocean turbulence models which include
TKE injection due to wave breaking on reproducing temperature profile
measurements over a daily (diurnal) cycle.
2. Evaluate current methods and explore alternative methods of acquiring
whitecap coverage observations. Attempt to separate whitecap coverage
observations into its actively breaking stage (stage A) and its maturing
stage (stage B).
3. Obtain an extensive dataset of WA and WB which conform to acceptable standards of quality control and data certainty.
4. Provide an investigation into the variability of WA and WB and their
correlations with environmental parameters such as wind speed, SST
and atmospheric stability.
5. Examine the ratio of WA /WB and conclude if it is a constant.
7
Introduction
6. Validate a whitecap model using various wave model parameters.
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3074–3079, doi:10.1002/grl.50584.
Terray, E., M. Donelan, Y. Agrawal, W. Drennan, K. Kahma, A. Williams,
P. Hwang, and S. Kitaigorodskii (1996), Estimates of kinetic energy
dissipation under breaking waves, J. Phys. Oceanogr., 26, 792–807, doi:
10.1175/1520-0485(1996)026¡0792:EOKEDU¿2.0.CO;2.
17
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andPhysical Sciences, 304, No. 1483, 155–210.
Toba, Y., and M. Chaen (1973), Quantitative expression of the breaking of
wind waves on the sea surface, Rec. Oceanogr. Works Japan, 12, 1–11.
Wanninkhof, R., and W. McGillis (1999), A cubic relationship between
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Wanninkhof, R., W. Asher, D. Ho, C. Sweeney, and W. McGillis
(2009),
Advances in quantifying air-sea gas exchange and en-
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Annu. Rev. Mar. Sci.,
1,
213–244,
doi:
doi:10.1146/annurev.marine.010908.163742.
Woolf, D. K. (1997), Bubbles and their role in gas exchange, in The Sea
Surface and Global Change, edited by P. Liss and R. Duce, pp. 173–205,
Cambridge Univ. Press, Cambridge.
Zappa, C., W. Asher, and A. Jessup (2001), Microscale wave breaking
and air-water gas transfer, J. Geophys. Res., 106 (C5), 9385–9391, doi:
10.1029/2000JC000262.
18
2 Summary of Research Papers
The work presented in this thesis consists of three peer-reviewed articles
of which I am lead author. For each of the three articles, I provide major
contributions.
First article:
Near-surface diurnal warming simulations: validation with high
resolution profile measurements
Scanlon, B., G.A. Wick and B. Ward (2013), Ocean Science, vol. 9,
number 6, pp. 977–986, doi:10.5194/os-9-977-2013.
This article involves the application of various configurations of a 1-dimensional
second moment closure turbulence model, solar absorption model, and wave
breaking model, in replicating upper ocean measured temperature profiles.
Such attempts to replicate the upper ocean temperature profiles prove to be
a very important, as accurate estimates of sea surface temperature (SST)
are required for estimating accurate heat flux across the air–sea interface.
Three unique datasets are provided, showcasing highly stratified upper ocean
during daytime high solar irradiance and low wind conditions (near Baja,
19
Summary of Research Papers
California), well mixed upper ocean during a night-time to morning-time
transition in moderately low winds and high salinity conditions (Gulf of
Lions, Mediterranean Sea), and day-night transition in low wind conditions
(Seychelles–Chagos Thermocline Ridge, Indian Ocean). High resolution
temperature profiles were measured using the Air–Sea Interaction Profiler
(ASIP) and its earlier variant Skin Depth Experimental Profiler (SkinDeEP).
Model and observation comparisons reveal that the model configurations,
especially those that include a wave breaking model, show difficulties reproducing observed conditions. G. Wick provided the model simulation
runs. B. Ward provided the high resolution measurements. I am
credited with the analysis of the data, forming of conclusions and
writing of the manuscript.
Second article:
Oceanic wave breaking coverage separation techniques for active
and maturing whitecaps
Scanlon, B. and B. Ward (2013), Methods in Oc., vol. 8, pp. 1–12,
doi:10.1016/j.mio.2014.03.001.
This article provides a new standardised technique of processing sea surface
imagery with the goal of extracting estimates of actively breaking (stage A)
whitecap coverage (WA ) and maturing (stage B) whitecap coverage (WB ),
following definitions outlined in Monahan and Lu (1990). This work was
motivated by two main concerns, (i) to exploit whitecap coverage as a proxy
for quantifying wave breaking, and (ii), previous techniques demonstrated
high variability between various whitecap parameterizations (see Anguelova
20
Summary of Research Papers
and Webster , 2006). The published technique is called the Spatial Separation
of Whitecap Pixels (SSWP), and relies on two key requirements. Firstly an
appropriate pixel value threshold must be selected such that whitecap pixels
and those of background sea are distinguished. Secondly, sufficient manual
evaluation of whitecap regions (grouped whitecap pixels) are categorized
as either representing actively breaking whitecaps or maturing whitecaps.
This manual evaluation is preformed by appealing to four characteristics
of the whitecap region, its location (with respect to the wave crest), its
visual intensity, its shape and its texture. Once all whitecap pixels are
accounted for, stage A and stage B pixels are each summed to provide
estimates of WA and WB coverage. A large dataset of images (64,540) of
the North Atlantic Ocean, obtained during the summer (June/July) of 2011
onboard the R/V-Knorr were processed, providing 207 10-minute averaged
estimates of WA and WB . A secondary image analysis technique, involving the distinguishing of whitecap regions as either stage A or stage B, is
introduced and named the Pixel Intensity Separation Technique (PITS).
PITS, as the name suggests, relies only on the pixel intensity information
to perform separation. This method is evaluated against the SSWP for the
entire dataset, revealing poorer performance and larger errors in WA and WB
estimates. I am credited with the creation of the SSWP method,
the manual processing of 64,540 images, the analysis and writing
of the manuscript.
21
Summary of Research Papers
Third article:
Modelling whitecap fraction with a wave model
Scanlon, B., Ø. Breivik, J. R. Bidlot, P. A.E.M. Janssen, A. H. Callaghan
and B. Ward (2015), J. Phys. Oc., doi:10.1175/JPO-D-15-0158.1, in press.
This article describes the use of a semi–empirical equation to derive whitecap
coverage using wave-field and meteorological forcing. The semi–empirical
equation is based on the assumption that wave breaking is the dominant
source of wave-field dissipation. The study incorporates high resolution
European Center for Medium Range Forecasting (ECMWF) wave model
(WAM) estimates, providing 1-hourly input estimates for the semi-empirical
function. Resulting 1-hourly estimates of modeled whitecap coverage were
then compared to 1-hourly WA and total whitecap coverage (WT ) observations from the North Atlantic dataset. The comparison shows good
agreement, and reveals that model estimates of whitecap coverage are more
closely related to observations of WA than WT . I am credited with the
manual processing of 114,265 images, analysis and writing of the
manuscript.
22
3 Research Papers
3.1 Near-Surface Diurnal Warming Simulations:
Validation with High Resolution Profile
Measurements
23
Research Papers 2.1
Ocean Science
Open Access
Ocean Sci., 9, 977–986, 2013
www.ocean-sci.net/9/977/2013/
doi:10.5194/os-9-977-2013
© Author(s) 2013. CC Attribution 3.0 License.
Near-surface diurnal warming simulations: validation with high
resolution profile measurements
B. Scanlon1 , G. A. Wick2 , and B. Ward1
1 School
2 NOAA
of Physics and Ryan Institute, National University of Ireland, Galway, Ireland
ESRL PSD, 325 Broadway Boulder, CO 80305, USA
Correspondence to: B. Ward ([email protected])
Received: 28 September 2012 – Published in Ocean Sci. Discuss.: 20 December 2012
Revised: 15 October 2013 – Accepted: 18 October 2013 – Published: 19 November 2013
Abstract.
Sea surface temperature (SST) is an important property
for governing the exchange of energy between the ocean and
the atmosphere. Common in situ methods of measuring SST
often require a cool-skin and warm-layer adjustment in the
presence of diurnal warming effects. A critical requirement
for an ocean submodel is that it can simulate the change in
SST over diurnal, seasonal and annual cycles. In this paper we use high-resolution near-surface profiles of SST to
validate simulated near-surface temperature profiles from a
modified version of the Kantha and Clayson 1-D mixed-layer
model. Additional model enhancements such as the incorporation of a more recent parameterization of turbulence generated by wave breaking and a recent solar absorption model
are also validated. The model simulations show a strong variability in highly stratified conditions, with different models
providing the best results depending on the specific criteria
and conditions. In general, the models with enhanced wave
breaking effects provided underestimated temperature profiles while the more coarse baseline and blended approaches
produced the most accurate SST estimates.
1
Introduction
Accurate measurements of sea surface temperature (SST) for
the upper ocean are important for air–sea exchange of heat
(Fairall et al., 1996b) and gas (Ward et al., 2004a). It has
been shown that SST values with an accuracy of ±0.2 K are
required to compute the air–sea heat fluxes to an accuracy
of 10 W m−2 (Fairall et al., 1996a). Bulk formula heat flux
calculations rely on SST values to compute sensible and la-
tent turbulent heat fluxes as well as emitted longwave radiation from the ocean surface, and these models are most
sensitive to SST variability in the lower latitudes. According to Fairall et al. (1996b) the most appropriate value of
SST for these formulae is the temperature of the cool-skin
layer, known as the skin temperature (SSTSkin ). The coolskin layer (or the molecular sublayer) is ∼ 1 mm thick, and
is the upper most layer of the sea surface and is in direct
contact with the atmosphere. The skin temperature is cooled
by the combined effects of the net longwave radiative flux,
the sensible heat flux and the latent heat flux and is typically 0.1–0.5 K lower than the temperature of the subskin
layer immediately below (Wick et al., 1996; Donlon et al.,
2002). The cool skin is almost always present, although its
total effect may be compensated by the presence of a warm
layer (Fairall et al., 1996b). Common in situ methods of
SST measurement obtain temperature at a depth, often 1–4m,
called Tdepth , or commonly the bulk temperature measurement. These bulk temperatures are the most commonly available measurements obtained from buoys and ships (Gentemann et al., 2009). It is often required that these bulk measurements be adjusted for diurnal warm-layer and cool-skin
effects.
In the upper ocean, diurnal warming cycles occur due to
the solar heating and oceanic heat loss fluctuations (Price
et al., 1986) and are responsible for high variations of SST.
For example, in summer heating conditions with low wind,
the depth of the diurnal warm layer can typically be on the
order of 1 m (mean depth), and the surface amplitude (skin
temperature minus bulk temperature) can be as large as 3 K
(Stramma et al., 1986; Soloviev and Lukas, 1996). In such
conditions, turbulent mixing near the surface is mainly driven
Published by Copernicus Publications on behalf of the European Geosciences Union.
Research Papers 2.1
978
by wind-induced shear and convection. This convection is
driven by densification due to evaporation and possible net
surface cooling. Daytime solar heating effects within a stratified upper ocean are isolated to the surface layers. The heating of these layers create a positive buoyancy flux which
restricts deepening of the warm layer (Soloviev and Lukas,
1996), further enhancing the effects of stratification. In moderate wind conditions, solar heat is mixed vertically to a
greater depth than what can be achieved directly by radiation. In such cases, the positive surface buoyancy fluxes are
overcome by wind driven shear which deepens the diurnal
warm layer typically to 10 m depth. In turn, the surface amplitude is typically reduced to 0.2 K (Price et al., 1986).
Previous studies using models and near-surface temperature profile measurements have demonstrated the potential
for significant variability in the near-surface temperature especially during the daytime at low winds and with strong
solar heating (Fairall et al., 1996a; Soloviev and Schluessel, 1996; Webster et al., 1996; Donlon, 1999; Gentemann
and Minnett, 2009; Gentemann et al., 2009). Clearly, onedimensional models which only consider transport in the vertical direction have limitations and cannot account for advective effects. Advection can introduce errors in modelled
temperature gradients from horizontal currents of a different temperature as noted by Kantha and Clayson (1994). The
1-D models, however, can be very informative in evaluating
the mixing processes associated with stratification and diurnal warming. The goal of this paper is to compare model
simulations to observed high resolution temperature profile
measurements in low to moderate wind and high solar irradiance environments to evaluate the model’s skill to accurately
reproduce the temperature profile. It is important to note that
this study evaluates the ability of the models to exactly reproduce a specific realization of observations. It does not address
a more traditional statistical evaluation of model uncertainty.
Observed temperature profiles of the upper 5 m of the
ocean were measured by the Skin Depth Experimental Profiler (SkinDeEP) (Ward et al., 2004b) and also by its successor the Air–Sea Interaction Profiler (ASIP) (Ward et al.,
2012). The profiles presented here were obtained during
three separate field experiments: Gulf of California in 1999
(hereafter GC99), Gulf of Lions (Mediterranean) in 2003
(hereafter GL03), and the Indian Ocean in 2007 (hereafter
IO07). SkinDeEP is an autonomous profiler capable of measuring temperature to a sub-centimetre resolution. At it’s typical rising velocity of 0.5 m s−1 , the resolution is 3 mm (see
Ward et al. (2004b) for a complete description of SkinDeEP).
ASIP is similar in concept to SkinDeEP, but has a much
larger sensor range, can profile to 100 m, and has a larger battery capacity. Coupling the high resolution profile data from
the near-surface along with M-AERI radiometric data of the
true skin temperature, provides a complete temperature profile of the upper ocean.
This article attempts to validate the model simulations of
a 1-D second moment turbulence closure mixed-layer model
Ocean Sci., 9, 977–986, 2013
B. Scanlon et al.: Near-surface diurnal warming simulations
based on Kantha and Clayson (1994) for the GC99, GL03,
and IO07 time periods, using available meteorological data
and bulk measurements while neglecting the effects of advection. Further refinements to the model, including wave breaking effects (Kantha and Clayson, 2004) and a recent solar
transmission model (Ohlmann and Siegel, 2000), are incorporated into the model for validation. Section 2 discusses the
cruise data, instrumentation and provides a theoretical background for the models used in this study. Section 3 shows the
results from the comparisons of the measured SkinDeEP data
and the modelled simulations, followed by our conclusions.
2
2.1
Material and methods
Instruments
The surface temperature profiles were obtained from either
SkinDeEP (Ward et al., 2004b) or ASIP (Ward et al., 2012).
Both of these instruments are autonomous vertical profilers
designed to study the upper ocean with high resolution sensors. For this study, we are concerned with temperature profiles in the upper 5 m, which are provided by the FP07 thermometer mounted on both profilers.
SkinDeEP has the ability to obtain more than 100 consecutive profiles without intervention and contains a CPU capable of high-frequency sampling and data storage (Ward,
2006). Autonomous profiling is accomplished with a volume
adjusted buoyancy variance system. While in operation, it
was attached to a spar buoy via 50 m of a synthetic, high
breaking strain tether line. Profiling started with the instrument sinking to its programmed depth which was monitored
by the onboard external pressure sensor, at which the buoyancy was changed to positive and temperature measurements
were acquired as it rose to the surface. The temperature data
was provided with the FP07 thermistor, which was calibrated
against a slower, accurate thermometer.
ASIP is an autonomous vertically profiling instrument designed to profile from below so as to provide undisturbed
measurements all the way to the surface. It is equipped with
high resolution sensors for the measurement of temperature, salinity, light, oxygen, and turbulence. There are three
thrusters which submerge it to a programmed depth (maximum 100 m), whereupon it ascends through the water column towards the surface under its own buoyancy, recording
data at 1000 Hz, generating 192 kbytes s−1 which is stored
with a single board computer.
The skin temperature for all cruises was continuously measured by the Marine-Atmospheric Emitted Radiance Interferometer (M-AERI, Minnett et al., 2001); a passive infrared
radiometric interferometer which makes radiance measurements in the 500–3000 cm−1 wave number range with a resolution of 0.5 cm−1 . The radiometer comprises of a gold rotating mirror that allows for both sea and sky views at complementary angles to nadir and zenith. The accuracy of the
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979
Table 1. Times, location and number of profiles for the deployments of the three case studies.
Date
Time (Local)
Latitude
Longitude
GC99
GL03
IO07
283
113/114
39/40
11:12–14:13
23:08–11:23
19:02–7:20
22◦ 31.48 N
42◦ 18.47 N
7◦ 59.77 S
109◦ 35.43 W
5◦ 05.65 E
67◦ 27.70 E
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Region
# of profiles
161
117
72
|
description of the GL99 meteorological conditions can be obtained in Ward (2006).
Additional data is provided by SkinDeEP from the GL03
experiment in the Gulf of Lions onboard the R/V Urania during April 2003. The profiler obtained 576 different profiles of
the upper sea surface in 3 deployments over 3 days. Due to a
technical error during deployment 1 and 2, SkinDeEP failed
to successfully record temperature values in the upper metre.
The error was corrected before the final deployment, 3, took
place. For the basis of this paper, profiles from deployment 3
of this cruise are the only measurements deemed suitable and
the rest shall be ignored. This deployment represents the situation where a well mixed nighttime water column is being
subjected to strong morning-time solar heating. Solar shortwave radiation rises from a minimum value to 876 W m−2 .
The mean wind speed is 6.29 ± 0.52 m s−1 for the period
Fig. 1. Time series of the downwelling shortwave radiation, wind
(Fig. 1).
Fig. 1: Time series
of and
the downwelling
shortwave
radiation,
wind
speed,
skin temperature
for the GC99,
GL03
andspeed,
IO07 and
peri-skin temperature
for the GC99, GL03
and IO07 periods
respectively.
The grey
vertical
column
marks theThe
timedata
of collected from the IO07 cruise represents a high
ods respectively.
The grey
vertical column
marks
the time
of the
resolution view of the temperature structure in a highly stratthe deploymentdeployment
period. Theperiod.
data isThe
60 data
minute
averaged.
is 60
min averaged.
ified area of the Indian–Pacific warm pool, the “Seychelles–
Chagos Thermocline Ridge”. The 10th deployment of the
cruise occurred on 8–9 February and resulted in 72 profiles
derived SST measurements are better than 0.05 K (Minnett
captured in highly stratified conditions. The period started
et al., 2001). Real-time calibration is continuously carried
at 19:02 LT and finished at 07:21 the next morning. The
out by viewing two internal blackbody cavities, one set to
mean wind speed was 4.35 ± 0.38 m s−1 . The solar heat flux
20
◦
60 C and the other to ambient temperature.
ramped up from 0 to 102 W m−2 towards the end of the deThe M-AERI skin temperature and SkinDeEP/ASIP temployment (Fig. 1). Table 1 displays additional information
perature profile measurements used collectively create a high
regarding the GC99, GL03 and IO07 deployments.
resolution temperature profile of the upper few metres of the
For all three field campaigns, meteorological sensors were
sea surface.
deployed to provide a time series of the following parameters: wind speed and direction; air temperature; relative hu2.2 Observations
midity; barometric pressure; downwelling long- and shortwave radiation. There was also gyroscopic information availThe GC99 data set was obtained over a 12 day period in Ocable to determine the ship’s speed, heading, and bearing for
tober 1999 near Baja California. Ten successful deployments
wind speed correction. Air–sea heat fluxes were calculated
of SkinDeEP (denoted by the day of month) were obtained,
using the COARE bulk flux algorithms (Fairall et al., 1996b).
leading to a total of 976 high resolution upper ocean profiles.
The deployments were carried out from the R/V Melville
2.3 Models
mainly during early afternoon periods when the waters were
maximally stratified. Over the 12 days, the solar heat flux was
high and the wind varied from 1–9 m s−1 . For each day the
Five variations of the Kantha and Clayson (1994) (KC94
downwelling shortwave radiation reached over 800 W m−2
hereafter) second moment closure, one-dimensional mixedlayer model provide 1 min resolution simulations of the upand wind speeds were relatively low with a mean range of
3.5 ± 1.8 m s−1 across all the deployments. Deployment 10
per ocean for the durations of the GC99, GL03 and IO07
occurs in idealized weather conditions for this study with a
cruises. The first, or, “baseline” configuration most closely
corresponds to that described in KC94. The model name is
mean wind speed of 1.1 m s−1 and a mean shortwave radiation of 802 W m−2 (peaking at 912 W m−2 ) (Fig. 1). A full
shortened to “Base” for representation in tables and plots.
Discussion Paper
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Discussion Paper
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Discussion Paper
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980
B. Scanlon et al.: Near-surface diurnal warming simulations
Table 2. Summary of the five model versions used for evaluation.
Model
version
Solar
absorption
Turbulence
coefficients
near surface TKE
assumptions
Base
EWB
Blend
PS81
PS81
PS81
EST
BST
OS00
OS00
KC94
KC94
KC94,
revised to KC04
KC94
KC94,
revised to KC04
Law of the wall
KC04
Law of the wall for wind < 2 m s−1 ,
KC04 for wind > 2 m s−1
KC04
Law of the wall for wind < 2 m s−1 ,
KC04 for wind > 2 m s−1
The basic turbulence scheme is that of KC94, but the vertical resolution is enhanced to simulate the details of the nearsurface temperature profile. A nine-wavelength band solar
absorption model of Paulson and Simpson (1981) (PS81
hereafter) is used in this configuration to account for solar
heating effects within the water column. It is a common assumption in ocean modelling to assume that the Karman–
Prandtl law of the wall is valid near the air–sea interface.
This assumption works well in shear flows adjacent to a rigid
boundary but fails in the presence of breaking waves near
the surface (Craig and Banner, 1994). This is due to the turbulent kinetic energy (TKE) equation being based on local
shear production and dissipation near the surface. Kantha
and Clayson (2004) (hereafter KC04) suggest that the influence of wave breaking strongly elevates the dissipation rate
in the upper few metres of the ocean and the effects cannot be ignored (see also Terray et al., 1996; Agrawal et al.,
1992). A second version of the model incorporating the TKE
equation of KC04 to account for these effects is termed the
“enhanced wave breaking model” (shortened to EWB in figures). This addition incorporates TKE injection parameters
due to breaking waves and Langmuir circulation. Weller and
Price (1988) found that stratified thermal layers in shallow
diurnal mixed layers can be rapidly destroyed by Langmuir
circulation. Thus the inclusion of a parameter for Langmuir
cells is important. The new parameterization for TKE input
at the surface is proportional to a power law of the waterside friction velocity u∗. The inclusion of these parameters
increases TKE and dissipation rates in the upper ocean, leading to enhanced mixing in the mixed layer. KC04 reported
the effects of including Langmuir circulation in the model
resulted in lower SST values. The reader is referred to Kantha and Clayson (2004) for more information.
The third model used in this study is named the “blended
model” (shortened to “blend” in figures). This model transitions between the use of the baseline model and the enhanced wave breaking model at a wind speed of 2 m s−1 .
The turbulence scheme below 2 m s−1 is that of the baseline
model while it shifts toward that of the enhanced wave breaking model at higher winds. This blending was introduced in
an attempt to reproduce the range of diurnal warming am-
Ocean Sci., 9, 977–986, 2013
plitudes observed in previous shipborne observations of the
surface temperature (not shown). The turbulence coefficients
are also revised within this model to follow Kantha (2003).
Solar insolation is a very important parameter for the effects of diurnal warming. It has been reported that between
60 and 90 % of solar irradiance is attenuated within the upper 10 m of the ocean (Ohlmann et al., 1998). Variations in
the assumed absorption rate of insolation can have a significant effect on the simulated profiles. The “PS81” nine-band
solar transmission model, of Paulson and Simpson (1981) is
used for the three models described so far. This is also the
scheme currently used in the Profiles of Ocean Surface Heating (POSH) model (Gentemann et al., 2009). This solar transmission model computes solar transmission through the air–
sea interface by fixing the sea surface albedo to a constant
value of 0.055 which has been recorded to produce instantaneous errors of ± 40 W m−2 (Ohlmann and Siegel, 2000).
The reader is referred to Fairall et al. (1996b) and Ohlmann
and Siegel (2000) for further information.
The fourth model version tested incorporates a more recent
solar absorption profile developed by Ohlmann and Siegel
(2000) (hereafter OS00) along with the “enhanced wave
breaking model” and is called the “enhanced solar transmission model” (shortened to “EST” in figures). It is a two–
equation solar transmission parameterization that depends on
upper ocean chlorophyll concentration, cloud amount and solar zenith angle. In a high solar insolation and low wind condition study carried out by OS00, they found the new parameterization to give a mean 12 W m−2 reduction in the quantity of solar radiation attenuated in the top few metres of the
ocean compared with previous parameterizations. The new
transmission parameterization gives a slightly deeper warm
layer and a decrease in the warm-layer temperature correction which often reaches 0.2 K (Ohlmann and Siegel, 2000).
The final version of model tested is an enhancement of
the “blended model”. It transitions between the baseline and
enhanced wave breaking models in the same fashion as the
blended model but also incorporates the OS00 two–equation
solar transmission model described for the enhanced solar
transmission model in place of the PS81 nine-band model. It
is called the “blended solar transmission model” (shortened
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981
|
Figure 2 illustrates the time evolution of the SSTskin estimations from the five models and observed temperatures for
the GL03 case study. Both blended models produce identical
temperature estimates for this period.
Results
Discussion Paper
3
|
In this section, the model simulations of the five model versions discussed in the previous section are compared to high
resolution in situ measurements. For comparison, the modelsimulated and measured temperature profiles are bin averaged to 2 cm depth intervals, with increased resolution nearer
the surface at depths of 0, 0.0025, 0.0075 and 0.015 m.
Discussion Paper
3.1
Model performance in day-time stratification
|
Fig. 2. Time-series of the five model simulations for the GL03 peconditions
Fig. 2: Time-series
of the
fiveobserved
model simulations
forSST
the measurements.
GL03 period plotted
riod plotted
with
skin and ship
The with observed
skin and shipgrey
SSTvertical
measurements.
The
grey
vertical
column
represents
the
GL03
deployment
column represents the GL03 deployment period for
Observational measurements from GC99 are used in the case
period for SkinDeEP.
SkinDeEP.
of model validation in highly stratified conditions. The aver-
|
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Discussion Paper
to BST in figures). A summary of the main differences between the five model versions discussed is shown in Table 2.
The air–sea heat fluxes used to force the Kantha and
Clayson model versions were 21
calculated using the TOGA
COARE bulk flux algorithm and transfer coefficients from
Fairall et al. (1996b). Meteorological data along with the calculated heat fluxes for the duration of the cruises were used as
inputs for the model simulations. Values were interpolated to
the resolution of the model time step and input to the model at
each time step. The models were initialized with isothermal
and constant salinity profiles based on observations from the
research vessels at the start time of each run. Model execution began at midnight local solar time the day before the period of the comparison with the observed profiles to allow the
model to spin up. While the modelled profiles were allowed
to evolve freely, the modelled temperature profiles were relaxed to ship-based underway SST measurements at each
time step to minimize advective effects. This involved the
entire temperature profile being shifted such that the model
temperature agrees with the measured subsurface temperature from the research vessel at the appropriate depth. The
time step employed in the models was 1 min. The vertical
resolution of the model was 0.02 m between depths of 0.03
and 4.99 m and scaled to 0.15 m for depths thereafter. A finer
resolution near the surface defined by temperature values at
0.0025, 0.0075 and 0.015 m depths was used to represent the
upper few centimetres of the ocean. To extend temperature
estimates from the shallowest layer of the model at 0.0025 m
to the skin, the skin layer parameterization of Fairall et al.
(1996a) is incorporated in the model.
age solar irradiance is 802 W m−2 (peaking at 912 W m−2 )
and the mean wind speed is 1.1 m s−2 for the duration of
the deployment (Fig. 1). Diurnal warming effects are very
evident in this data set with warm-layer depths observed
between 0.2 and 1.0 m throughout this deployment period
(Fig. 3, top left). Comparing the simulations for each of
the five different mixing schemes shows interesting results.
Time-series plots for the five models show the temporal evolution of the temperature differences between modelled and
measured profiles (Fig. 3). The optimal temperature difference interval (±0.2 K) is coloured white in the plots. This
interval represents required SST values to compute heat
fluxes to within a ± 10 W m−2 accuracy. The baseline model
achieves the greatest white area of the three curves, providing
good simulation results for this example of highly stratified
conditions. This is mainly due to the baseline model predicting the most accurate warm-layer depth, resulting in a minimal mean temperature difference of 0.05 K from 0.5 to 5 m
depth (Fig. 4). All five mixing schemes struggle to resolve the
upper half metre correctly. It is important to note that it is difficult to conduct point-to-point comparisons given the potential for advective effects not considered in one-dimensional
models. It is still interesting, however, to compare the relative performance of the different models. The two blended
models achieve the highest temperature differences of the
five models with an overestimation of 2.5 K for a brief period that morning. This occurs at the beginning of the deployment when the water column was observed to be well
mixed (Fig. 3). All the models predict a diurnal warm layer
at 1 m depth during this period, which accounts for the simulated temperature overestimations. The blended and baseline
models overpredict temperatures during another period between 11:45 and 12:15 LT, when the solar heat flux drops to
700 W m−2 (Fig. 1). The observed warm-layer depth deepens by half a metre during this period (Fig. 3, top left). The
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Table 3. Standard deviations associated with the mean temperature
difference profiles for the three case studies.
EWB
Blend
EST
BST
0.0855
0.0906
0.0348
0.0947
0.0906
0.0347
0.0826
0.0939
0.0348
0.0957
0.0909
0.0356
0.0870
0.0939
0.0355
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Observational measurements from GL03 are used to validate
model simulations in conditions corresponding to nighttime
cooling and the initiation of diurnal warming. The deployment started at 23:08 (CET) and continued throughout the
night until 11:23 (CET) the next morning. The mean wind
speed is 6.29 ± 0.52 m s−1 and the solar heat flux steadily
rises from 0 to 876 W m−2 due to the morning solar heating
(Fig. 1). The modelled simulated and observational data were
bin averaged to depth intervals of 2 cm for the 117 profiles,
files for the deployment. The enhanced model and blended
model simulations become quite singular (Fig. 6). The five
models provide a mean temperature overestimation of 0.05 K
from 0.0025 to 5 m depth, while the baseline model over
predicts by 0.085 K. All the models struggle to simulate the
cool skin temperature correctly. The cool skin correction applied in the models was too weak (Fig. 6) and the simulated
SSTSkin values were overestimated by nearly 0.3 K. It is clear
that the enhanced and blended models simulated the depth
of the diurnal warm layer quite well as the temperature difference profile in Fig. 6 is relatively straight. The baseline
model simulates a shallow, diurnal mixed layer which can
|
Model performance in nighttime conditions
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3.2
|
five models do not simulate this temporary deepening which
could be related to their one-dimensional nature. The blended
and baseline models strongly overestimate temperature during this period (Fig. 2), which strongly affects the models’
overall performance. The enhanced models perform well in
this brief period, which is due to the overestimated warmlayer depths now matching the observations (Fig. 3).
The models are best compared by averaging their performance over multiple events. Mean temperature profiles
for the five model versions were computed for the duration of GC99 (Fig. 4). The standard deviations corresponding to these mean temperature profiles are given in Table 3,
showing to be in close proximity of each other. On average
the baseline mixing model overpredicts the SSTSkin value
by 0.28 K. The enhanced wave breaking and solar transmisFig. 3: Time-seriesFig.
temperature
depth
plots for
GC99
study:
plot and temper3. Time-series
temperature
depth
plotscase
for the
GC99observational
case study:
sion models underpredict SSTSkin values by 0.85 K and 1.0 K
observational
plotobserved)
and temperature
difference
(modelled
minus obature
difference
(modeled
minus
plots
for
the
5
model
versions.
Red
curve
represents
respectively, for the entire deployment while the blended
−2the
served) plots
for
five model
versions.
Redrepresents
curve represents
obsolar irradiance
(Wm
). The
white
area used
an ideal∆T
T of ±0.2 K.
model over predicts SSTSkin by 0.7 K (Fig. 4).observed
The blended
−2
served solar irradiance (W m ). The white area used represents an
solar transmission model gives the best results as it under
ideal1T of ±0.2 K.
predicts SSTSkin by 0.11 K and also provides the best results
down to a depth of 0.1 m.
22
The enhanced wave breaking and solar transmission modwith a higher resolution near the surface like that used in the
els predict deeper than observed warm-layer depths in Fig. 4.
previous section.
This affects the simulations by underestimating temperature
The plots (Fig. 5) show the times series of the meawithin the observed warm layer and overestimating the temsured profiles and temperature differences (model minus
perature approximately 1 m below this layer depth (Fig. 4).
measured) of the five model versions for this period. Due to
This is evident in the EWB and EST plots in Fig. 3, where
the small temperature changes observed, the white temperathe yellow coloured areas in the centre of the plots represent
ture difference interval represents 0.1 K for clarity (Fig. 5).
the temperature overestimation. This is due to the enhanced
The measured time-series plot (Fig. 5) shows a well mixed
models overestimating mixing in the upper few metres. This
water column for most of the deployment period. A warm
overestimation of mixing deepens the diurnal thermocline
layer is formed at 10:00 LT with the increase of morning soand creates an underestimation in temperature in the layers
lar heating. The plot in Fig. 6 shows the mean temperature
above, which can be observed as the blue coloured areas.
difference profile of the modelled minus the measured pro-
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Base
GC99
GL03
IO07
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Fig. 4. GC99 data set: differences between the modelled and in situ
Fig. 4: GC99 dataset: differences between the modelled and in-situ measurements for the Base
measurements
for the
Base EST
(blue),
Blend
(yellow),
(green),
(blue), Blend
(yellow), EWB
(green),
(red)
and BST
(cyan)EWB
models.
The surface points
EST (red)between
and BST
(cyan)and
models.
Theskin
surface
points are the difare the differences
modelled
M-AERI
temperatures.
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23
Fig. 5: Time-seriesFig.
temperature
depthtemperature–depth
plots for GL03 case
observational
5. Time-series
plotsstudy:
for the
GL03 case plot and temperbe observed in Fig. 6, as the temperature difference curve
study: observational
plot andplots
temperature
(modelled miature difference (modeled
minus observed)
for thedifference
5 model versions.
Red curve represents
changes slope rapidly below 2 m depth. Due to this, the temnus observed)
plots
for the
five area
model
versions.
Red curve
repreobserved solar irradiance
(Wm−2
). The
white
used
represents
an ideal
∆T T of ±0.1 K.
−2
perature has been overestimated near the surface and undersents observed solar irradiance (W m ). The white area used repestimated below the observed mixed layer (Fig. 5). The enresents an ideal 1T T of ±0.1 K.
hanced and blended models are within the ±0.2 K temperature difference. It is evident that the enhanced and blended
24
temperature for the majority of the deployment, caused by all
models produce the best results for this period for nighttime
the models estimating the warm-layer depth deeper than that
well mixed conditions.
of the observations. The models quickly react to the solar
heating toward the end of the measuring period, increasing
3.3 Model performance for day–night transition
the temperature of the upper 1 m by 0.4 K. The observed data
shows no signs of warming in the upper metre during this
ASIP measured temperature profiles from the IO07 data set
period of solar heating.
are used in this study to validate the models’ performance
The mean temperature profiles for each of the models are
in the highly stratified Cirene region of the Indian–Pacific
shown in Fig. 8. The five models strongly underestimate the
warm pool. The downwelling shortwave radiation and wind
temperature in the upper 5 m. The diagonally shaped temspeed for this modelling period are illustrated in Fig. 1. The
perature profile in Fig. 8 shows that this underestimation is
deployment takes place over nighttime and continues for a
caused by the models incorrectly estimating the warm-layer
brief period after sunrise. The measuring period begins at
depth well below that of the observed warm-layer depth. The
19:02 LT with a diurnal warm-layer depth of 5 m and a surhigh sensitivity of the models to solar heat flux is evident in
face amplitude of 0.7 K. A total of 72 profile measurements,
the curve above 0.5 m depth in Fig. 8. All the models produce
spaced approximately 10 min apart, run until 06:21 LT the
very similar mean temperature profiles and standard devianext morning. The warm-layer depth increases to 20 m and
tions (Table 3). All models, on average, underestimate the
surface amplitude reduces to 0.1 K over the period. A timetop metre of the warm layer by 0.45 K.
series plot of the observed temperature structure of the upper
The cool skin correction model applied in the simulations
5 m can be observed (Fig. 7, top left). ASIP profiling ceased
is on average 0.17 K above the required correction (Fig. 8).
between 00:28 and 01:41 LT, explaining the abrupt temperaThis incorrectly improves the SSTSkin compared with the unture change in the middle of the time-series plot.
derestimated SSTSubskin directly beneath.
Time-series plots of the temperature difference for the five
model versions against observations are shown for this period
(Fig. 7). It is evident that the temperature simulations struggle to replicate observations. The models underestimate the
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ferences between modelled and M-AERI skin temperatures.
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Fig. 6. GL03 data set: differences between the modelled and in situ
Fig. 6: GL03 dataset: differences between the modelled and in-situ measurements for the Base
measurements
for the
BaseEST
(blue),
(yellow),
(green),
(blue), Blend
(yellow), EWB
(green),
(red)Blend
and BST
(cyan) EWB
models.
The surface points
EST (red)between
and BST
(cyan)and
models.
Theskin
surface
points are the difare the differences
modelled
M-AERI
temperatures.
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|
Fig. 7: Time-seriesFig.
temperature
depth
plots for IO07plots
caseforstudy:
observational
7. Time-series
temperature–depth
the IO07
case study: plot and temperature difference (modeled
minus
plots for
the 5 model
versions.
Red curve represents
observational
plotobserved)
and temperature
difference
(modelled
minus ob−2the
served) plots
five white
model area
versions.
curve represents
In this section, all the available observed profiles
(1165)
observed
solar irradiance
(Wmfor
). The
usedRed
represents
an idealob-∆T of ±0.2 K.
served solar irradiance (W m−2 ). The white area used represents an
are collectively used to validate the five model versions.
ideal 1T of ±0.2 K.
A mean temperature profile for these profiles is shown in
Fig. 9. A temperature gradient exists at 0.2 m depth, im26
plying that strong effects of stratification are evident. The
from the temperature profile simulated by the blended solar
mean diurnal warming (SSTSubskin − TDepth ) is about 0.7 K
transmission model in Fig. 10. The blended solar transmisfor all observations.
sion model performs the best for depths from the subskin to
The mean temperature difference profiles for the five mod0.1 m, and achieves the closest SSTSubskin of all five models
els using all of the available profiles are shown in Fig. 10. The
with −0.05 K, with the baseline model achieving 0.06 K. The
conditions are mixed in a low to moderate wind environment
enhanced models show strong temperature underestimations
and with strong solar heating present (Fig. 1). The majority
above 0.2 m depth, influenced by the increased mixing paof deployments show strong characteristics of stratification
rameters associated with the addition of the KC04 enhancein the water column (Fig. 9). Overall, the baseline model
ment. The little difference between the results from the two
simulations provide the most accurate SSTSkin values with a
enhanced model versions implies that the OS00 solar transslight mean underestimation of 0.016 K. The blended model
mission enhancement has a low impact on the results comalso works well with a mean overestimation of 0.045 K. The
pared to that of the KC04 enhancement.
enhanced models show strong temperature underestimations
The cool-skin correction in the plot (Fig. 10) is very strong
throughout the warm layer (Fig. 7) which strongly affects the
for all the models. It causes an underestimation of 0.09 K
cool-skin temperature estimations. The enhanced models unwith respect to the warm-layer correction. In particular, this
derestimate SSTSkin by 0.30 K. The blended solar transmishas a strong impact on the overall performance of the blended
sion model underestimates SSTSkin by 0.12 K.
solar transmission model.
Comparing Figs. 9 and 10, it is clear that the baseline
model predicts the most accurate mixed-layer depth, within
negligible temperature variations up to 0.1 m depth. A mi4 Conclusions
nor temperature overestimation occurs above 0.1 m depth
for the baseline and blended model versions, caused by the
A strong variability in the results was shown to exist beuse of the nine-band solar absorption model. The addition
tween the models for highly stratified conditions (Fig. 4).
of the OS00 solar transmission model corrects this warmOverall, the baseline model produces the most accurate teming overestimation above this depth, which can be observed
perature estimates for the cruise periods used in this study.
Overall model performance
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ing a well-mixed upper ocean. For this study, the Karman–
Prandtl law of the wall assumption provides more accurate
SST values than the estimates achieved from the KC04 enhanced wave breaking model when the upper ocean is maximally stratified. Overall, the OS00 solar transmission model
provides more accurate temperature estimates in the diurnal
mixed layer compared to the nine-band absorption model.
The blended solar transmission model which transitions between the two surface turbulence approaches and includes
the OS00 model provides very good results immediately below the surface.
The cool-skin correction applied in the models produced
underestimations when compared to the measured SSTSkin .
On average the cool-skin correction underestimated SSTSkin
by 0.09 K for all the models. A revised cool-skin correction
could considerably improve the performance of the blended
Fig. 9. Mean observed temperature profile for all available data
Fig. 9: Mean observed temperature profile for all available data (1,165 profiles collectively
(1165 profiles collectively from GC99, GL03 and IO07 data sets)
solar transmission model (Fig. 10).
from GC99, GL03 and IO07 datasets) referenced to the mean SSTSkin value. The shaded region
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the 95% confidence interval.
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referenced
the meaninterval.
SSTSkin value. The shaded region represents
represents
the 95%to
confidence
Acknowledgements. Support for B. Scanlon was provided by the
Research Council of Norway (Grant 207541: OILWAVE) and
the EU FP7 project CARBOCHANGE under grant agreement
no. 264879. B. Ward was supported by the FP7 International
Reintegration Grant IRG-224776. The captain and crew of the R/V
Melville, R/V Urania, and R/V Suroit are thanked for their able
assistance. We are very grateful to Peter Minnett who provided the
M-AERI data for this study.
|
28
The enhanced models showed a strong temperature underestimation in the diurnal mixed layer for simulations in highly
stratified conditions. This is caused by the models’ overestimation of the mixed-layer depth, a direct result of the models’ high prediction of mixing near the surface. This is in
agreement with previous studies (Kantha and Clayson, 2004;
Ohlmann and Siegel, 2000) which have recorded reduced
temperatures in the diurnal mixed layer and increased mixedlayer depths. The enhanced models work well when wind
induced mixing at the surface is a dominant factor, creatwww.ocean-sci.net/9/977/2013/
Edited by: R. Sabia
Ocean Sci., 9, 977–986, 2013
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EST and BST models, respectively. The transparent colour-coded
regions represent the 95 % confidence
29 intervals.
|
27
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ferences between modelled and M-AERI skin temperatures.
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10.
Mean temperature
difference
fordata
all(1,165
available
datacollectively
Fig. 10:Fig.
Mean
temperature
difference profile
for allprofile
available
profiles
Fig.dataset:
8. IO07
data set: between
differences
between the
and in situ
from
andand
IO07
from
GC99,
GL03 andcollectively
IO07 datasets).
Thethe
blue,GC99,
yellow,GL03
green, red
cyandata
profiles repreFig. 8: IO07
differences
the modelled
and modelled
in-situ measurements
for the
the(1165
Base profiles
measurements
for the
BaseEST
(blue),
(yellow),
EWB (green),
The blue, yellow,
andBase,
cyanBlend,
profiles
represent
sent the sets).
mean temperature
differencegreen,
profilesred
of the
EWB,
EST andthe
BST models,
(blue), Blend
(yellow), EWB
(green),
(red)Blend
and BST
(cyan) models.
The surface
points
EST
(red)
and
BST
(cyan)
models.
The
surface
points
are
the
difrespectively.
The
transparent
colour-coded
regions
represent
the
95%
confidence
intervals.
mean temperature difference profiles of the Base, Blend, EWB,
are the differences between modelled and M-AERI skin temperatures.
Research Papers 2.1
986
References
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Research Papers 2.2
3.2 Oceanic wave breaking coverage separation
techniques for active and maturing
whitecaps
Research Papers 2.2
Methods in Oceanography 8 (2013) 1–12
Contents lists available at ScienceDirect
Methods in Oceanography
journal homepage: www.elsevier.com/locate/mio
Full length article
Oceanic wave breaking coverage separation
techniques for active and maturing whitecaps
Brian Scanlon, Brian Ward ∗
School of Physics and Ryan Institute, National University of Ireland Galway, Galway, Ireland
article
info
Article history:
Received 22 October 2013
Accepted 21 March 2014
Keywords:
Breaking waves
Active and maturing whitecaps
Image processing
∗
abstract
Whitecaps on the ocean surface mark localized areas where interactions between the atmosphere and ocean are enhanced. Contemporary methods of quantifying total whitecap coverage rely
on converting color sea surface images into their binary equivalent using specific threshold-based automated algorithms. However, there are very few studies that have separated and quantified
whitecap coverage into its active (stage-A) and maturing (stage-B)
evolutionary stages, which can potentially provide more suitable
parameters for use in breaking wave models, air–sea gas transfer,
aerosol production, and oceanic albedo studies. Previous active and
maturing whitecap studies have used a pixel intensity separation
technique, which involves first separating the whitecap and background pixels, and subsequently establishing a second threshold to
distinguish between active and maturing whitecaps. In this study,
a dataset of more than 64,000 images from the North Atlantic were
initially processed to determine the total whitecap coverage using
the Automated Whitecap Extraction method. The whitecap pixels
of each image were then distinguished as either stage-A or stage-B
whitecaps by applying a spatial separation technique which does
not rely solely on pixel intensity information but also on the location (relative to the wave crest), visual intensity, texture and shape
of each whitecap. The comparison between the spatial separation
and pixel intensity separation techniques yielded average relative
errors of 34.8% and −44.0% for stage-A and -B coverage, respectively. The pixel intensity method was found to be less suitable
when compared to the spatial separation method as it relies on the
Corresponding author. Tel.: +353 91 493029; fax: +353 91 493029.
E-mail address: [email protected] (B. Ward).
http://dx.doi.org/10.1016/j.mio.2014.03.001
2211-1220/© 2014 Elsevier B.V. All rights reserved.
Research Papers 2.2
2
B. Scanlon, B. Ward / Methods in Oceanography 8 (2013) 1–12
assumption that the pixel intensity for stage-A is always greater
than that for stage-B.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Whitecap coverage on the ocean surface is a direct result of breaking waves and is a visual
representation of areas on the ocean surface where enhanced air–sea interactions of gas and aerosols
occur (Anguelova and Webster, 2006). Many studies have been carried out to quantify the area of
ocean surface covered by whitecaps (W ) (Monahan and O’Muircheartaigh, 1980; Anguelova and
Webster, 2006; Sugihara et al., 2007; Callaghan et al., 2008; Goddjin-Murphy et al., 2010) and
there have been many attempts to parameterize whitecap coverage with wind speed (see Figure 1
in Anguelova and Webster, 2006, for a summary of parameterizations over the past 42 years).
According to the nomenclature of Monahan and Lu (1990), there are two stages of evolution in the
lifetime of a whitecap. At the initial occurrence of a wave breaking, the wave crest velocity exceeds
that of the wave, spills, traps air, and entrains it below the sea surface. A condensed bubble plume
is created beneath the surface. This initial phase is known as stage-A or active whitecapping and has
a characteristic lifetime O (1 s). Due to the strong gravitational forces and wave momentum present,
a high mixing potential is created at the air–sea interface. Directly after the gravitationally driven
stage-A event, bubbles are overcome by turbulence and buoyancy forces, the bubble plume expands,
returns to the sea surface forming a large whitecap, and decays through bubble bursting processes.
This phase is known as stage-B or maturing whitecap, and it is during this phase that the majority of
bubble bursting occurs. Stage-B whitecaps typically have longer lifetime than that of stage-A, often
being observed for times up to 10’s of seconds (Callaghan et al., 2013). Fig. 1 shows a schematic of
the evolution of a typical whitecap, from the stage-A occurrence to the evolution of a stage-B. Both
stages of whitecapping can be quantified by measuring the area of the image containing the active
and maturing whitecaps.
Active whitecaps play a strong role in the air–sea gas transfer due to their high mixing potential.
Monahan and Spillane (1984), Woolf (1997) and Asher and Wanninkhof (1998) have attempted to
use whitecap coverage estimates to obtain more accurate models for gas transfer velocities. Andreas
and Monahan (2000) reported that stage-A whitecaps cycle roughly 4 orders of magnitude more air
through the near surface ocean than do stage-B whitecaps for a given wind speed. Stage-A values have
been regarded as the most suitable parameter for quantifying the rate of wave breaking, playing a vital
role in modeling turbulence injected into the upper ocean due to wave breaking. Wave modelers such
as Hanson and Phillips (1999) have used W estimates to parameterize the dissipation of wave-field
energy as a wave breaks.
Decaying whitecaps, due to their bubble bursting nature, have been previously quantified and
related to studies involving sea-salt aerosol particle production (Monahan et al., 1986), underlying the
importance of the quantification of stage-B whitecaps. Bubble bursting in stage-B whitecaps result
in film and jet droplets being produced, creating atmospheric aerosols which have been reported
to impact on air–sea sensible and latent heat fluxes (Andreas et al., 1995). Anguelova and Webster
(2006) states that sea spray processes must be adequately parameterized and included in climate
models. Surfactant concentrations at the air–sea interface can strongly affect the persistence of stageB whitecaps (Callaghan et al., 2013). Discriminating stage-A from W could potentially remove the
dependence of surfactants from whitecap estimates, providing a more relevant parameter for gastransfer models and rate of wave breaking.
Methods of quantifying W have developed over the past several decades, and it has generally
involved the analysis of photographic and videographic images of the sea surface where areas of
whitecap were identified and quantified. Initially, this involved labor-intensive methods whereby
photographs of sea surface were physically dissected to remove the areas of whitecapping and
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3
Fig. 1. Schematic illustrating the evolution of a typical breaking wave: a spilling wave crest (I), bubble plume formation (II),
evolution into stage-B whitecap (III), and decay of the whitecap (IV).
subsequently weighed, in order to determine values of W . This method was developed by Monahan
(1969) and was widely used up into the late 1980s (Monahan, 1971; Toba and Chaen, 1973; Monahan
et al., 1981). More recent methods involve the acquisition of high-resolution digital images of the
sea surface at rates of 1 Hz or better using digital camera technology. These raw images lend
themselves to image processing techniques, such as the Automated Whitecap Extraction (AWE)
algorithm (Callaghan and White, 2008) specifically developed for quantifying whitecap coverage. This
advancement in technology allows for more accurate estimates of W as well as the possibility to
process thousands of images rapidly. Such algorithms can distinguish image pixels as either whitecap
or background using an automatically determined pixel intensity threshold. This threshold can vary
from one image to the next due to background ambience illumination fluctuations, wave slope, image
capturing angle, and the presence of sun glint.
Previous studies have considered alternative methods of studying whitecap coverage using
satellite radiometric data (Anguelova and Webster, 2006), acoustic sensors to measure the rate of
bubble formation (Monahan and Lu, 1990), the rate of wave breaking (Ding and Farmer, 1994), and
parametric estimates of total energy dissipation rate in wave models (Anguelova and Hwang, 2012).
Although there is a strong motivation to distinguish stage-A and stage-B whitecaps, there has
been little success in the development of an automated technique. This is due to the complexity
of determining the stages of the evolution of whitecaps based on the visual characteristics, which
can be highly variable from one image to the next. A few studies have attempted to distinguish total
whitecap coverage into its two stages (WA ) and (WB ) (Ross and Cardone, 1974; Bondur and Sharkov,
1982; Monahan and Woolf, 1989). The technique applied by Monahan and Woolf (1989) involved the
determination of a second pixel intensity threshold to distinguish between stages A and B whitecaps
for individual images. The underlying assumption for this method is that the pixel intensities of stageA whitecaps exceeds that of stage-B whitecaps.
This article introduces a new technique, called the spatial separation of whitecap pixels (SSWP)
which allows a user to manually distinguish pixel groups as either contributions towards WA or WB
by evaluating their location on the wave-field, brightness, texture and slope through the observation
of the original image. The pixel intensity threshold separation technique (PITS) is evaluated by
comparing its results to that from our SSWP method. Conclusions are provided as to the most suitable
method for distinguishing stages of whitecaps for use in future analysis.
2. Digital image processing of sea surface images
Digital images of the sea surface are comprised of many elements such as ocean background,
whitecaps, sun glint, sea gulls, and residual foam formed along wind rows (Langmuir circulation).
These digital images comprise of a number of pixels, depending on the image resolution. For 8-bit
cameras, the pixels have intensity values ranging from 0 to 255 for their three constituent colors: red,
green and blue. Sea surface images are commonly converted to grayscale, which reduces the pixel
values from three scales to one.
Once converted to grayscale, the pixel values can be used to distinguish the regions of whitecap
pixels from non-breaking background sea by assuming that the pixel intensity of whitecaps is greater
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than that of the background sea. This thresholding method is accepted by many authors as being the
most suitable for distinguishing whitecap regions in images and has been widely in use since the early
1970s (Nordberg et al., 1971; Monahan, 1993; Asher and Wanninkhof, 1998; Sugihara et al., 2007;
Callaghan and White, 2008).
The image pixels can be categorized into 256 bins (i) depending on their pixel intensity values (I ).
The pixel population, PP (i), represents the number of pixels in the ith bin for a sea surface image of
m × nresolution:
PP (i) =
m


j =1
n


I (j, k) == i
,
(1)
k=1
where I (j, k) is the pixel intensity value at coordinates (j, k) of the image. The percentage whitecap
coverage (W ) can be obtained by integrating PP (i) for values of i above a threshold T :
 255
T
W (%) = i=
255
i=0
PP (i)di
PP (i)di
×
100
1
.
(2)
By applying a suitable threshold, the whitecap pixel intensity spectra (WPIS) can be distinguished
from the PP (i). There has been much research into selecting the most appropriate pixel intensity
value T for distinguishing whitecaps in an ocean surface image (Monahan, 1993; Sugihara et al., 2007;
Callaghan and White, 2008). The AWE algorithm (Callaghan and White, 2008) was used in this study to
find estimates for T . The algorithm can calculate the most suitable threshold as an automated process,
allowing for large amounts of images to be processed quickly and efficiently. The AWE algorithm has
been previously used in whitecap threshold applications for Callaghan and White (2008), Callaghan
et al. (2008) and Goddjin-Murphy et al. (2010) and has proven to be a robust method for automated
thresholding.
Other methods such as batch grayscale thresholding (BGT) have been used to extract W values
from time-series of images by applying a singular threshold value. Authors such as Sugihara et al.
(2007) have used this method successfully from stable camera platform views of the sea surface and
from airborne vehicles (Bobak et al., 2011) to achieve estimates of whitecap coverage from 10 minute
time-series of images. The method assumes that the pixel intensity distribution of whitecaps and
background sea is uniform for all images captured within a relatively short period allowing for a
singular pixel intensity threshold to be applied to the batch of images to distinguish regions of
whitecaps. The PP (i) for each image is computed and added together to create a PP (i) for the entire
batch. W (i), representing the series of whitecap coverage estimates for every possible threshold, is
then calculated using Eq. (2). The most suitable threshold is selected by locating the lowest percentage
difference between adjacent values in the W (i) series (Sugihara et al., 2007).
A modest area of the sea surface is required to be processed in order to achieve converging W
estimates. Callaghan and White (2008) states that a dataset of 100s of images will achieve convergence
for W estimates. Large image footprints can introduce larger deviations for mean pixel intensities for
background sea and whitecaps, making it more difficult to distinguish whitecaps using the threshold
technique. This is also true for high altitude images taken from airborne vehicles. Bobak et al.
(2011) discusses the negative impact of high altitudes for camera systems. Smaller image footprints
require larger numbers of images to achieve accurate W estimations for the particular conditions.
However, the processing of larger image sets requires longer capturing time, and as the meteorological
conditions at sea can fluctuate on short-timescales, this can introduce larger errors for calculating
complementary mean meteorological parameters.
For oceanic studies, it is a rare occurrence to find periods of steady meteorological conditions.
Changes in conditions can result in the W values not converging, making it important to reduce the
time of image capture and thus minimizing this effect. According to Callaghan and White (2008), the
convergence of 300 images can yield less than approximately 5% difference for mean W estimates,
based on a 20 minute capturing period. Sugihara et al. (2007) achieved mean estimates of W from
600 images in a 10 minute time frame but no information on the image footprint is given. An image
footprint of approximately 5000 m2 was used by Callaghan et al. (2008), which would provide an
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Fig. 2. Pixel intensity spectrum of background sea, stage-B and stage-A pixels for a typical image assuming normal
distributions. The vertical lines represent threshold values T and T∗ .
average total sea surface area of 2 × 106 m2 per W estimate (assuming an average of 400 images per
W datapoint). A high resolution camera capturing larger image footprints in a shorter time frame will
help minimize the effects of meteorological fluctuations and obtain an accurate representation of the
sea surface.
3. Active and mature whitecap separation
Previous methods (Monahan and Woolf, 1989) of separating stage-A and -B whitecaps relied on
a manual setting of a second pixel intensity threshold (T∗ ). This method assumed that the pixel
intensity spectrum of stage-A pixels (IA ) is greater than the pixel intensity spectrum of stage-B
pixels (IB ). According to Monahan (1993), the visible albedo of stage-A whitecaps (∼0.6) is greater
than that observed for stage-B whitecaps (0.2–0.5), and this can be used as a basis for the optical
separation. According to this method, pixel intensity spectra for individual images will comprise of
three distributions: background, stage-A, and stage-B pixels which can be separated by selecting two
appropriate thresholds T and T∗ (Fig. 2).
Application of the first threshold T is widely in use for separating background sea and whitecap
pixels (both stage-A and -B). The use of the secondary threshold to distinguish whitecaps into their
active and maturing stages assumes that the intensity spectra contained in PP (i) of stage-A (IA ) and
-B (IB ) can be distinguished solely on their intensity values.
According to Callaghan and White (2008), an individual whitecap region (both active and maturing)
consists of pixels of multiple intensities, typically appearing more intense in the middle of the
whitecap region and becoming less intense out towards the edges. This occurs due to the nature of a
whitecapping event where the visible signature for an underlying bubble plume beneath the surface
is typically at its deepest in the middle of the whitecap (Monahan and Lu, 1990). This can cause an
overlap in pixel intensity values for stage-A and stage-B whitecaps, with near edge pixels of a stageA region being similar in intensity to the pixels in the middle of a stage-B region. This makes the
separation of stage-A and -B pixels difficult, due to the overlap between IA and IB .
3.1. Spatially observed and separated technique
Accurate discrimination of stage-A and -B whitecaps can be achieved by visually inspecting
whitecap regions in an image and determining their stage of evolution based on their location relative
to the crest of the wave, shape and visual intensity. According to the definition of an active whitecap,
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Fig. 3. Raw sea surface image (a) and binary converted image using AWE threshold (b). An example ROI is shown to illustrate
how pixel groups are selected for being distinguished. The resulting image (c) displays the labeled stage-A (blue) and stage-B
(green) whitecap pixels. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
the location must be either in front of or on top of a wave crest. The region where an active whitecap
is confined is a small area on the ocean (with respect to the length scale of the wave) and is restricted
in expanding due to its relatively short lifetime. Once gravitational forces of the plunging bubble
plume are overcome by buoyancy forces, the whitecap enters the second stage of its evolution. This
gives rise to a maturing whitecap which is visibly larger in area, appears less bright, and has a less
uniform texture than an active whitecap. Stage-B whitecaps have been described as a hazy foam patch
by Monahan (1993). A new method, called the spatial separation of whitecap pixels (SSWP), allows
manual separation of whitecap pixels in order to distinguish them as either stage-A or -B.
The SSWP method allows whitecap pixels to be separated into their stages of evolution without
relying solely on pixel intensities. This manual method is based on inspecting the image and grouping
whitecap pixels as either contributions to stage-A or stage-B, with spatial freedom, using a graphical
input device system. Despite the subjective nature of this analysis, the SSWP method is a valuable
tool and can allow a user to accurately determine the stage of evolution of a whitecap through
strict adherence to the stage-A and -B definitions outlined previously and by appealing objectively
to the whitecaps visual characteristics within the image. Fig. 3 is an example of a sea surface image
containing both active and maturing whitecaps along with the SSWP processed image showing the
stage-A pixels colored in blue and the stage-B pixels colored green.
The SSWP method relies on the use of one threshold (T ) to distinguish whitecap pixels from
unbroken background water using the AWE algorithm (Callaghan and White, 2008). The W pixels
are then discriminated by manually drawing regions of interest (ROI) and specifying them as either A
or B whitecaps. The W pixels are then color coded (as in Fig. 3) to help re-evaluate and identify errors
(similar to those used in Fig. 3c). The processing algorithm was designed to be maximally efficient,
requiring minimal input from the user and maintain high fluidity when processing consecutive
images. The user can easily and quickly distinguish the stages of whitecaps and extract high quality
results. After the user separates the whitecap pixels of an image, the results are displayed to help
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Fig. 4. Histogram of the wind speeds in 1 m s−1 bins for the 69 30-minute periods.
flag any mistakes made. The method requires approximately 10 s per image, allowing for a typical
dataset of 900 images to be processed in 3 h. This processing method also allows for errors such as
contamination due to seagulls or sun glint to be removed which can often be present after applying
the AWE threshold.
4. Results and discussion
A dataset of sea surface images was obtained in the North Atlantic onboard the R/V Knorr in the
summer of 2011. The camera was mounted on the O4 deck at a height of 19 m above sea level and at
an angle of 75° to the nadir. This provides an image footprint of 7592 m2 of the sea surface. The camera
had a focal length of 70 mm and obtained images at 0.5 Hz. The image resolution of the captured image
is 2560 × 1920 and is cropped to 1231 × 810 during the AWE algorithm process.
A set of 69 30-minute imaging periods were selected, in favorable overcast conditions, and
processed using the SSWP method. This amounted to over 64,540 images having their whitecap
contents distinguished, with individual WA and WB values extracted. Wind speed ranged from 3.0 to
16.8 m s−1 (Fig. 4), water temperature ranged from 8.5 to 23.8 ° C and atmospheric stability (water–air
temperature) ranged from −3.4 to 7.0 ° C for these selected image capturing periods.
The BGT (batch grayscale thresholding) method and AWE algorithm were both considered for
distinguishing whitecap pixels from each image by calculating specific T values. The AWE-derived
T values were applied to each image and manually inspected during the SSWP analysis. The AWE
algorithm was found to produce superior threshold values for individual images. The data were then
split into 10- and 30-minute datasets (300 and 900 images respectively) and BGT analysis was carried
out to obtain the most suitable T value. An average relative error (and standard deviation σ ) for W
of 5478% (σ = 10,940) and 13 966% (σ = 26,243) is introduced for 10- and 30-minute periods
respectively when applying the BGT derived T values. The large deviations represent the distribution
of averaged error of the 69 30-minute and 207 10-minute periods. While the BGT method can achieve
modest automated whitecap results when paired with large datasets of images and statistical analysis,
it is not implemented in this study for the following reasons: first, the images in this study were
obtained onboard the R/V Knorr in open seas, introducing an unstable platform and changing the
angle of inclination of image capture. Second, the images in this study were all manually inspected
and evaluated leaving the idea of quick batch analysis redundant. Third, the AWE can apply individual
thresholds to each image, providing an accurate WPIS for this study. However, it is interesting to note
the large error introduced when using BGT methods on images obtained from an unstable platform.
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Fig. 5. Four sea surface images (a)–(d) in the first row with SSWP distinguished WA (blue) and WB (green) regions in the
second row. The third row shows the results when using the PITS method of separation by applying a T∗ threshold. The fourth
row shows the SSWP whitecap pixel distributions. Table 1 provides relevant values for the images. (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1
Complementary data for the images displayed in Fig. 5. Wind represents the nearest 1 minute true wind speed (m s−1 ) averaged
over a 30 minute window.
Image
(a)
(b)
(c)
(d)
Wind
3.6
7.4
12.7
16.4
T
177
195
178
174
T∗
201
225
238
228
IA ( ± σ )
217.3 (±22.7)
235.2 (±17.8)
242.6 (±20.6)
228.8 (±25.3)
IB (± σ )
200.2 (±14.5)
219.8 (±14.2)
213.9 (±20.3)
207.6 (±18.5)
Esep (%)
SSWP (%)
Wa
Wb
Wa
0.15
0.32
0.94
0.48
0.05
0.37
1.30
6.75
−16.6
Wb
50.1
1.1
0.3
183.3
−1.0
−0.2
−13.1
Assuming that the SSWP method achieves the best possible estimate of WA and WB from sea surface
images, the results can be used as a basis to compare and evaluate the PITS method results for the
same dataset of images. Extraction of WA and WB estimates using the PITS method can be achieved
by analyzing the SSWP distinguished pixel intensities spectrums for stage-A and -B whitecap regions
(IA and IB ) in each image and attempting to calculate a second pixel intensity threshold T∗ to best
separate them. Assuming that the PITS is a viable separation technique, then the mean pixel intensity
for stage-A pixels must be greater than the mean of stage-B pixels (i.e., IA > IB ). If we assume a normal
distribution for stage-A and -B pixel intensity values, then the deviations of IA and IB around their mean
values must be less than IA − IB so as to achieve modest separation error (due to overlap of IA and IB
spectra (Fig. 2)).
A detailed overview of the image processing is introduced using a small number of images as
examples. Four images were selected showing different breaking wave events (Fig. 5). Each of these
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Fig. 6. Esep values for various T∗ thresholds used for Fig. 3.
images was selected for a different wind speed range, i.e., 3.6, 7.4, 12.7, and 16.4 m s−1 . These images
are then analyzed using the SSWP and PITS techniques to determine values of WA and WB .
The second row of images in Fig. 5 show the SSWP results with marked areas of stage-A (blue) and
stage-B (green) whitecaps. The third row in 5 shows the distribution of stage-A and stage-B pixels by
separation using a intensity threshold T∗ (refer to Table 1 for values). The fourth row of Fig. 5 shows
the intensity spectra of stage-A (IA ) and of stage-B (IB ) whitecaps. Also included in these images are
the normal distributions shown to ±3 standard deviations using the mean values IA and IB with their
respective deviation values shown in Table 1.
The first threshold T for each image is set by the AWE algorithm. Pixel intensities below T are
considered that of unbroken background sea and the pixel intensities exceeding T are considered that
of whitecaps. These pixels were then grouped, spatially separated and distinguished as either stage-A
or stage-B whitecaps using the SSWP method. Extracting the pixel intensity spectra of both stages of
whitecaps, the mean values were found providing IA and IB . If IA > IB , all intensity values between
these two means were tested as a potential T∗ threshold. The most appropriate T∗ was obtained by
comparing the relative change in pixel numbers for stage-A and -B and selecting the value with the
lowest relative error. A separation error (Esep ) is defined to quantify this relative error and calculate
the most appropriate T∗ value:
 255
Esep =
i=T∗
PP (i)di −
 255
i=0
 T∗
Esep =
i=T
i =0
IA di
PP (i)di
PP (i)di −
 255


PP (i)di
×
100
1
. . . for stage-A
(3)
IB di
×
100
1
. . . for stage-B.
Fig. 6 shows the Esep range for all T∗ values between IA and IB , for image (c) in Fig. 5. For this
individual image, the majority of IA have intensities above 250 (Fig. 5 column (c), row 4). IA was
calculated to be 242.6, with a standard deviation of 20.6. The IB spectrum was more evenly spread
across the range between T and the maximum pixel value (255), achieving a IB of 213.9, with a
standard deviation of 20.3. The value for a second threshold T∗ ∈ IB < i < IA was obtained on the
basis of achieving the closest WA and WB values to those obtained by the SSWP method. For T∗ = 238,
WA and WB values are calculated with the lowest Esep values of 0.3% and −0.2% respectively.
Incorporating the second threshold into the original images displayed on the top row of Fig. 5,
illustrations of the spatial distribution of the PITS method are shown on the third row of Fig. 5. For
images (c) and (d), it can be clearly observed that the outer edges of the stage-A whitecap regions
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Table 2
Definition of specific types of sea surface images, based on the whitecap
content.
Type
Content
Condition (if any)
Esep
Class 2a
Class 2b
Class 1
Class 0
WA & WB
WA & WB
WA or WB
Neither WA or WB
I¯A > I¯B
I¯B > I¯A
(Eq. (3))
Not defined
=0
=0
have lower pixel intensities than T∗ and cannot be distinguished as WA without capturing more high
intensity pixels from the center of stage-B whitecap regions.
4.1. Comparison for a 30 minute dataset
The PITS method is further evaluated by extracting SSWP-derived IA and IB spectra for 917 images
as part of one 30 minute dataset. This dataset corresponds to a mean wind speed of 11.4 (±0.8) m s−1 ,
providing a suitable high rate of wave breaking. The viability of employing a secondary threshold T∗
to the WPIS of each image to separate WA from WB is evaluated using Esep values in the same fashion
as Eq. (3). Certain criteria are in place to allow for processing of images containing different types of
whitecap content.
In summary, images containing both WA and WB regions but with averaged stage-B pixel intensities
exceeding that of stage-A, (IA < IB ) are not eligible for the PITS technique. These images are called
‘Class 2b’ images. In the case of images containing only one stage of evolution of a whitecap, it can
be distinguished sufficiently using only the first threshold T . These images are called ‘Class 1’ images
and result in Esep errors equal to zero after applying the PITS technique. Similarly, Esep values are also
zero for a third image type which contains no whitecap pixels, called ‘Class 0’ images. The final type of
image, called ‘Class 2a’, contains examples of both stages of whitecap evolution and meets the criterion
that IA > IB . These images are processed in the same fashion as the images in Fig. 5 and Esep values are
found using Eq. (3). These image types are summarized in Table 2.
For this particular image dataset, Esep was calculated to be 68.5% and 16.2% for estimating WA and
WB using the PITS method, respectively. Image classes 2a, 1 and 0, with a breakdown of 37.2% for 2a,
35% for 1 and 9.0% for 0 were used to calculate these final Esep values. The percentage of ‘Class 2b’
images in the dataset was 18.8%, an indication of the number of images which contradict the initial
assumption of IA > IB , and thus could not be processed using the PITS method.
4.2. Comparison for the entire dataset
The entire dataset of 64,540 images was used to evaluate the PITS method. Considering all the
available images (classes 2a, 1 and 0), 68.9% and 74.3% are the average Esep values for WA and WB
respectively, with 21.6% of the total images being of class 2b.
These high values demonstrate that the PITS method is not suitable for obtaining accurate WA and
WB estimates. The WA and WB values obtained from the PITS method (for images of class 2a, 1 and
0) compared to those of the SSWP (for all image types), provide relative errors of 34.8% and −44.0%
respectively.
Fig. 7 shows the averaged WA and WB values for each of the 69 30-minute periods derived from
the SSWP method and plotted against that derived from the PITS method. The vertical and horizontal
error bars for each datapoint represent the 95% confidence intervals. It is interesting to note that the
PITS method overestimates WA and underestimates WB when compared to the SSWP-derived values
in this study (Fig. 7).
The PITS- and SSWP-derived WA error bars are observed to be of similar magnitude (change of
15.4% on average), while the PITS-derived WB error bars are significantly lower (−48% on average)
than the SSWP-derived WB error bars (Fig. 7). It is important to note that the PITS-derived WA and WB
values are averaged from a sample population of images which exclude images of class 2b (21.6% of
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Fig. 7. SSWP-derived active (WA ) and maturing (WB ) whitecap coverage plotted against that derived from the PITS method.
The error bars represent the 95% confidence intervals.
total images). The absence of this class of image is quantified by appealing to the changes in average
and standard deviation estimates for the overall whitecap coverage W of the entire data, which are
−22.2% and −31.3% respectively. These values show that this reduction in images plays a vital role in
explaining the observed changes in variance of averaged WA and WB estimates when using the PITS
method.
However this does not fully account for the observed variance changes induced by the PITS method.
Further analysis of the SSWP- and PITS-derived values conducted for images of class 2a, 1, and 0
removes the changes of variance due to this under sampling and reveals variance changes of 2.9%
and −23.6% for WA and WB averages respectively. This implies that the PITS method significantly
reduces the variability of the periodic averages of WB . This is caused by a PITS-induced convergence of
WB estimates of individual images, revealing an underestimation in the quantification of WB regions
which is scaled to the size of the whitecap, with the largest maturing events being underestimated the
most. This underestimation occurs for class 2a images when IA and IB overlap quite extensively (refer
to the bottom row Fig. 5) allowing for large numbers of high intensity stage-B pixels to be interpreted
as contributions towards WA when the second threshold is applied.
5. Conclusions
A method for whitecap discrimination between stage-A and stage-B whitecapping has been
presented. This technique allows images to be processed by determining a region-of-interest for the
two types of whitecapping. The separation is achieved manually by observing the sea surface image
and evaluating the whitecap pixels with respect to the crest of the wave, its visual intensity, shape
and texture, thereby determining if the whitecap is actively breaking or maturing.
A second pixel intensity threshold separation (PITS) method was evaluated by comparing the
WA and WB values, extracted from 64,540 high resolution sea surface images, to those extracted
by the SSWP method. The PITS method employs a secondary threshold to separate whitecap pixels
dependent on pixel intensity, a method used in the previous studies.
The Batch Grayscale Threshold (BGT) method introduces large errors when distinguishing
whitecap coverage estimates from the batches of images captured from an unstable camera platform,
compared with those distinguished by the Automated Whitecap Extraction (AWE) algorithm. The
application of the AWE algorithm is recommended for future analysis.
The comparison study reveals that the PITS method introduces significant separation errors, an
average of over 68.9% (relative error), compared with those attained from the SSWP method. This
Research Papers 2.2
12
B. Scanlon, B. Ward / Methods in Oceanography 8 (2013) 1–12
results in changes to mean whitecap coverage estimates for stage-A and -B of 34.8% and −44.0%
respectively, when compared to SSWP derived coverage values.
Separation of whitecap pixels into their evolutionary stages, defined by (Monahan and Lu, 1990),
is best carried out by spatial separation by appealing to all available characteristics such as location
(with respect to wave crest), intensity, shape and texture rather than solely relying on a pixel intensity
threshold.
Acknowledgments
The authors gratefully acknowledge financial support from the EU FP7 project CARBOCHANGE
under Grant agreement no. 264879. BS received support from the NUIG College of Science Fellowship
Program. BW was funded to participate in the Knorr11 under Grant 08/US/I1455 provided by Science
Foundation Ireland. Adrian H. Callaghan provided whitecap analysis on the images with the AWE
algorithm. The authors would like to thank the Captain and Crew of the R/V Knorr, as well as Scott
Miller the Chief Scientist.
References
Andreas, E.L., Edson, E.B., Monahan, E.C., Rouault, M.P., Smith, S.D., 1995. The spray contribution to the net evaporation from
the sea: a review of recent progress. Bound. Layer Meteorol. 72, 3–52.
Andreas, E.L., Monahan, E.C., 2000. The role of whitecap bubbles in air–sea heat and moisture exchange. J. Phys. Oceanogr. 30,
433–442.
Anguelova, M.D., Hwang, P.A., 2012. Whitecap fraction of actively breaking waves: toward a database applicable for dynamic
processes in the upper ocean. In: 18th Air-Sea Interaction Conference. 9–13 July, Boston, MA.
Anguelova, M.D., Webster, F., 2006. Whitecap coverage from satellite measurements: a first step toward modeling the variability
of oceanic whitecaps. J. Geophys. Res. 111, http://dx.doi.org/10.1029/2005JC003158.
Asher, W.E., Wanninkhof, R., 1998. The effect of buble-mediated gas transfer on purposeful dual-gaseous tracer experiments.
J. Geophys. Res. 103, 10555–10560. http://dx.doi.org/10.1029/2012JC008147.
Bobak, J.P., Asher, W.E., Dowgiallo, D.J., Anguelova, M.D., 2011. Aerial radiometric and video measurements of whitecap
coverage. IEEE Trans. Geosci. Remote Sens. 49, 2183–2193. http://dx.doi.org/10.1109/TGRS.2010.2103565.
Bondur, V.G., Sharkov, E.A., 1982. Statistical properties of whitecaps on a rough sea. Oceanology 22, 274–279.
Callaghan, A.H., Deane, G.B., Stokes, M.D., 2013. Two regimes of laboratory whitecap foam decay: bubble-plume controlled and
surfactant stabilized. J. Phys. Oceanogr. 117, http://dx.doi.org/10.1175/JPO-D-12-0148.1.
Callaghan, A.H., de Leeuw, G., O’Dowd, C.D., 2008. Relationship of oceanic whitecap coverage to wind speed and wind history.
Geophys. Res. Lett. 35, http://dx.doi.org/10.1029/2008JC036165.
Callaghan, A.H., White, M., 2008. Automated processing of sea surface images for the determination of whitecap coverage.
J. Atmos. Ocean. Tech. 113, 383–394. http://dx.doi.org/10.1175/2008JTECHO634.1.
Ding, L., Farmer, D.M., 1994. Observations of breaking wave statistics. J. Phys. Oceanogr. 24, 1368–1387.
Goddjin-Murphy, L., Woolf, D.K., Callaghan, A.H., 2010. Parameterizations and algorithms for oceanic whitecap coverage.
J. Phys. Oceanogr. 41, 742–756.
Hanson, J.L., Phillips, O.M., 1999. Wind sea growth and dissipation in the open ocean. J. Phys. Oceanogr. 29, 1633–1648.
Monahan, E.C., 1969. Fresh water whitecaps. J. Atmos. Sci. 26, 1026–1029.
Monahan, E.C., 1971. Oceanic whitecaps. J. Phys. Oceanogr. 1, 139–144.
Monahan, E.C., 1993. Occurence and evolution of acoustically relevant sub-surface bubble plumes and their associated,
remotely monitorable, surface whitecaps. In: Kerman, B. (Ed.), Natural Physical Sources of Underwater Sound. Springer,
New York, pp. 503–517.
Monahan, E.C., Lu, M., 1990. Acoustically relevant bubble assemblages and their dependence on meteorological parameters.
IEEE J. Ocean. Eng. 15, 340–349.
Monahan, E.C., O’Muircheartaigh, I.G., 1980. Optimal power-law description of oceanic whitecap coverage dependance on wind
speed. J. Phys. Oceanogr. 10, 2094–2099.
Monahan, E.C., O’Muircheartaigh, I.G., FitzGerald, M.P., 1981. Determination of surface wind speed from remotely measured
whitecap coverage, a feasibility assessment. In: Proceedings of an EARSeL-ESA Symposium, Application of Remote Sensing
Data on the Continental Shelf, Voss, Norway, 19–20 May 1981, European Space Agency, SP-167. pp. 103–109.
Monahan, E.C., Spiel, D.E., Davidson, K.L., 1986. A model of marine aerosol generation via whitecaps and wave disruption.
In: Monahan, E.C., MacNiocaill, G. (Eds.), Oceanic Whitecaps and their Role in Air-Sea Exchange Processes. Springer,
pp. 167–174.
Monahan, E.C., Spillane, M.C., 1984. The role of oceanic whitecaps in air–sea gas exchange. In: Brutsaert, W., Jirka, G.H. (Eds.),
Gas Transfer at Water Surfaces. D. Reidel Publishing Company, Dordrecht, pp. 495–503.
Monahan, E.C., Woolf, D., 1989. Comments on ‘variations of whitecap coverage with wind stress and water temperature’.
J. Phys. Oceanogr. 19, 706–709.
Nordberg, W., Conway, J., Ross, D.B., Wilheit, T., 1971. Measurements of microwave emission from a foam-covered, wind-driven
sea. J. Atmospheric Sci. 28, 429–435.
Ross, D.B., Cardone, V., 1974. Observations of oceanic whitecaps and their relation to remote measurements of surface wind
speed. J. Geophys. Res. 79, 444–452.
Sugihara, Y., Tsumori, H., Ohga, T., Yoshioka, H., Serizawa, S., 2007. Variation of whitecap coverage with wave-field conditions.
J. Mar. Syst. 66, 47–60.
Toba, Y., Chaen, M., 1973. Quantitative expression of the breaking of wind waves on the sea surface. Rec. Oceanogr. Works Japan
12, 1–11.
Woolf, D.K., 1997. Bubbles and their role in gas exchange. In: The Sea Surface and Global Change. pp. 173–205.
Research Papers 2.3
3.3 Modelling whitecap fraction with a wave
model
Research Papers 2.3
JOURNAL OF PHYSICAL OCEANOGRAPHY
Modelling whitecap fraction with a wave model
B RIAN S CANLON
AirSea Lab, School of Physics and Ryan Institute, NUI Galway, Galway, Ireland.
Ø YVIND B REIVIK
Norwegian Meteorological Institute, Bergen, Norway
J EAN -R AYMOND B IDLOT AND P ETER A.E.M. JANSSEN
European Centre for Medium-Range Weather Forecasts, Reading, UK
A DRIAN H. C ALLAGHAN
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
B RIAN WARD∗
AirSea Lab, School of Physics and Ryan Institute, NUI Galway, Galway, Ireland.
ABSTRACT
High resolution measurements of actively breaking whitecap fraction (WFA ) and total whitecap fraction
(WFT ) from the Knorr11 field experiment in the Atlantic Ocean are compared with estimates of whitecap
fraction modeled from the dissipation source term of the ECMWF wave model. The results reveal a strong
linear relationship between model results and observed measurements. This indicates that the wave model
dissipation is an accurate estimate of total whitecap fraction. The study also reveals that the dissipation source
term is more closely related to WFA than WFT , which includes the additional contribution from maturing (stage
B) whitecaps.
1. Introduction
Asher and Wanninkhof 1998; Woolf et al. 2007). Whitecaps are also important as they affect the brightness temperature of the sea surface, as seen by passive radiometer instruments (Monahan and O’Muircheartaigh 1986;
Anguelova and Webster 2006; Salisbury et al. 2013), as
well as affecting the ocean color, as seen by satellite-borne
instruments in the visible and near infrared wavelength
range (Gordon 1997; Frouin et al. 2001). Whitecaps correlate strongly with the energy dissipated through wave
breaking (Cardone 1969; Monahan 1986; Kraan et al.
1996; Cavaleri et al. 2007; Thompson et al. 2009), increasing the turbulence in the upper ocean (Craig and Banner 1994; Terray et al. 1996; Kantha and Clayson 2004;
Gemmrich 2010; Gemmrich et al. 2013).
This study is concerned with the comparison of whitecap estimates from the dissipation source term of the
ECMWF wave model to in-situ whitecap estimates from
the Knorr11 campaign in the North Atlantic. Obtaining a
robust relationship during this comparison can provide the
basis for the development of global predictions of whitecap coverage. The paper is organized as follows: section 2
provides information on the measurements of total white-
Accurate estimates of the energy dissipated from the
oceanic wave field due to wave breaking is a vital requirement for improving wave models, upper-ocean turbulence
models, and knowledge of ocean–atmosphere interactions
for gas transfer.
Whitecaps appear when the wind exceeds approximately 3 m s−1 under open ocean conditions (Monahan
1971; Stramska and Petelski 2003; Scanlon and Ward
2015). The occurrence of whitecaps increases with the
duration, fetch (Nordberg et al. 1971), and intensity of
the wind (Komen et al. 1994). With persistent wind forcing, the waves will eventually reach an equilibrium state,
where the energy dissipated from wave breaking balances
the energy injected by the wind.
Whitecaps from breaking waves mark regions of enhanced air-sea transfer of gases through bubble-mediated
processes (Monahan and Spillane 1984; Woolf 1997;
∗ Corresponding author address: Brian Ward, AirSea Lab, School of
Physics and Ryan Institute, NUI Galway, Galway, Ireland.
E-mail: [email protected]
Generated using v4.3.2 of the AMS LATEX template
1
Research Papers 2.3
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JOURNAL OF PHYSICAL OCEANOGRAPHY
20
15
the AWE algorithm, after which the overlying pixel values (those deemed part of a whitecap) are set to 1, while
pixel values below the threshold are set to 0. This results
in binary images consisting of maximum pixel values representing whitecap regions and minimum pixel values representing background sea. Subsequent manual inspections
of whitecap regions are carried out using the Spatial Separation of Whitecap Pixels (SSWP) method (Scanlon and
Ward 2013), after which the regions are classified as either
actively breaking (stage A) or decaying (stage B) whitecaps, as defined in Monahan and Lu (1990).
!
"
U10N m s−1
HS (m)
T̄ (s)
s
10
5
0
180
185
190
195
Day of year
3. The dissipation source term in spectral wave models
F IG . 1. Time series of neutral wind speed (U10N ), modeled significant wave height (HS ), mean period of the modeled wind-wave spectra
(T̄ ) and modeled wave slope s (α = 10) are provided to illustrate the
conditions encountered during the North Atlantic campaign of 2011.
The grey columns mark the periods during which whitecap coverage
fraction was measured.
Third generation spectral wave models (Hasselmann
et al. 1988; Tolman 1991; Komen et al. 1994; Ris et al.
1999; Tolman et al. 2002; Janssen et al. 2004; Holthuijsen
2007; Cavaleri et al. 2007) solve the action balance equation (Komen et al. 1994; Janssen et al. 2004), which in
deep water with no current refraction reduces to the following energy balance equation:
cap fraction WFT and actively breaking whitecap fraction
WFA , and the conditions encountered during the cruise in
the North-West Atlantic Ocean with the R/V Knorr in
2011. Section 3 describes the empirical function of Kraan
et al. (1996) used to model the whitecap coverage from
the dissipation source term of the wave model developed
by the European Centre for Medium Range Weather Forecasts (ECMWF), referred to as ECWAM. We then compare these estimates against observed whitecap fractions
WFT and WFA . Section 4 provides conclusions and final
remarks.
2. Observational Whitecap Estimates
The observations of whitecap events are taken from
a camera (5 mega pixel Arecont Vision, 16 mm focal
length lens) mounted on the R/V Knorr during a field campaign covering the period 2011-06-20 to 2011-07-17 in the
North Atlantic (for full details on the Knorr11 research
cruise see Sutherland et al. 2013; Bell et al. 2013; Sutherland et al. 2014; Scanlon and Ward 2015). The camera
was mounted on the O4 deck at a height of 14.6 metres
above the ocean surface and at an angle of about 75 ◦ from
the nadir, resulting in effective image footprints of approximately 7,600 m2 of the sea surface.
A total of 114,265 images were selected for analysis,
providing 128 hourly periods that cover a wide range of
conditions (Fig 1) e.g. 0.9 < U10N < 18.8 m s−1 (neutral
wind speed); 1.3 < HS < 3.9 m (significant wave height).
The conversion of raw sea surface images to binary images, from which the fraction of whitecap cover can be
estimated, is carried out using the Automated Whitecap
Extraction (AWE) algorithm (Callaghan and White 2009).
During this process, a threshold value is obtained from
∂F
+ ∇ · (cg F) = Sin + Snl + Sds ,
∂t
(1)
written here in flux form. Here F(k) is the spectral energy density at wavenumber k, and cg is the corresponding vector group velocity. The source terms refer to wind
input (Sin ), nonlinear transfer S(nl ), and dissipation (Sds ),
respectively.
The turbulent kinetic energy (TKE) flux from breaking
waves into the ocean, Φoc , is related [see e.g. Janssen et al.
(2004); Rascle et al. (2006); Janssen (2012); Janssen et al.
(2013); Breivik et al. (2015)] to the dissipation source
function of a spectral model as:
Φoc = ρw g
Z 2π Z ∞
0
0
Sds dωdθ [W m−2 ]
(2)
As has been discussed by Craig and Banner (1994), the
energy flux (Eq 2) should approximately relate to the third
power of the friction velocity:
Φoc ∝ ρa u3? ,
(3)
p
where u? = τ/ρa . This flux is also related to the total
whitecap fraction WFT , as first discussed by Ross and Cardone (1974) and later among others (Kraan et al. 1996;
Goddjin-Murphy et al. 2011). We follow Kraan et al.
(1996) and assume that there is a linear relationship between the energy dissipation and the whitecap fraction,
Φoc = γρw gWF ωp E.
(4)
Here γ represents the average fraction of total wave energy dissipated per whitecap event, set to 0.01 in our case,
following Kraan et al. (1996). In Eq (4) the total wave
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JOURNAL OF PHYSICAL OCEANOGRAPHY
1.2 × 28(u? /c) cos(θ − φ ) > 1,
(5)
where c is the phase speed of the waves, θ is the direction
of the waves and φ is the wind direction ( see ECMWF
(Sec 6.7 2013)). The mean wind-sea period is used instead
of the peak period as it is a more stable parameter:
T̄ = m−1 /m0 .
(6)
The moments are defined as:
mn =
Z 2π Z ∞
0
0
f n F( f , θ )d f dθ .
(7)
For the computation of the wind sea mean period, the swell
components are left out by setting the appropriate wave
amplitudes of F( f , θ ) in Eq (7) to zero.
a. The ECWAM model integration
The most recent global uncoupled version of ECWAM
[see ECMWF (2013), model cycle 41R1] was run for
the period June-July 2011 on 11 km resolution with onehourly output of integrated wave parameters. Wind fields
with six-hourly temporal resolution were taken from the
operational analyses at 16 km resolution, interpolated to
the ECWAM 11-km grid. Fig 2 shows ECWAM neutral
mod plotted against measured neutral wind
wind speed U10N
speed U10N . Both time-series are time-averaged estimates
of the 128 hourly whitecap measurement periods, and display good agreement.
20
(m s!1 )
M=0.95, C=0.24, R 2 =0.90
mod
U10N
energy per unit mass is ρw gE, which is modulated by the
wave variance E = (Hs /4)2 . The term ωp = 2π/Tp is the
radian peak frequency.
Here, we make the implicit assumption that airentraining whitecaps represent the dominant mechanism
of wave energy dissipation, and neglect any contribution from non-entraining microscale breaking, and other
dissipative mechanisms. However, we acknowledge recent studies which suggest that energy dissipation by microscale breaking waves may be an important energy sink
in certain sea states (Sutherland and Melville 2013).
Although Kraan et al. (1996) suggests to use the peak
frequency in Eq (4), we have in the following chosen to
instead use the mean frequency of the wind sea part of
the wave spectra ω̄ = 2π/T̄ (Fig 1) as it is more important for the whitecap production. Swell-dominated seas
exhibit less whitecap coverage than pure wind seas (Sugihara et al. 2007; Callaghan et al. 2008b; Goddjin-Murphy
et al. 2011). The swell separation scheme of ECWAM defines wind sea as those wave components of the spectrum
that are subject to wind forcing. The remaining part of the
spectrum is assumed to be non-local swell. The separation
between wind sea and swell is thus a function of the relative direction as well as the speed difference between the
wind (or friction velocity) and the wave component:
15
10
5
0
0
5
10
U10N
(m s!1 )
15
20
F IG . 2. A total of 128 hourly averages of measured wind speed U10N
mod . Shaded region illusplotted compared with modeled estimates U10N
trates the 95% confidence interval.
The 1-hourly ECWAM wave energy dissipation flux
Φoc is used in Eq (4) to obtain modeled whitecap fraction
estimates:
Φoc
WFmod =
,
(8)
γρw gω̄E
where ω̄ = 2π/T̄ . For default settings [γ=0.01, following Kraan et al. (1996)], the model whitecap estimates are
computed for each of the 128 hourly periods and compared with measured WFT and WFA estimates. For comparison, a scale of 1/3-power coverage is used, aiding in data
linearity in terms of u? , identified as the most dominant
forcing term (Eq 3). This scaling minimises the effects of
model error propagation due to polynomial expansion of
uncertainties and errors associated with u? and also helps
to increase the influence of low wind-speed measurements
in the fitting process. Linear fitting techniques are employed to investigate and evaluate important properties:
WFmod = MWF +C,
(9)
where M is the slope, WF is a generic term for observed
whitecap fraction and C is the intercept. The linear relationships are evaluated using the squared correlation coefficient, R2 . Once linearity is established, agreement of
model estimates with observations is evaluated using both
M and C. Due to the high population of outliers, the robust
bisquare method of reweighing residuals (Huber 1996) is
employed during comparison, to extract best fit relationships.
In our model, the wind energy input is included in the
Φoc term (Eq 3). Fig 3 shows this relation by plotting 1/3power model estimates of Φoc /ρa against u? . Linear fitting
Research Papers 2.3
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JOURNAL OF PHYSICAL OCEANOGRAPHY
1.4
Φoc = 4.64ρa (u⋆ )3 , R2 = 0.99
Φoc = 0.013 W m−2 (HS08)
u⋆T = 0.065 m s−1 (SW15)
0.8
WF A > 0
WF A = 0
1
0.6
1
Φoc
ρa
21/3
(m s−1 )
1.2
0.4
WF T > 0
WF T = 0
0.2
0
0
0.1
0.2
0.3
0.4
0.5
u⋆ (m s−1 )
0.6
0.7
0.8
F IG . 3. Extraction of the model relation of wave energy dissipation Φoc and wind energy input ρa u3? , by means of plotting the 128 1hourly model estimates of (Φ/ρa )1/3 against u? . Observed Φoc threshold for whitecap production by Hwang and Sletten (2008) (HS08) and
u? threshold for actively breaking whitecap production by Scanlon and
Ward (2015) (SW15) are provided for illustration.
reveals an expected cubed power u? relation with model
estimates of Φoc . We consider the inclusion of a friction
velocity threshold u?T , which introduces an intercept term
in Fig 3 and Eq (3) such that:
Φoc ∝ ρa (u? − u?T )3 .
(10)
Such thresholding methods (Eq 10), as introduced
by Monahan and O’Muircheartaigh (1986), have been
employed by many studies attempting to quantify
whitecap coverage with wind speed (Monahan and
O’Muircheartaigh 1986; Asher and Wanninkhof 1998;
Reising et al. 2002; Callaghan et al. 2008a; Scanlon and
Ward 2015) and energy dissipation (Hwang and Sletten
2008). In such mentioned studies, whitecap coverage was
indeed observed to occur above specific thresholds of wind
energy input. Fig 3 illustrates two such examples of observed thresholds: (i) wave energy dissipation threshold
(HS08) obtained by Hwang and Sletten (2008) which considers whitecap observations from a multitude of previous studies, and (ii) the adopted friction velocity threshold
(SW15) at which actively breaking whitecaps are observed
to occur (Scanlon and Ward 2015).
We also consider the influence of wave slope s through
the empirical relation
γ = γ0 tanh s,
(11)
where s = αkHs , and γ0 is a constant (see Fig 1 for a timeseries of s). Here α is a constant, k is the mean wavenumber and Hs is the significant wave height. Assuming the
deep water relation k = ω 2 /g, the WFmod values are recalculated using Eq (11) and Eq (8) and compared with WFT
and WFA observations.
It is important to make the distinction that our estimates
of wave slope are acquired from averaged open ocean
wave spectra parameters which are subjected to non-local
contributions of swell, and may not accurately reflect the
locally measured wave slopes upon which breaking occurs, and thus may not be a sufficient proxy for wave crest
acceleration prediction and wave stability. Such locally
measured wave slopes have been related to the energy dissipated by wave breaking events (Melville and Rapp 1985)
and to breaking probabilities (Banner et al. 2010). In our
case, the wave slope can be interpreted as a proxy for the
presence of swell, such that higher wave slopes are associated with wave-fields comprised of locally generated
wind-waves and minimal contributions due to the presence of swell, and lower wave slopes relating to the strong
presence of swell. In such cases, wave slope has been observed to adjust the wind-wave energy transfer (Taylor and
Yelland 2001). While we already introduce a method of
removing swell from the analysis by using the mean period of the wind-wave spectra T̄ in Eq (8), it is interesting
to analyse if additional wave slope dependencies are observed for the fraction of energy dissipated due to whitecap coverage γ.
b. Comparison results
Fig 4a shows the 1/3-power plot of WFmod against measured whitecap fraction WF , for default settings (γ=0.01),
showing good linearity with one another (R2 =0.78 and
R2 =0.74, for WFT and WFA respectively) despite poor
quantitative agreement (M 6= 1). A bias towards model
estimates at low coverage (and wind) values can also be
observed.
The slope M of the best fits in Fig 4a can be tuned by
adjusting the value of γ, achieving better agreements between model and measured quantities. However such adjustments to γ also affect the magnitude of the intercept C.
This value C can be viewed as quantification of the positive (or negative) bias of the modeled WFmod estimates, and
thus values of C should be minimised.
In Fig 4b, supplemental tuning of WFmod , using WFT
measurements as comparison, was achieved by setting γ =
0.0074. This resulted in an improved agreement (M = 1),
at a cost of introducing a higher intercept (C=0.045). For
the case when using WFA as comparison, setting γ = 0.034
achieved the same improved agreement (M = 1), but with
a reduced intercept of C=0.021 (Tab 1).
Further success at minimising the model bias (C) at low
coverage (and wind) conditions was achieved by introducing a friction velocity u? threshold into the whitecap
Research Papers 2.3
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JOURNAL OF PHYSICAL OCEANOGRAPHY
TABLE 1. Fit results for various model modifications when compared
with observations.
0.4
(a)
!
WFmod
"1=3
WFT
0.01 (default)
WFA
0.01 (default)
WFT
0.0074
WFA
0.0342
u? thresholding:
WFT
0.0078
WFA
0.0360
0.2
W FA (.=0.01)
0.1
W FT (.=0.01)
M (σ )
C (σ )
R2
0.90 (0.04)
1.53 (0.08)
1 (0.05)
1 (0.05)
0.040 (0.007)
0.032 (0.008)
0.045 (0.007)
0.021 (0.005)
0.78
0.74
0.78
0.74
1 (0.04)
1 (0.05)
0.0074 (0.006)
-7.5×10−5 (0.004)
0.82
0.77
γ
Observ.
0.3
W FA (M=1.5, C=0.033, R2 =0.74)
W FT (M=0.9, C=0.041, R2 =0.78)
0
100
WFT (γ=0.0078)
0.4
W
10-1
(b)
FA
(γ=0.0360)
10-2
0.3
WFmod
0.2
10-4
10-5
10-6
!
WFmod
"1=3
10-3
W FA (.=0.036)
0.1
-7
10
W FT (.=0.0078)
2
W FA (M=1, C=0.021, R =0.74)
10-8 -8
10
W FT (M=1, C=0.045, R2 =0.78)
0
0
0.1
0.2
WF
0.3
WFmod
=


Φoc
γρw gω̄E
0
u? −u?T
u?
3
u? ≤ u?T ,
10-5
10-4
10-3
10-2
10-1
100
0.4
1=3
u? > u?T
10-6
WF
F IG . 4. A total of 128 hourly averages of measured whitecap fraction WFT , and of measured actively breaking whitecap fraction WFA ,
plotted against modeled estimates of whitecap fraction WFmod derived
from Eq (8). The model coefficient γ is set to 0.01 in (a), and then tuned
to 0.034 for WFA and 0.007 for WFT to obtain best agreements in (b). A
1/3-power scale is employed for both fitting and illustration purposes.
Shaded regions represent 95% confidence intervals.
model:
10-7
(12)
where u?T =0.065 m s−1 is the friction velocity threshold,
an equivalent (assuming a neutral drag coefficient) adaptation to the observed U10N threshold for the onsetting of actively breaking whitecaps (Scanlon and Ward 2015). The
consequence of Eq (12) is that a minimum value of wind
energy is required for whitecaps to occur. Table 1 displays the performance of the different configurations of
F IG . 5. A log-log plot of WFmod versus observed WF , including the
u? -related model modification (Eq 12). γ is set to 0.036 & 0.0078
(Tab 1) to achieve best agreement with WFA and WFT respectively. The
diagonal line shows the objective best linear agreement (M=1, C=0 in
Eq 9).
the whitecap semi empirical model, when compared with
observations. The inclusion of the threshold term (Eq 12)
provides improved agreement (M = 1, C ≈ 0) and linearity
(R2 ) with observations, significantly reducing the model
bias C. The modeled whitecap fractions WFmod show best
agreement with observed WFA (M=1, C=-7.5×10−5 ).
Concurrently, the influence of wave slope is implemented in Eq (12) by using Eq (11) and setting γ0 =
0.0360 & 0.0078 for WFA and WFT respectively. The implementation provides no improvement (not shown), even
for cases involving various multiples of s by adjusting α
from small to large numbers. This suggests that the semiempirical model sufficiently considers the effects of wave
slope (Melville and Rapp 1985; Melville 1994; Taylor and
Yelland 2001; Banner et al. 2010).
Fig 5 presents the model estimates WFmod achieved using the semi empirical equation (8) with the applied fric-
Research Papers 2.3
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JOURNAL OF PHYSICAL OCEANOGRAPHY
tion velocity threshold modification (12) plotted against
WF observations in logarithmic space. Fig 5 comparison
showcases the best agreement obtained in this study between model and observed data.
When we use WFA instead of WFT as a basis for tuning
γ, strongly reduced model bias (C) and larger γ values (4.5
times greater) are obtained. As γ is defined as the average
fraction of total wave energy dissipated from whitecaps,
it implies that WFA (i.e. the actively breaking whitecap
fraction) is more related to dissipation by wave breaking.
The reduced γ values obtained when using WFT indicate
that the contribution of decaying foam coverage (stage B)
in WFT measurements are an inferior source for wave-field
dissipation.
One plausible explanation for this may be due to the
effect of water chemistry on whitecap foam stabilisation,
which is not directly linked to wave energy dissipation.
Callaghan et al. (2013) explicitly showed that the addition
of soluble surfactant at a concentration of 207 micro grams
per litre to seawater in laboratory experiments of breaking
waves, extended the lifetime of whitecap foam by about
a factor of 3. Furthermore, field studies have shown that
whitecap decay times are highly variable, indicating the
potential importance of natural surfactants may play in
oceanic whitecap foam decay (Callaghan et al. 2012).
4. Conclusions
Whitecap fraction values estimated from the dissipation
source term using an empirical relation (Kraan et al. 1996)
provide robust linear agreement with hourly averages of
open ocean whitecap observations.
Tuning the γ parameter allows for further agreement
with observations (M=1), most notably when combined
with a u?T threshold modification (Eq 12). Reduced
model biases (C) and considerably higher values of γ
are achieved for comparisons involving WFA observations.
This indicates that the actively breaking whitecap fraction
is more strongly related to the dissipation source term in
ECWAM, than for the case with total whitecapping WFT ,
which includes the stage-B contribution.
However due to the remaining scatter in the modeldata comparison, we suggest that further study needs to
be carried to further refine and characterise the relationship between whitecap foam signatures and wave breaking
energy dissipation. In particular, the provisions of bulk
estimation of wave energy dissipation due to microscale
breaking and additional sampling of wider ranges of environmental conditions and sea states would prove beneficial.
We conclude that our modeled whitecap estimates are
suitable proxies for total whitecap fraction and actively
breaking whitecap fraction, and thus for applications that
incorporate them such as quantifying air-sea exchange of
bubble mediated gasses. This implies that global estimates
of WFT and WFA could be derived from a wave model,
and this could be used for further improving calibration
of satellite estimates of whitecap coverage. The availability of global whitecap estimates could also benefit a wide
range of studies that involve, or are influenced by, whitecaps.
Acknowledgments. We would like to thank the two
anonymous reviewers for helpful and constructive suggestions for how to improve the manuscript. B. Scanlon was
funded for this research by a College of Science (NUIG)
PhD Fellowship. B. Ward received funding from the Office of Naval Research under award N62909-14-1-N296
and the Norwegian Research Council under the PETROMAKS2 233901 project. Ø. Breivik was supported by
the European Union project MyWave (grant FP7-SPACE2011-284455). A.H. Callaghan acknowledges current financial support from NSF Grant OCE-1434866, and earlier financial support from the Irish Research Council, cofunded by Marie Curie Actions under FP7, during the
North Atlantic field campaign. We also thank the captain and crew of the R/V Knorr, and Chief Scientist on
the Knorr11 experiment - Dr. Scott Miller. The model
integrations and forcing fields presented in this study are
archived in ECMWF’s MARS and ECFS databases. For
more information on how to access MARS and ECFS, see
http://old.ecmwf.int/services/archive/.
Research Papers 2.3
JOURNAL OF PHYSICAL OCEANOGRAPHY
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4 Conclusions and Future Work
4.1 Synopsis
This study focuses on wave breaking at the ocean surface, a process which
adds heightened complexity when attempting to predict interactions between
the upper ocean and lower atmosphere.
In section 3.1, we provided a comparison study between model predictions
and in-situ observations of SST. The model predictions were computed
using 5 different configurations of turbulence and solar absorption schemes.
The turbulence schemes employed consisted of law of the wall scaling of
turbulent kinetic energy (TKE), and additional TKE injection due to wave
breaking. Most notably, the incorporation of the wave breaking process
provided diurnal warm layer depths inconsistent with observations and thus
underestimated predictions of SST.
In section 3.2, we provided a method of measuring whitecap coverage in its
active stage (actively spilling crests) and in its maturing stage (decaying
foam) from digital images of the sea surface, called the Spatial Separation
of Whitecap Pixels (SSWP) method. Despite the SSWP method requiring
manual operation, accurate results can be achieved from the digital imagery.
56
Conclusions and Future Work
An additional method of separation, called the Pixel Intensity Threshold
Separation (PITS) was introduced. The PITS method relies on pixel intensity
information to distinguish whitecap regions as active or maturing. The
performance of the PITS method was evaluated by comparing PITS-derived
coverage with SSWP-derived coverage for 64,540 images. The comparison
revealed that the PITS method cannot accurately distinguish the two stages
of whitecaps. Thus we conclude that the PITS method is unsuitable.
In section 3.3, we acquired observations of actively breaking and total whitecap coverage from 114,265 images using the SSWP method and utilized them
to investigate a semi empirical whitecap model of Kraan et al. (1996). The
semi empirical model was forced by a timeseries of wave energy dissipation,
significant wave height and mean period of the wind-waves from a high resolution rerun of ECWAM wave model. The comparison of observations with
model predictions demonstrated linear agreement and allowed for tuning of
the implicit γ coefficient, which from definition quantifies the average fraction
of wave energy lost per breaking event. Highest values of γ were obtained
when the model was tuned with actively breaking whitecap observations,
demonstrating the importance of active breakers as a major source of wave
energy dissipation. Lower γ values (4.5 times lower) were obtained when
the model was tuned with total whitecap coverage observations. As total
whitecap coverage consists of actively breaking and maturing stages, we
deduce that the lower γ values are a result of the inclusion of maturing
whitecap coverage.
Conclusions and Future Work
4.2 Conclusions
Considerable temperature biases were observed for various model configurations in section 3.1. In particular, the inclusion of TKE injection due to
wave breaking following Kantha and Clayson (2004) overestimated upper
ocean mixing and thus resulting in deeper MLD and cooler SST predictions.
This demonstrates the need for more reliable and condition-representative
parameterizations of upper ocean mixing which consider TKE injection due
to wave breaking.
A new method of separation of whitecap coverage into its active and maturing stages of evolution was presented. In section 3.2, we provide a Spatial
Separation of Whitecap Pixels (SSWP) method and evaluate its performance
against alternative methods. Although the method relies on manual operation, it provides a framework to achieve accurate estimates of WA and
WB .
An extensive dataset of WA and WB was acquired over the course of this study,
totaling 125,860 images or 622 10-minute averages. The data was processed
using the SSWP method and high level of quality control. Unfortunately
an investigation into the variability of WA and WB with primary (wind
speed) and additional (SST, atmospheric stability, wave-field development)
environmental parameters is not presented in this study. Comments on the
ratio of WA /WB are also not presented.
A whitecap model based on wave model parameters has been established in
section 3.3. The whitecap model allows for predictions of stage A and total
whitecap coverage to be calculated from globally-operational state-of-the-art
Conclusions and Future Work
wave models such as ECWAM. As ECWAM provides global 6-hourly wavefield parameters at a grid resolution of 0.5 degrees, representative whitecap
predictions can thus be calculated and provide benefit global studies involving
air–sea gas transfer, aerosol production and calibration of satellite-sensed
whitecap algorithms.
4.3 Future Work
To acquire and process additional sea surface imagery in future studies using
the SSWP method would prove beneficial for two reasons.
1. To analyse the influence of secondary parameters on whitecap coverage
requires a large dataset of observations which represent wide ranges
of environmental conditions. A large dataset of obserations will be
required. This will prove to be a difficult task to accomplish, requiring
extensive numbers of observations and significant processing time.
2. To further investigate the γ coefficient and its dependencies to environmental parameters. It is not currently known if γ is a constant nor
if it is globally representative.
Thus it is my intention to acquire additional observations to build the
dataset of WA and WB to sufficiently represent cold, moderate and warm SST
conditions and among other ranges of additional environmental parameters.
I hope to explore the use of alternative imaging methods such as stereoscopic
and Infrared-capable setups. Stereoscopic imaging can estimate the rate of
change of wave-field elevation. This will allow for wave peaks and troughs to
Conclusions and Future Work
be distinguished in a sea surface image and thus create an opportunity for
the development of an automated version of the SSWP method. Similarly
Infrared imaging can allow for a method of separating stage A and stage
B solely based on temperature thresholding (see Jessup et al., 1997; Zappa
et al., 2001; Marmorino and Smith, 2005; Sutherland and Melville, 2013).
Such imaging systems would require a stable platform and thus establishing
a suitable location to conduct monitoring would be of vital importance.
In addition to bulk estimates of the various whitecap coverage stages WA
and WB , breaking crest length framework (Phillips, 1985) could be adopted
which would provide crest length spectral information of wave breaking
events. Such framework has been adopted to relate breaking events to upper
ocean TKE (Thompson et al., 2009; Sutherland and Melville, 2013).