ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-1545-2016Observations of surface momentum exchange over the marginal ice zone and
recommendations for its parametrisationElvidgeA. D.andy.elvidge@metoffice.gov.ukRenfrewI. A.WeissA. I.BrooksI. M.Lachlan-CopeT. A.KingJ. C.https://orcid.org/0000-0003-3315-7568School of Environmental Sciences, University of East Anglia, Norwich,
UKBritish Antarctic Survey, Cambridge, UKSchool of Earth and Environment, University of Leeds, Leeds, UKpresent address: Atmospheric Processes and Parametrisations, Met Office, Fitzroy Road,
Exeter, UKA. D. Elvidge (andy.elvidge@metoffice.gov.uk)10February20161631545156317August20151October20155January201615January2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/1545/2016/acp-16-1545-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/1545/2016/acp-16-1545-2016.pdf
Comprehensive aircraft observations are used to
characterise surface roughness over the Arctic marginal ice zone (MIZ) and
consequently make recommendations for the parametrisation of surface
momentum exchange in the MIZ. These observations were gathered in the
Barents Sea and Fram Strait from two aircraft as part of the Aerosol–Cloud
Coupling And Climate Interactions in the Arctic (ACCACIA) project. They
represent a doubling of the total number of such aircraft observations
currently available over the Arctic MIZ. The eddy covariance method is used
to derive estimates of the 10 m neutral drag coefficient (CDN10) from
turbulent wind velocity measurements, and a novel method using albedo and
surface temperature is employed to derive ice fraction. Peak surface
roughness is found at ice fractions in the range 0.6 to 0.8 (with a mean
interquartile range in CDN10 of 1.25 to 2.85 × 10-3).
CDN10 as a function of ice fraction is found to be well approximated by
the negatively skewed distribution provided by a leading parametrisation
scheme (Lüpkes et al., 2012) tailored for sea-ice drag over the MIZ in
which the two constituent components of drag – skin and form drag – are
separately quantified. Current parametrisation schemes used in the weather
and climate models are compared with our results and the majority are found
to be physically unjustified and unrepresentative. The Lüpkes et al. (2012) scheme is recommended in a computationally simple form, with adjusted
parameter settings. A good agreement holds for subsets of the data from
different locations, despite differences in sea-ice conditions. Ice
conditions in the Barents Sea, characterised by small, unconsolidated ice
floes, are found to be associated with higher CDN10 values –
especially at the higher ice fractions – than those of Fram Strait, where
typically larger, smoother floes are observed. Consequently, the important
influence of sea-ice morphology and floe size on surface roughness is
recognised, and improvement in the representation of this in
parametrisation schemes is suggested for future study.
Introduction
Sea-ice movement is determined by five separate forces: a drag force from
the atmosphere, a drag force from the ocean, internal sea-ice stresses, a
downhill ocean-surface slope force, and the Coriolis force (e.g. Notz, 2012).
The two drag forces are associated with a surface exchange of momentum
across the atmosphere–ice or the ice–ocean boundary respectively. These
exchanges impact the dynamical evolution of both atmosphere and ocean; here
we focus on the interaction with the atmosphere only. Within the atmospheric
surface layer (where the turbulent stress remains close to its surface
value) the wind speed, Uz, is related to the
surface stress through
U=u∗κlnzz0-φ,
where u∗ is the friction velocity, κ is the von
Karman constant (0.4), z0 is the roughness length for velocity, and
φ is a stratification correction function (see, for example, Stull, 1988 for further details about this similarity theory approach). The
aerodynamic roughness length, z0, describes the level at which the wind
speed described by Eq. (1) becomes 0 and represents the physical
roughness of the surface (Stull, 1988). The momentum exchange (or wind
stress) is then
τ=ρu∗2=ρCDU2,
where ρ is the density and CD is the drag coefficient for the
fluid at height z. Combining Eqs. (1) and (2) we can directly relate
the drag coefficient and roughness length; for example, for neutrally
stratified conditions and z=10 m,
CDN10=u∗U10N2=κ2ln1010z0z02.
Over a rough surface the drag has two components: a surface skin drag caused
by friction and a form drag caused by pressure forces from the moving fluid
impacting on roughness elements (Arya, 1973, 1975). The form drag acts on
sea-ice ridges, on floe edges, on melt pond edges, and on surface undulations
of all types. In other words, it is a function of the morphology of the sea
ice and consequently it is strongly related to ice concentration and
thickness.
To parametrise surface drag in numerical weather prediction, or climate or
Earth system models, the above formulae are implemented to determine the
surface stress for a given fluid velocity and stability
Note a
turning angle between the fluid and the ice surface is also required if the
surface-layer Ekman spiral is not resolved (Notz, 2012; Tsamados et al.,
2014).
. To do this CD, or equivalently z0, must be prescribed and
so observations of these parameters for different sea-ice surfaces are
required. To calculate these for the atmosphere–ice boundary, for example,
observations of surface-layer momentum flux, wind speed, and atmospheric
stability are required. These are challenging observations to make over sea
ice and even more challenging over the marginal ice zone (MIZ).
Over the main sea-ice pack, with ice fraction, A, close to 1, early
studies based on tower or aircraft observations of turbulent fluxes
estimated CDN10 in the range ∼ 1–4 × 10-3
for continuous sea ice, depending on the ice morphology. In a comprehensive
review, Overland (1985) breaks down this range by morphology and location:
for large flat floes CDN10 ranges 1.2–1.9 × 10-3 and
a median of 1.5 × 10-3 is given (e.g. based on Banke and Smith,
1971 over the Canadian Arctic); for rough ice with pressure ridges
CDN10 ranges 1.7–3.7 × 10-3; over first year ice in
marginal seas (e.g. the Beaufort Sea or Gulf of St Lawrence) the CDN10
subjective median values are 2.2–3.0 × 10-3. More
recently, Castellani et al. (2014) use airborne-derived laser altimeter data
gathered between 1995 and 2011 in conjunction with a sea-ice drag
parametrisation scheme to demonstrate the considerable topographic and
geographic variability in CDN10 over Arctic pack ice, with values
ranging between 1.5 and 3 × 10-3, largely corroborating the
results of earlier studies.
For the MIZ, data are not so readily available. On the “inner MIZ”, with
ice fractions of 0.8–0.9 and consisting of small and rafted floes, Overland
(1985) report only a few data sets, with CDN10 in the range
2.6–3.7 × 10-3; while for the “outer MIZ”, with A= 0.3–0.4,
the only two values provided are CDN10= 2.2 and
2.8 × 10-3 from MIZEX-1984 over the Greenland Sea (Overland,
1985) and from the Antarctic MIZ using an indirect balance method (Andreas
et al., 1984). Further drag measurements over the MIZ using aircraft were
made by Hartman et al. (1994) and Mai et al. (1996) as part of the “REFLEX”
and “REFLEX II” experiments over Fram Strait. Hartman et al. (1994) obtained
16 CDN10 values with ranges of CDN10=1.0–2.3 ×
10-3 for A=0.5–0.8 and CDN10=1.1–1.6 × 10-3
for A=0.9–1.0. They found generally higher CDN10 values over ice
fractions of 0.5–0.8. Mai et al. (1996) found a similar range over their 85 12-km runs,
with CDN in the range ∼ 1.3 × 10-3 over open water, to a maximum of ∼ 2.6 × 10-3 at A= 0.5–0.6, then decreasing to about 1.8 × 10-3
for A= 1. Schröder et al. (2003) largely corroborate
these results with their 32 runs, finding a mean CDN10 of 2.6 × 10-3 for A= 0.5 over Fram Strait and a mean CDN10 of
1.6 × 10-3 for A= 0.86 over the Baltic Sea. These
aircraft-based MIZ drag results are compiled together in Lüpkes and
Birnbaum (2005). In short, they suggest that CDN10 peaks over the MIZ
(A≈0.5–0.6) and decreases for lower or higher ice fractions.
Reviewing the above, however, it is clear that further surface drag
measurements over the MIZ are critical for validating and
developing parametrisations of surface exchange over sea ice. At present
there are only about 150 individual data points for the MIZ from aircraft
observations in the literature and the majority of these are from the same
research group and platform. The majority were also made more than 20
years ago and, as has been well documented, Arctic sea ice is changing in
extent and characteristics (e.g. Kwok and Rothrock, 2009; Markus et al.,
2009). It is clear that new additional observations are urgently required.
Improvements to the representation of sea ice are planned for many global
weather forecasting models in order to aid both seasonal forecasting and
shorter-term forecasting for the polar regions (e.g. ECMWF, 2013). These
models typically have grid sizes of 10–25 km, meaning they will have the
resolution to represent gradients in ice fraction across the MIZ and
therefore need to parametrise MIZ interactions with the atmosphere. In
addition, higher-resolution regional coupled atmosphere–ocean–ice models are
providing improved skill and starting to be used operationally (Pellerin et al., 2004; Smith et al., 2013); while climate and Earth system models are also
increasing in resolution and these will all require accurate surface
exchange over the MIZ. Recent ocean–ice and atmosphere–ocean–ice modelling
studies have demonstrated considerable sensitivity to surface exchange
parametrisation over sea ice, particularly in their simulations of sea-ice
thickness and extent (Tsamados et al., 2014; Rae et al., 2014) and the polar
ocean (Stössel et al., 2008; Roy et al., 2015). Simulations of the
near-surface atmosphere can also be significantly affected (Rae et al.,
2014).
Here we present over 200 new estimates of surface drag over the MIZ in Fram
Strait and the Barents Sea from two independent research aircraft. This
represents a more than doubling of the CDN estimates currently
available for surface exchange parameterisation development. Only low-level
legs (mainly 30–40 m a.s.l.) are used to provide quality-controlled
eddy covariance estimates of the turbulent momentum flux. We use these data
to provide a validation of the leading parametrisation schemes and make
recommendations for parameter settings. In the next section we present a
brief review of surface exchange parametrisations. Section 3 covers data
and methods and Sect. 4 presents our results. In Sect. 5 recommendations
for the parametrisation of drag in the MIZ are made, before our conclusions
in Sect. 6. Note that a summary of notation is provided at the end of
the paper.
Parametrising surface momentum exchange over sea iceBackground
All atmospheric models require an exchange of momentum with the surface for
accurate simulations. Over sea ice this has generally been treated rather
crudely, usually with a constant drag coefficient prescribed for all sea-ice
types and thicknesses (e.g. Notz, 2012; Lüpkes et al., 2013). For model
grid boxes that are partially ice-covered a “mosaic method” is commonly
employed, which typically calculates the flux over the ice and water
surfaces separately, then averages these in proportion to the surface areas
(e.g. Claussen, 1990; Vihma, 1995). Unfortunately, using this approach with a
constant drag coefficient does not represent momentum exchange over the MIZ
correctly. It results in a linear function of CDN with A rather than
the maximum in drag at intermediate ice concentrations supported by
observations.
Both empirical and physical-based parametrisations of surface drag have
recently been developed. Andreas et al. (2010) composited together all
available MIZ CDN observations (primarily from Hartmann et al., 1994 and
Mai et al., 1996) with the vast number of summertime sea-ice pack CDN
observations from the SHEBA project (Uttal et al., 2002) for A>0.7. They argued that summertime sea ice, replete with melt ponds and leads,
was morphologically similar to the MIZ and so these data sets could be
combined. Plotting CDN against A, and ignoring various outliers, they
found a maximum in CDN around A=0.6. They empirically fitted by
eye a second-order polynomial to this data set:
103CDN=1.5+2.233A-2.333A2.
Here, CDN is simply a function of ice fraction (A), and other
morphological characteristics are neglected.
A series of physical-based parametrisation schemes for surface drag has
also been developed based on trying to capture the effect of form drag by
equating sea-ice characteristics to roughness elements. The form drag is
added to the skin drag to give a total surface drag, as represented in these
schemes by
CDN=1-ACDNw+ACDNi+CDNf,
where CDNw and CDNi are the neutral skin drag coefficients over
open water and continuous ice respectively, and CDNf is the neutral
form drag coefficient. This approach has its basis in work by Arya (1973,
1975) that has been developed and refined – see Hanssen-Bauer and Gjessing
(1988), Garbrecht et al. (1999, 2002), Birnbaum and Lüpkes (2002),
Lüpkes and Birnbaum (2005), Lüpkes et al. (2012), and Lüpkes and
Gryanik (2015).
Amongst the leading MIZ drag schemes currently being implemented is that set
out in Lüpkes et al. (2012; referred to hereafter as L2012). This scheme
has been adapted for use in the Los Alamos sea-ice model CICE (Tsamados et
al., 2014; Hunke et al., 2015). It determines neutral 10-m drag coefficients
(CDN10) over 3-dimensional ice floes as a function of sea-ice
morphological parameters: sea-ice fraction as a minimum and, optionally,
freeboard height and floe size. Lüpkes et al. (2013) illustrate the
substantial impact such a parametrisation has on CDN for summertime
Arctic sea ice in contrast to the constant exchange coefficient approach
that is currently standard in climate models.
Derivation of form drag
As a result of its sensitivity to sea-ice morphology, representing the form
drag component of CDN in a parametrisation scheme is a complex
procedure. Its derivation in the L2012 scheme is best approached by
considering a domain, of area St, containing N identical ice floes of
cross-wind length Di and freeboard height hf. If the area fraction
of ice within the domain is given by A,
St=csNDi2A,
where cs relates the deviation of the mean floe area from that of a
square (so that cs=1 for a square and, for example,
cs=πr24r2=π4 for a circle). The total
form drag acting on the frontal areas of ice floes within the domain is
provided by
fd=NcwSc2Di∫z0whfρ[Uz]22dz.
Here, cw is the fraction of the available force which effectively acts
on each floe (Garbrecht et al., 1999); Sc is the sheltering function,
which tends towards 0 for small distances between floes (implying a large
sheltering effect) and tends towards 1 for large distances; z0w is the
mean local roughness length over open water; and U(z) is the upstream wind
speed. Recall from Eq. (1) that U(z) increases logarithmically with
height, so the 10 m neutral wind speed is
UN10=u∗/κln10/z0w.
Noting that the surface wind stress due to form drag is simply the frontal
force per unit area τd=fd/St, CDNf can be evaluated at
the 10 m height according to Eqs. (3) and (8) as follows:
CDN10f=τdρUN102=fd/Stρu∗/κ2ln210/z0w.
Equations (6) and (7) are inserted into Eq. (9), and the integral in Eq. (7) is
solved with the aid of Eq. (8) to yield
CDN10f=AhfDiSc2ce2lnhf/z0w-12+1-2z0w/hfln210/z0w,
where the effective resistance coefficient ce=cw/cs. Finally,
following the removal of insignificant terms in the above (resulting in a
deviation typically less than 1 % according to L2012), we obtain
CDN10f=AhfDiSc2ce2ln2hf/z0wln210/z0w.
The L2012 parametrisation: equation summary
The overall drag coefficient is the sum of the skin and form drag
components, so substituting Eq. (1) into Eq. (5):
CDN10=1-ACDN10w+ACDN10i+AhfDiSc2ce2ln2hf/z0wln210/z0w.
Note that our Eqs. (11) and (12) are identical to L2012 Eqs. (51) and
(22). L2012 defines CDN10w and CDN10i as skin drag terms. However,
this assumes there is no form drag over open water or continuous sea ice,
since the form drag contribution given by Eq. (11) only accounts for form
drag on ice floe edges. In reality, additional form drag can be produced in
the ocean due to waves, and over ice due to ridging and other roughness
features caused by deformation and melt. Consequently, CDN10w and
CDN10i are better expressed as the total (skin and form) drag over open
water and continuous sea ice, respectively. The former is provided by
CDN10w=κ2ln-2(10/z0w),
using Eq. (3). Note that z0w is usually provided in models as a
function of the surface stress on the sea surface and the gravitational
restoring force via a modified Charnock relation
z0w=αu∗2g+bυu∗,
where α is the Charnock constant, b is the smooth-flow constant,
and υ is the dynamic viscosity of air (e.g. Fairall et al., 2003).
L2012 set α=0.018 and b=0. It is more common to include
the smooth-flow term, usually with b=0.11, so that there is some
momentum exchange at low wind speeds (e.g. Renfrew et al., 2002; Fairall et al., 2003). The first term leads to an increase in roughness, and hence drag
coefficient, as the wind speed increases. This increase is related to
wave-induced roughness and is now reasonably well constrained for low to
moderate wind speeds, but there is some uncertainty at higher wind speeds
(Fairall et al., 2003; Petersen and Renfrew 2009; Cook and Renfrew 2015).
Various values for the Charnock “constant” are used, typically between 0.011
and 0.018. In the Fairall et al. (2003) review they suggest that α should
linearly increase from 0.011 to 0.018 (between UN10=10–18 m s-1), although they note some uncertainty in α for UN10
above 10 m s-1.
For the drag over continuous ice, L2012 recommend CDN10i=1.6 × 10-3. This is consistent with the range of values for the
total drag over large flat floes, CDN=1.2–1.9 × 10-3,
given in Overland (1985) making the assumption that the form drag over flat
floes is negligible. This choice for CDN10i is also typical of the
values commonly set in numerical models (Lüpkes et al., 2013).
L2012 provides three formulations for the sheltering function, Sc. The
form chosen for the CICE model (Tsamados et al., 2014) is
Sc=1-exp-sDwhf,
where s is a dimensionless constant and the distance between floes,
Dw=Di1-A/A (after Lüpkes and
Birnbaum, 2005). Equations (12)–(15) together with the recommended parameters
set out in Table 1 establish the parametrisation of CDN10 as a
function of A, hf, Di, and u∗. In many models, however,
freeboard heights and floe lengths are not available. In this instance,
L2012 provides further simplifications to present both hf and Di
in terms of A:
hf=hmaxA+hmin(1-A),Di=DminA∗A∗-Aβ,
where
A∗=11-(Dmin/Dmax)1/β
and β is a tuning constant. Recommended values for the constant
parameters hmin, hmax, Dmin, Dmax, and β are
provided in Table 1, taken from an analysis of laser altimeter observations
of these summarised in L2012.
Parameter settings for the form drag component of the L2012
scheme (Lüpkes et al., 2012): as recommended in L2012, as used in CICE
(Tsamados et al., 2014), and as recommended here (E2016A and E2016B).
The data used for this study are from research flights over the Arctic MIZ
using two aircraft: a DHC6 Twin Otter operated by the British Antarctic
Survey and equipped with the Meteorological Airborne Science INstrumentation
(MASIN) and the UK Facility for Airborne Atmospheric Measurement (FAAM)
BAe-146. Data from eight flights are used here, conducted between 21 and 31 March 2013 as part of the first ACCACIA (Aerosol–Cloud Coupling and Climate
Interactions in the Arctic) field campaign. The relevant flight legs are
located both to the northwest of Svalbard over Fram Strait and southeast of
Svalbard in the Barents Sea (Fig. 1). Wintertime sea ice in the Barents Sea
is relatively thin and, owing to a cool southward-flowing surface ocean
current and cyclone activity in the region, tends to extend further south
than in Fram Strait where the warm North Atlantic Current has a greater
influence (Johannessen and Foster, 1978; Sorteberg and Kvingedal, 2006).
Map of Svalbard (landmass in grey) and the surrounding
ocean and sea ice. The blue–white shading conveys the mean sea-ice fraction
from the satellite-derived Operational Sea Surface and Sea Ice Analysis
(OSTIA) for the March 2013 field campaign, while contours at 0.5 ice
fraction illustrated the maximum (dashed black) and minimum (solid black)
extents. The relevant flight legs are plotted in colour and listed in
chronological order in the legend. Coloured squares show the locations of
the images shown in Figs. 5 and 6.
To estimate surface momentum flux from the aircraft requires high-frequency
measurements of wind velocity and altitude, along with an estimate of
atmospheric stability. To measure 3-D winds the MASIN Twin Otter uses a
nine-port Best Aircraft Turbulence (BAT) probe (Garman et al., 2006) mounted
on the end of a boom above the cockpit and extending forward of the
aircraft's nose; while the BAE146 uses a five-port radome probe on the nose of
the aircraft. To measure altitude at low levels both aircraft use radar
altimeters. To measure air temperatures both aircraft use Rosemount sensors
(non-deiced and deiced), while to measure sea surface temperature (SST) both
aircraft use Heimann infrared thermometers. For the calculation of albedo
(used to derive estimates of sea-ice concentration), both aircraft use
Eppley PSP pyranometers to measure shortwave radiation. Further details
about the instrumentation – calibration, sampling rate, resolution, and
accuracy – can be found in King et al. (2008) and Fiedler et al. (2010) for
the MASIN Twin Otter, and in Renfrew et al. (2008) and Petersen and Renfrew (2009) for turbulence measurements on the BAE146. For brevity these details
are not reproduced here.
In general, the aircraft measurements are processed identically. One
exception is in the calibration of SST. Here the MASIN Twin Otter uses black-body calibrations in conjunction with corrections for emissivity based on
SST measurements of the same surface at different altitudes, whereas for the
BAE146 the Heimann infrared SST is adjusted by a constant offset for each
flight determined by the ARIES (Airborne Research Interferometer Evaluation
System) instrument, which can estimate the emissivity accurately by rotating
the field of view in flight, thus obtaining very accurate SST estimates (see
Newman et al., 2005; or Cook and Renfrew, 2015 for a discussion).
Derivation of surface drag coefficients from the aircraft
observations
Summary of flights during the March 2013 ACCACIA field
campaign. Flight numbers preceded by the letter “B” use the FAAM BAE146; the
other flights use the MASIN Twin Otter.
To estimate flight-level momentum flux – from which CDN10 may be
derived – we use the well-established eddy covariance method. This is
commonly used in aircraft-based flux research (e.g. French et al., 2007) and
has previously been used with both MASIN data (e.g. Fiedler et al., 2010;
Weiss et al., 2011) and FAAM data (e.g. Petersen and Renfrew, 2009; Cook and
Renfrew, 2015). It requires that flight legs are straight and level and
conducted as close to the surface as is logistically feasible (the vast
majority of our data were measured at heights under 40 m – see Table 2).
These flight legs are then divided into flux runs of equal duration, with velocity
perturbations calculated from linearly detrended run averages. The
flight-level momentum flux (τ) for each run is calculated from the
covariance between the perturbation of the horizontal wind components from
their means (u′, v′) and that of the vertical wind component (w′) as
follows:
τ=ρ‾u′w′‾2+v′w′‾2,
where ρ‾ is the mean run air density. It is assumed that the
measurements are made in the surface layer, and that this is a constant-flux
layer so τ is not adjusted for height (see Petersen and Renfrew, 2009
for a discussion). For the great majority of flights, a mean altitude of
∼ 34 m suggests that this is a good assumption. Even so, despite
this assumption being widely adopted and generally accepted as necessary,
its accuracy is a point of contention (see Garbrecht et al., 2002) and is
an issue for future work. The surface roughness length, z0, is derived
using Eqs. (1) and (2). The stability correction φ in Eq. (1)
is an empirically derived function of z and the Obukhov length, L, a parameter
related to stratification. We use the corrections of Dyer (1974) for stable
conditions and Beljaars and Holtslag (1991) for unstable conditions. The
neutral drag coefficient at 10 m (CDN10) is then evaluated for each run
via Eq. (3).
Each flux run is subject to a quality control procedure, details of which can be
found in Appendix A. Through this quality control procedure, it was
determined that a flux-run length of ∼ 9 km was optimum. For this run
length, 14 from the total 209 runs available are rejected following quality
control, which leaves a total of 195 usable flux runs.
In order to test our observations against the L2012 parametrisation
described in Sect. 2, an estimate of the ice fraction A is required. For
this, two methods have been developed using the simultaneous aircraft
observations: the first uses albedo (from shortwave radiation); the second
uses SST (from the downward infrared thermometer with some adjustments
based on the albedo). The sensitivity to choices made in our estimation of
A in both approaches is tested via the adoption of two different criteria
– one based on flight video evidence, the other based on theory. For
detailed description of our methodology for estimating A please see
Appendix B.
ResultsComplete data set
CDN10 as a function of ice fraction A: (a)Aa
(from albedo); (b)ASST (from sea surface temperature with a no ice transition at -3.4 ∘C;
(c)Aa2 (from albedo with alternative tie points); and
(d)ASST2 (from SST with a no ice transition at -1.8 ∘C). Observational data
are arranged in ice fraction bins of interval 0.2. Box and whisker plots
show the median (black square), interquartile range (boxes), and 9th and
91st percentiles (whiskers) within each bin. The number of data points
within each bin is indicated at the bin-median level. The L2012 scheme is
illustrated by curves anchored at our observed values for A=0 and A=1,
using parameter settings E2016A (black curve) and E2016B (grey curve)
in Table 1.
Our observations enable investigation into the relationship between sea-ice
drag and ice fraction. Figure 2 shows CDN10 plotted as a function of
A for all flux-runs and for all methods used to derive A (see Appendix B). These
are ice fraction derived via albedo (Aa) and via surface temperature
(ASST) using no ice transition tie points set according to inspection of our in-flight
videos and also to values expected theoretically (ASST2) or as
previously observed (Aa2). The observational data are partitioned into
ice fraction bins using intervals in A of 0.2 (corresponding to a total of
six bins). This interval was chosen as it permits a relatively large number of
data points in each bin (between 11 and 65; see Fig. 2), whilst providing a
sufficient number of bins to assess the sensitivity of CDN10 to A.
The distribution of values within each bin is represented by the median, the
interquartile range, and the 9th and 91st percentiles.
In all four panels in Fig. 2, the lowest median drag coefficients are found
at the upper and lower limits of ice fraction (in the A=0, 0.2, and 1 bins),
whilst the highest median drag coefficients are in the 0.6 and 0.8
bins. This describes a unimodal, negatively skewed distribution (i.e. with a
longer tail towards lower A). This distribution qualitatively conforms to
the L2012 parametrisation using typical parameter settings (this is
revisited in Sect. 4.3). Across all ice fractions our results lie within
the range of those obtained in previous studies (see review in Sect. 1 and
Andreas et al., 2010).
The small interquartile range in CDN10 evident in Fig. 2 in the A=0 bin reflects the small variability in wind velocity during the field
campaign, with run-averaged wind speeds averaging 7 m s-1 (close to the
climatological mean for the Arctic summer), peaking at 13 m s-1 (see
Table 2) and being from a generally consistent direction (northerly, i.e.
off-ice). Note that over the open ocean (away from ice), surface roughness
is a strong function of wave height and therefore wind speed. Our
bin-averaged CDN10 values over open sea water compare well with those
expected by inputting observed wind speeds into the well-established COARE
bulk flux algorithm of Fairall et al. (2003). Values derived from COARE
Version 3.0 consistently lie within the interquartile range.
For data points over continuous ice (A=1) our observed median values
of CDN10 are towards the lower end of the range for large flat floes
given in Overland (1985) of 1.2–3.7. However, relative to that for
CDN10w, there is a high degree of variability in CDN10i within
bins. This reflects significant heterogeneity in ice conditions and hence
roughness, as previously discussed (e.g. Overland, 1985), and as was
visually apparent from the aircraft throughout our field campaign. For this
reason, over uninterrupted ice CDN10 is region specific, unlike over
open water. In our observations these values are indeed found to vary
systematically and considerably with location and this is investigated
further below. Even greater scatter in CDN10 is apparent within the
intermediate ice fraction bins (0.2, 0.4, 0.6 and 0.8) as form drag here is
affected not only by variability in ice roughness, but also by variability
in the frontal area of floes (governed by floe size and freeboard height).
Furthermore, the upper limit of ice roughness is likely to be greater here
due to deformation as a result of waves and floe advection (Kohout et al.,
2014).
It is apparent from Fig. 2 that our results are qualitatively similar for
all derivations of A. In particular, apart for some minor shifts in
CDN10 due to the rearrangement of data points between adjacent bins,
the impact of varying the no ice transition tie point is small – compare panel (a) with panel
(c) and panel (b) with panel (d). This implies that our results are relatively
robust.
Variability within the data set
To further explore the observed sensitivity of CDN10 with A as well
as the scatter in CDN10 within ice fraction bins, we now focus on
subsets of the data. Given the dependence of surface roughness not only on
ice fraction but also on sea-ice properties, a logical divide would be based
on location. As is apparent in Fig. 1, the flights were conducted either to the
northwest of Svalbard in Fram Strait or to the southeast of Svalbard in the
Barents Sea. Conveniently, this split apportions approximately equal numbers
of data points to each location. Results from Fram Strait are shown in Fig. 3,
whilst those from the Barents Sea are shown in Fig. 4. Given the lack of
sensitivity of results to varying the no ice transition tie point, only Aa and ASST
are shown here.
Significant differences in the distribution of CDN10 as a function of
A for these two locations are apparent, especially towards the higher ice
fractions. The Barents Sea is characterised by far greater values of
CDN10 for A≥0.6, with median CDN10≈ 2.5 × 10-3 at A=1, compared to less than 1.2 × 10-3
in Fram Strait (note that at lower ice fraction there is more
consistency in CDN10 between the locations). These differences imply
rougher sea-ice conditions in the Barents Sea, a result that might be
expected given the typically thinner ice, a less sharp ocean–ice transition
here (i.e. a geographically larger MIZ, see Fig. 1), and greater variability
in the position of the ice edge in the Barents Sea during the field campaign
– suggestive of ice melt, deformation, and changeable ice conditions. Such
heterogeneity is reflected by the considerably greater scatter in
CDN10, whilst the wider MIZ is implied by a considerably larger
proportion of data points residing within the intermediate ice fraction bins
(0.2, 0.4, 0.6, and 0.8) for the Barents Sea data (around 69 %) compared to
Fram Strait data (35–51 %).
As in Fig. 2, but for Barents Sea flights only (see Table 2 for details of flights).
As in Fig. 2, but for Fram Strait flights only (see Table 2 for details of flights).
(a) Photograph taken from the FAAM aircraft during
Flight B760 flux-run marked with an arrow in Fig. 7; and (b) still from video recorded
from the MASIN aircraft during Flight 185. The image locations are marked in
Fig. 1.
The systematic differences in ice conditions between these locations are
also apparent in flight videos and photographs. Figure 5 shows images from
two Barents Sea flights: a photograph from the port-side of the FAAM
aircraft during Flight B760 and a still taken from the forward-looking video
camera 10 days later during MASIN Flight 185 (see Fig. 1 for image
locations). Each of these images is representative of sea-ice conditions
associated with the highest individual values of CDN10 observed during
each flight (4.7 and 5.7 × 10-3 respectively) and correspond to
ice fractions of ∼ 0.8 and ∼ 0.6, respectively.
The ice morphology depicted in the two photos is comparable, constituting
relatively small, broken floes (of order tens of metres in scale) with raised
edges implying collisions between the floes. Whilst evidently widespread in
the Barents Sea MIZ, such conditions are not apparent in video footage and
photographs made during two of the three Fram Strait flights (182 and 183).
During these flights, ice morphology in the MIZ appears quite different:
consisting of larger floes often separated by large leads and a more
distinct ice edge (as depicted for Flight 182 in Fig. 6). The jagged, small
floes illustrated in Fig. 5 are associated with high CDN10 values. Such
conditions in the wintertime MIZ resemble dynamically rough summertime
melt-season ice (Andreas et al., 2010), and smaller floes are associated
with greater drag due to an increased frontal area. Note that this roughness
extends to the highest ice concentrations (in the A=1 bin; Fig. 3),
despite the fact that floe sizes will tend to increase as A approaches 1.
This is perhaps unsurprising: the photographs of Fig. 5 show that where
floes have been fused together – giving a local ice fraction of 1 – the
ice noticeably retains its rough, deformed characteristics. Video footage
from the third Fram Strait flight (Flight 184) reveals ice conditions more
like those observed in the Barents Sea, and indeed this flight was
associated with greater drag coefficients than the other two – comparable
to those of the Barents Sea flights. Note that whilst the relevant Flight
182 and 183 legs overlap, Flight 184 was conducted further east (Fig. 1).
Photograph taken from the MASIN aircraft between legs 3
and 4 during Flight 182 at an altitude of ∼ 100 m. The
location is marked in Fig. 1.
To delve more deeply into the relationship between CDN10 and ice
fraction, we now examine two particular flights – one from each research
aircraft. We focus on the flights with the greatest number of flux-runs from each
aircraft: FAAM Flight B760 and MASIN Flight 181 (Table 2). Figures 7 and 8
show distributions of Aa, ASST, and CDN10 for all flux-runs in map form
for both flights. Note there is generally good agreement between Aa and
ASST where data are available for both (a pyranometer malfunction during
B760 limits the availability of Aa). In Flight 181, the aircraft
traversed the relatively broken ice immediately southeast of Svalbard, and
over the ice edge and open water further south. The B760 leg traversed
north–south over the ice edge at a similar location. From these figures it
is apparent that in general the highest values of CDN10 relate to MIZ
conditions. This is especially clear for Flight B760, due to the simple
gradient in ice fraction; towards the south, CDN10 is small over open
water; moving northward over the MIZ CDN10 increases and exhibits more
variability, reflecting typically heterogeneous ice conditions in the MIZ,
and for the northernmost runs CDN10 decreases again as more
consolidated pack ice is encountered (Fig. 7). As discussed above, sea-ice
conditions during the B760 flux-run for which peak CDN10 is observed (arrow in
Fig. 7) are captured in the photograph shown in Fig. 5a.
Spatial maps of ice fraction (a)Aa, (b)ASST, and
(c) drag coefficient CDN10 for all flux-runs during FAAM Flight B760. The
background greyscale shading is OSTIA sea-ice concentration (lighter shades
indicating higher ice concentrations).
Figure 9 shows CDN10 as a function of A for Flight 181. The
distribution is similar to that described previously, with CDN10
peaking in the A=0.6 and 0.8 bins. Comparing Fig. 9 with Fig. 3 shows
that drag coefficients are towards the lower end of the range for the
Barents Sea. Note that a similar plot is not shown for Flight B760 due to
the sparsity of data. Of all our flights only 181 provides sufficient data
across the range of ice fractions to make presentation in this form
worthwhile.
Validation and modifications to the L2012 parametrisation
The curves shown in Figs. 2, 3, 4, and 9 represent the L2012
parametrisation. They result from setting the observed median z0w,
CDN10w, and CDN10i in Eq. (12) – to fix the end points of the
curves – then adopting new parameter settings for the form component of
drag, CDN10f. These were chosen to provide a good fit to our
observational results whilst also largely satisfying previously gathered
empirical evidence. In fact, the parameter settings recommended by L2012
provide a near-satisfactory fit to our observations, and only minor
optimization is recommended.
Of the parameters dictating the form component of the drag coefficient
(CDN10f; see Eq. 11), hmin, hmax, Dmin, Dmax, and
β are all appointed in L2012 according to previous observations.
Values assigned to the effective resistance coefficient ce and
sheltering parameter s are considerably less well verified, making them
preferential for tuning. Increasing s from the value
recommended in L2012 such as to bring about a better fit to our data has
minimal effect on CDN10 for all but the highest ice fractions, whereas,
as evident from Eq. (12), CDN10 is equally sensitive across the full
range of A to changes in ce. Reducing ce from 0.3 to 0.17 and
keeping all other parameters as recommended in L2012 (E2016A in Table 1)
provides a generally good fit to our observations and this is illustrated by
the black curved lines in Figs. 2, 3, 4, and 9. This curve passes close to
median values and comfortably through the interquartile range of all ice
fraction bins in Fig. 2, demonstrating the skill of the L2012
parametrisation in capturing the sensitivity of CDN10 to A when
averaged over a large data set.
Spatial maps of ice fraction (a)Aa, (b)ASST, and
(c) drag coefficient CDN10 for all flux-runs during MASIN Flight 181, as Fig. 7.
As in Fig. 2, but for Flight 181 only (see Table 2 for
flight details).
The fit using the E2016A settings is not perfect. In particular, there is a
suggestion that for the full data set (Fig. 2) CDN10 is underestimated
at high ice fraction (the A=0.8 and 0.6 bins) and overestimated at A= 0.2. As indicated by our results and those of previous studies,
CDN10 at high ice fractions is governed by sea-ice morphology and as
such its variability is large and location dependent. Consequently,
discrepancies here are unsurprising. A possible explanation for the
overestimate at lower ice fractions is that the parametrisation does not
take into account the attenuating effect of sea ice on waves (e.g. Wadhams
et al., 1988). To compute the form drag coefficient (Eq. 11) we use observed
z0w, averaged over all flux-runs where A=0. In the MIZ, this assumes these
values to be representative of the water between ice floes. However, given
the sensitivity of z0 to wave amplitude (discussed in Sect. 4.1) and
the attenuation of waves in the MIZ, these values may in fact be
overestimates, leading to an overestimation of CDN10.
With these discrepancies in mind, we define a second set of parameters, for
which β (a morphological exponent describing the dependence of
Di – the floe dimension – on A) is adjusted as well as ce. In L2012 a β value of
1 is derived empirically by fitting their parametrisation for Di (Eq. 17)
to laser scanner observations from Fram Strait obtained by Hartmann et
al. (1992) and Kottmeier et al. (1994). However, L2012 also found that by
changing only β, their parametrisation was able to explain the
variability in CDN10 derived from various observational sources. For
example, β=1.4 better represented observations made during REFLEX
in the eastern Fram Strait (Hartmann et al., 1994), whilst β=0.3
better represented observations made in the Antarctic (Andreas et al., 1984)
and the western Fram Strait (Guest and Davidson, 1987). Reducing β
has the effect of reducing Di and consequently amplifying CDN10
for all ice fractions, though particularly towards the higher fractions
(though note that Di will always eventually converge on Dmax at A=1, according to Eq. 17). Consequently, setting a low value for β
helps explain particularly high drag coefficients at A≈0.8,
justifying our second parameter set, for which we reduce β to 0.2
(the lowest value recommended in L2012) in addition to further reducing
ce to 0.13, to account for the reduction in CDN10 across all
values of A which comes from reducing β. Figure 2 shows that these
parameter settings (E2016B in Table 1) provide in general a marginally
better fit to the complete data set than the E2016A settings.
The parametrisation is shown to also provide a generally good fit to
subsets of the data. For example, the black and grey curves in Figs. 3 and
4 (the Barents Sea and Fram Strait subsets) denote as before the scheme
using the E2016A and E2016B parameter settings respectively, and fit well
despite the different ice morphologies and related contrasting values of
CDN10 at A=1. For the Barents Sea observations, the curve again
passes through the interquartile range of all bins – though a little higher
than the median values – both for Aa and ASST. For the Fram
Strait observations there is good agreement in the case of Aa, whilst
for ASST the form drag is generally overestimated. Finally, the
parametrisation also provides an accurate representation of the Flight 181
observations (Fig. 9). It is important to note that the success of the
scheme for different localities characterised by different ice conditions
depends crucially on an accurate representation of CDN10 at A=1.
As mentioned in Sect. 2.3, in Eq. (12), CDN10 at A= 1 is provided
by CDN10i, defined in L2012 as the skin drag over sea ice. However, given that over rough, ridged
sea ice, there is a form drag component in addition to skin drag, this term
is more suitably expanded and expressed as the total (skin and form) drag over continuous sea ice, and considered to be a variable
quantity, dependent on ice conditions.
As discussed in Sect. 4.2, our observations suggest that ice conditions in
the MIZ characterised by relatively small, unconsolidated “pancake” ice
floes at intermediate ice concentrations are characterised by higher drag
coefficients than larger floes. The roughness extends locally to the highest
ice concentrations, suggesting a case could be made for the use of Di
at intermediate ice fractions as a proxy for local MIZ surface roughness.
Although this is partially implicit in the L2012 scheme in the sense that it
accounts for smaller floes exerting greater form drag for a given ice
concentration due to a greater frontal area (see Eq. 11), it seems
likely given our observations that smaller floes are often associated with
larger CDN10 due to other, unaccounted-for reasons – for example,
greater deformation and ridge-forming as a result of more frequent floe
collisions due to smaller gaps between the floes or to floe advection caused
by reduced ocean wave attenuation in areas of smaller floes. Note that this
additional roughness corresponds to that discussed in the above paragraph as
requiring inclusion in the CDN10i term in Eq. (12). Accounting for
variability in the surface roughness of continuous sea ice has previously
received some attention in the literature (Garbrecht et al., 2002; Andreas,
2011), though there is as yet no clear solution to this problem, and further
progress in this area is beyond the scope of this study; see Conclusions for
recommendations for future work.
Implications and parametrisation recommendations
It is clear that the physically based parametrisation of L2012
qualitatively fits our observations of surface drag (i.e. momentum exchange)
over the MIZ very well. The recommended settings provided by L2012 (see
Table 1) also quantitatively fit our observations well, although with some
tuning of ce (the effective resistance coefficient) and, optionally,
β (a sea-ice morphology exponent) this fit can be improved when
compared to median CDN10 values – see Figs. 2–4 and 9. We recommend
two settings for the L2012 parametrisation: E2016A with ce=0.17
and β=1 and E2016B with ce=0.1 and β=0.2 (see
Table 1). The E2016B setting enhances the negative skew of the CDN10
distribution, increasing (decreasing) values at high (low) ice
concentrations. These settings are illustrated as the black and grey lines
in Figs. 2–4 and 9.
(a) Effective sea-ice drag coefficient and (b) derived
effective roughness length as a function of ice concentration.
Parametrisations shown are: Lüpkes et al. (2012) with settings as
recommended here, namely L2012 E2016A with ce=0.17 and β=1 (black), and L2012 E2016B with ce=0.1 and β= 0.2 (grey); the default L2012 settings used in CICE5.1 (blue) as
described in Tsamados et al. (2014); the LIM3 interpolation (blue
dash-dotted); the HadGEM3 default used in the Met Office Unified Model
(green); the CCSM (and CAM5) interpolation (magenta); the ECMWF cycle 41
function (red) and the previous ECMWF cycle 40 interpolation (red dashed).
See Table 1 for other L2012 settings.
Our recommended L2012 settings are also plotted in Fig. 10 to allow a
comparison against several other parametrisations used in numerical
sea ice, climate or weather prediction models. Figure 10a shows the
effective 10 m neutral drag coefficient for a grid square with the ice
concentration indicated, i.e. it is an effectiveCDN10 calculated proportionally
for that mix of water and sea ice. To allow a direct comparison, the drag
coefficient over open water, CDN10w, is set to 1.1×10-3 for all
the algorithms. This value is appropriate for low-level winds of about 5 m s-1. It is simply chosen for illustrative purposes; similar
illustrations result for other values of CDN10w. Figure 10b shows the
effective roughness length – derived from the effective CDN10 using
Eq. (3) – as a function of sea-ice concentration. In addition to our
recommended L2012 parametrisation settings, we also show those set as
default in the sea-ice model CICE version 5.1 (see Tsamados et al., 2014;
Hunke et al., 2015). In these, ce=0.2, β=1, and the ice
flow sheltering constant s=0.18 (see Table 1). Note that there is a
typographical error in Table 2 of Tsamados et al. (2014), where the
parameters csf and csp are listed as equal to 0.2 (implying
ce=1) when these should have been listed as equal to 1 (M. Tsamados,
personal communication, 2015). When the corrected values are used, the
CICE5.1 parametrisation matches our observations reasonably well (Fig. 10); although it does not account for the negative skew in the observations.
The ECMWF introduced a new parametrisation of surface drag over sea ice in
cycle 41 of the Integrated Forecast System, which became operational on 12 May 2015.
This introduces a variable sea-ice roughness length
z0i=max[1, 0.931-A+6.05e-17A-0.52]×10-3 (see ECMWF documentation and Bidlot et al.,
2014). This parametrised an increase in drag coefficient over the MIZ which
was inspired by the observations described in Andreas et al. (2010), so is
consistent with L2012, and is close to our recommended settings for L2012
(Fig. 10).
All of the other parametrisations that are illustrated linearly interpolate
between the drag coefficient over open water and constant values for
CDN10i (or z0i). Consequently, they appear as straight lines in
Fig. 10a. In the case of the ECMWF (cycle 40 and earlier) a constant
z0i=1× 10-3 m (equivalent to CDN10i=1.89 × 10-3) is
set. This is also the default setting in the ECHAM climate model (see
Lüpkes et al., 2013) and in the WRF numerical weather prediction model
(Hines et al., 2015) – not shown in Fig. 10. In the CCSM (Community Climate
System Model) and CAM5 (Community Atmospheric Model) CDN10i is set to
1.6 × 10-3 (see Neale et al., 2010) and in LIM3 (the Louvain-la-Neuve Sea
Ice Model) CDN10i is set to 1.5 × 10-3 by default (see Vancoppenolle
et al., 2012). Previous versions of the CICE sea-ice model also used a
constant z0i set as 0.5 × 10-3 m. The Met Office use separate constant
values for “the MIZ” (set at A=0.7) and “full sea ice” and then linearly
interpolate. For their HadGEM3 climate model both z0i and z0MIZ are
set to 0.5 × 10-3 m for version 4.0 of their Global Sea Ice (GSI)
configuration, as illustrated in Fig. 10; while for UKESM1, using GSI6.0,
much higher values of z0i=3×10-3 m and z0MIZ=100× 10-3 m are planned (see Rae et al., 2015). These are equivalent to
CDN10 values of 2.4 and 7.5 × 10-3, respectively, so are not supported
by our observations (see Fig. 2).
Examining Fig. 10, only the new (cycle 41) ECMWF parametrisation is
qualitatively and quantitatively comparable to our recommended settings of
the L2012 parametrisation. At present most numerical weather and climate
prediction models do not have a maximum in drag coefficient over the MIZ.
Consequently, they are not consistent with our observations, nor those of
relevant previous compilations (e.g. Andreas et al., 2010; L2012).
It is clear that in configuring sea-ice models, CDN10 over sea ice has
commonly been used as a “tuning parameter”. In fact it was specifically
treated as such in the model sensitivity studies of, for example, Miller et
al. (2006) and Rae et al. (2014). Miller et al. (2006) used the CICE model
in standalone mode and varied three parameters widely, including CDN10
between 0.3–1.6 × 10-3, in an optimisation exercise. They found
significant variability in extent and thickness across their simulations and
concluded that determining an optimal set of parameters depended heavily on
the forcing and validation data used. Rae et al. (2014) carried out a
comprehensive fully coupled atmosphere–ocean–ice modelling sensitivity
study, testing a large number of sea-ice-related parameter settings within
their observational bounds. They found statistically significant sensitivity
to the two sets of roughness length settings they tested: “CTRL” (z0i=0.5 × 10-3 and z0MIZ=0.5 × 10-3 m)
and “ROUGH” (z0i=3× 10-3 and z0MIZ=100× 10-3 m). The rougher settings (also
consistent with those in the Met Office global operational model) generally
lead to simulations with a better sea-ice extent and volume compared to
observations. However, we would note again that they are not consistent with
our observations. Instead, our results would suggest these seemingly required
large roughness lengths must be compensating for other deficiencies in the
model configuration.
As discussed in Sect. 2, the exchange of momentum between the atmosphere
and sea ice depends heavily on sea-ice morphology, thickness, and
concentration. Prior to this study, observations of sea-ice drag were
relatively limited, especially for the MIZ (i.e. for ice fractions 0<A<1). Consequently, CDN10 has not previously been
well constrained by observations. Our data set doubles the number of
observations available over the MIZ and is based on independent research
platforms and analysis procedures to previously published data sets.
Importantly, our results are broadly consistent with these previous
observational compilations (e.g. Andreas et al., 2010; and L2012). This
corroboration provides further confidence in our recommendations. In short,
CDN10 is now better constrained and we recommend that its parametrisation
is consistent with our results.
Conclusions
We have investigated surface momentum exchange over the Arctic marginal ice
zone using what is currently the largest set of aircraft observed data of
its kind. Our results show that the momentum exchange is sensitive to sea
ice concentration and morphology. Neutral 10 m surface drag coefficients
(CDN10) are derived using the eddy covariance method and Monin–Obukhov
theory, and two methods (which provide qualitatively similar results) are
adopted for the derivation of ice fraction from our aircraft observations.
After averaging CDN10 data into ice fraction bins, the roughest surface
conditions (characterised by the highest surface drag coefficients) are
typically found in the ice fraction bins of 0.6 and 0.8, while the
smoothest surface conditions tend to be over open water and sometimes
(dependent on sea-ice conditions) over continuous sea ice. Consequently, a
good approximation for our observed CDN10 as a function of ice
concentration is provided by a negatively skewed distribution, in general
agreement with previous observational studies (Hartman et al., 1994; Mai et
al., 1996; Lüpkes and Birnbaum, 2005). However, we have found systematic
differences in roughness between different locations. Over deformed, 10 m scale pancake ice in the Barents Sea, drag coefficients are considerably
greater than over relatively homogeneous, non-deformed sea ice in Fram
Strait. This dependence on ice morphology governs the magnitude and
variability with ice fraction of CDN10, and is likely to be the major
cause of the considerable scatter in CDN10 within each ice fraction
bin.
Our observations have been used as a means to validate and tune one of the
leading sea-ice drag parametrisation schemes – that of Lüpkes et al. (2012) i.e. L2012. This scheme provides CDN10 as the sum of the drag
over open water and continuous sea ice, and the form drag on ice floe edges,
as given in Eq. (12) and repeated here:
CDN10=1-ACDN10w+ACDN10i+AhfDiSc2ce2ln2hf/z0wln210/z0w.
The final term on the right-hand side of this equation expresses the form
drag component, and is derived following the theory of pressure drag exerted
on a bluff body. This expression can be simplified following L2012 to be
given as a function of only ice fraction A and tuneable constants via
Eqs. (15) to (18). In this simple form, the scheme provides a generally
accurate representation of the observed distribution of CDN10 as a
function of sea-ice fraction. The agreement is optimized by adopting minor
parameter adjustments to those originally recommended in L2012. These new
settings are labelled as E2016A and E2016B in Table 1. E2016B arguably
provides a better fit, though with values of ce and β which are
at the limit of those physically plausible according to observations,
whereas for E2016A these values are well within the confines of those
observed. The scheme is shown to be robust, its success holding for subsets
of our data (e.g. for each of the Barents Sea and Fram Strait locations, and
for the single flight with the greatest number of data points) so long as it
is anchored at A=1 by an observed value for CDN10i.
Given the success of a sophisticated scheme such as that of L2012, the
representation of sea-ice drag in many weather and climate models seems
crude by comparison, with CDN10 often set with little consideration of
physical constraints and instead used as a tuning parameter. Our
comprehensive observations provide the best means yet to constrain
parametrisations of CDN10 over the MIZ. They clearly imply that
linearly interpolating between the open water surface drag (CDN10w) and
a fixed sea-ice surface drag (CDN10i), as many parametrisations do, is
not physically justified or representative. It is recommended that, as a
minimum, parametrisations incorporate a peak in CDN10 within the range
A=0.6 to 0.8 (as a guide, in the 0.6 and 0.8 ice fraction bins of our
observations, CDN10 has a mean interquartile range of 1.25 to 2.85 × 10-3
for all data – i.e. averaged across both bins for all
panels in Fig. 2). Note that the precise peak value will vary with sea-ice
morphology and, as found in Lüpkes and Gryanik (2015), stratification.
Though sophisticated, the simplest form of the L2012 scheme is not
computationally complex (having only one independent variable, A) and is
recommended for adoption in weather and climate models.
The sensitivity of CDN10 to ice fraction is now well established.
Consequently, we recommend that future work focuses on the remaining major
source of uncertainty: sensitivity to ice morphology. Our results suggest
that the simplification of the L2012 scheme by parametrising floe dimension
(Di) and freeboard (hf) in its expression for form drag on floe
edges using A provides sufficiently accurate results. Even so, as
discussed above, floe size and ice morphology has a major impact on surface
roughness and a more sophisticated representation of this should benefit
sea-ice and climate simulations. In particular, this study demonstrates that
setting an appropriate value of CDN10 at A=1 is vital to the
success of the L2012 parametrisation; given the observed variation with
location (and hence ice conditions), a constant value for CDN10 at A= 1 is clearly unsuitable for simulations over large areas such as the
entire Arctic. Here, we simply vary CDN10i in the L2012 scheme to
reflect the observed location-dependent ice roughness at A=1. In
sea-ice or climate models, perhaps CDN10 at A=1 should be determined from sea-ice model output – for example, Tsamados
et al. (2014) account for form drag on ice ridges. In operational models,
perhaps CDN10 at A=1 should be derived
from sea-ice thickness observations (e.g. from CryoSat-2).
Our observations indicate that floe size is a governing factor in local
variations of sea-ice roughness, even at the highest ice fractions.
Consequently, to account for MIZ roughness associated with local ice
conditions an option could be to accentuate the dependency of CDN10 on
floe size by expanding CDN10i to incorporate both the skin drag term
and an additional “local” sea-ice form drag term which would be inversely
proportional to a representative value of Di (e.g. average Di at a
given ice fraction). To pursue such an approach and in general to provide
clarity on this issue, future work would benefit greatly from incorporating
aircraft laser scanner data, from which detailed morphological information
on sea-ice conditions including floe shape, size, thickness, and roughness
features such as ridging can be derived.
Quality control of momentum flux data
In order to remove unsuitable data, a quality control procedure is utilised.
This procedure follows previous studies (e.g. French et al., 2007; Petersen
and Renfrew, 2009; Cook and Renfrew, 2015) and involves the visual
inspection of a series of statistical diagnostics describing the variability
of the perturbation wind components along each flux-run. “Bad” data points arise as
a result of instrument malfunction or the violation of assumptions made in
the methodology – notably that the turbulence is homogeneous along each run.
The criteria that determine a “good” run are as follows:
The power spectra of the along-wind velocity component should have a
well-defined decay slope (close to k-5/3 for wavenumber k).
The total covariance of the along-wind velocity and vertical velocity should
be far greater in magnitude than that of the cross-wind velocity and
vertical velocity (which should be small), indicating alignment of the shear
and stress vectors.
The cumulative summation of the covariance of the along-wind velocity and
the vertical velocity should be close to a constant slope, indicating
homogeneous covariance.
The cospectra of the covariance of the along-wind velocity and the vertical
velocity should have little power at wavenumbers smaller than about
10-4 m-1, implying that mesoscale circulation features are not
contributing significantly to the stress.
The cumulative summation of the cospectra should be shaped as ogives
(“S”-shaped, with flat ends) implying that all of the wavenumbers that
contribute to the total stress have been sampled and again that mesoscale
features are not present.
Quality control diagnostics for momentum flux (u′w′). Left
column shows a “good” run (Flight 181, leg 2, run 7); right column shows a
“bad” run (Flight 181, leg 5, run 11). The rows show (top) the cumulative
summation of u′w′ versus distance along the run, (middle) the frequency weighted
cospectra, and (bottom) the ogives (integrated cospectra) both as a function
of wavenumber. The cumulative summation is normalised by the total
covariance and the ogives by the total cospectra.
Examples of “good” and discarded runs are illustrated in Fig. A1 (where the
flux-run length is ∼ 9 km). In the “good” example, there is little
cross-wind spectral power and the cumulative summation has a near-constant
slope indicating homogeneous turbulence structure along the length of the
run. The “S”-shaped ogives and lack of power at small wavenumbers in the
cospectra suggest that the turbulence is fully captured and that the signal
is “unpolluted” by mesoscale circulations. For this typical case, the
majority of energy is in eddies ranging from about 30 to 500 m in size, with
no energy at all for wavelengths over 2500 m. This information helps inform
a suitable run duration, since it is important that the runs are long enough
to capture several eddies of sizes at least across the dominant range of the
spectrum. On the other hand, lengthening runs reduces the number of data
points and increases the risk of sampling organised mesoscale features
instead of pure turbulence.
Note that five different flux-run durations were trialled using a sample of the data set.
These durations varied between the two aircraft (according to their mean
flight speed) in order that they correspond to lengths of approximately 3,
6, 9, 12, and 15 km. Using the above quality control procedure it was
ascertained that a run length of 9 km procures the highest quality data and
so is used here. This is comparable to Weiss et al. (2010) and Fiedler et
al. (2010) who used 8 and 8.8 km; and a little shorter than Petersen and
Renfrew (2009) and Cook and Renfrew (2015) who used 12 km.
Deriving ice fraction A from the
aircraft observations
Two different remote sensing techniques are used to derive estimates of ice fractionA
from the aircraft observations, using proxies based on albedo and surface
temperature. These techniques rely on sea ice being more reflective and
colder than sea water. In both approaches the proxy is linked to A using
two tie points: one at the no icetransition between open water and the onset of ice (A→0) and another at the all ice transition between continuous ice and the appearance of some
water (A→1). This allows an estimate of ice concentration for each data
point, accounting for the fact that each measurement may sample multiple
floes. Ice fraction is then provided for each measurement by
AX=0forX≤XA→0(X-XA→0)(XA→1-XA→0)forXA→0<X<XA→11forX≥XA→1,
where X is the instantaneous value of the proxy and XA→0 and
XA→1 are the tie points for the no icetransition and the all icetransition respectively. Note that
the recorded aircraft data (1 Hz for the relevant diagnostics) and
approximate mean aircraft speed for straight and level runs (60 and 100 m s-1 for MASIN and FAAM respectively) translates to each measurement
point sampling over a distance of 60 and 100 m (≫Dmin), respectively.
We average over the 9 km run to obtain a representative ice fraction A.
Albedo is calculated from measurements of the upward and downward components
of the shortwave radiative flux: a=SWU/SWD. Aa is derived
using tie points aA→0=0.15 and aA→1=0.85, which were
chosen following careful review of video footage from four flights (two from
each aircraft: MASIN 182 and 185; FAAM B761 and B765). It is accepted that
these tie points are approximate and may vary depending on ice conditions;
however, there is good agreement between the flights for which video footage
was available. While these values are broadly consistent with textbook
albedo values (e.g. Curry and Webster, 1999), aA→0 is towards the
upper end of the expected range, so an alternative albedo-derived ice
fraction, Aa2, is calculated using aA→0=0.07 (matching that
used to approximate freezing point in the Weddell Sea in Weiss et al.,
2012). A limitation of the albedo approach is that Aa will be
underestimated for semi-transparent thin ice, as measurements will be
affected by the lower albedo of the sea water below.
In the SST approach, a lower tie point of
SSTA→0=-3.4 ∘C was ascertained following inspection
of the flight videos. It is recognised that this value is lower than might
be expected given typical ocean salinity. Indeed, salinity measurements made
by the RRS James Clark Ross as part of the ACCACIA field campaign suggests typical values of
between 30 and 35 (a little fresher than is typical, likely as a result of
spring melt), implying a freezing point of about -1.8 ∘C. It is
possible this discrepancy may be due to a cool skin being measured by the
aircraft's radiometers. In the vicinity of the MIZ, cool skin temperatures
are likely to be a result of the top few centimetres of the ocean containing
small fragments of ice (e.g. frazil) as was observed during the flights. In
addition, the radiatively driven “cool skin effect” (Fairall et al., 1996)
may also contribute. To account for this uncertainty, we also calculate two
different ice fractions using the SST approach; ASST uses the lower
value suggested by the video footage (-3.4 ∘C), while ASST2
uses the theoretical value based on observed salinities (-1.8 ∘C).
Due to the thin-ice problem, the SST approach is arguably more suitable than
the albedo approach at prescribing the onset of ice with a suitable fixed
no ice transition (so long as a suitable value is determined). However, there is a
fundamental problem in assigning an SST all ice transition that is suitable across multiple
flights. This is because the surface temperature over continuous ice varies
greatly according to the atmospheric conditions. Using a fixed value for
SSTA→1 could therefore lead to inconsistencies between flights
under different weather conditions; for example overestimating A in the
case of particularly cold ice floes as A→1. Consequently, in the SST
approach an adjustment of the SSTA→1 tie point using albedo is
used, which provides a robust estimate of SSTA→1 for any
atmospheric conditions. For each flight, SSTA→1 is set equal to
the median SST value for all flux-run data points where a is within the range
aA→1±0.05, i.e. between 0.8 and 0.9. Using this criterion,
SSTA→1 ranges from -23.6 to -9.6 ∘C between flights,
with this variability being a strong function of latitude (the colder values
being for the northernmost flights). The suitability of this method is
demonstrated by the high level of internal consistency in SST values
within the aA→1±0.05 range for each flight, with a mean standard
deviation (averaged across all flights) of only 1.3 ∘C.
Ice fraction calculated from aircraft observations using
the surface temperature method (ASST) plotted against that using the
albedo method (Aa). (a) Data points for every run (dots) and linear
regression (black line) are shown, using the default criteria for both
methods (aA→0=0.15 and SSTA→0=-3.4 ∘C).
Dots are coloured according to the OSTIA satellite-derived ice fraction, and
the one-to-one line (grey) is shown. (b) Linear regressions of all
combinations of observation-derived Aa and ASST.
Figure B1 compares the ice fractions estimated using the albedo and SST
methods. It shows that there is a near one-to-one relationship between Aa
and ASST, with a correlation coefficient of 0.94, a root-mean-square
error of 0.12 and a bias error of 0.03 for the video-assigned values of
aA→0 and SSTA→0. Linear regressions with the alternative
tie point values show only a small sensitivity to these settings. Overall,
Fig. B1 demonstrates that our methodologies are sound and that the estimates of ice
fraction are robust.
Notation.
Aice fractionαCharnock constantbsmooth-flow constant for the Charnock relationβconstant exponent describing the dependence of Di on ACDdrag coefficientCDN10drag coefficient for neutral stability at a height of 10 mCDNf10neutral form drag coefficient at a height of 10 mCDNi10neutral drag coefficient over sea ice at a height of 10 mCDNw10neutral drag coefficient over sea water at a height of 10 mceeffective resistance coefficientcsice floe shape parametercwfraction of the available force acting on each floeDicross-wind floe dimensionDmin, Dmaxminimum and maximum cross-wind floe dimensionDwdistance between floesfdtotal force acting on the frontal areas of ice floes within the areahffreeboard height of floeshmin,hmaxminimum and maximum freeboard height of floesκvon Karman constant (0.4)Nnumber of floes in area Stρair densitysice floe sheltering function constantScice floe sheltering functionStdomain area of N floesτmomentum fluxτdmomentum flux related to form dragUhorizontal wind speedU10Nadjusted 10-m neutral horizontal wind speedu∗friction velocityυdynamic viscosityφMonin-Obukhov stability correctionz0roughness lengthz0iroughness length for sea icez0wroughness length for open waterAcknowledgements
This work was funded by the NERC (grant numbers NE/I028653/1, NE/I028858/1, and
NE/I028297/1) as part of its Arctic Research Programme. We thank the FAAM
and MASIN pilots, crew, flight planners, and mission scientists; Christof
Lüpkes, Jean Bidlot, Jamie Rae, and John Edwards for discussions; and
Barbara Brooks for providing photographs.Edited by:
H. Wernli
References
Andreas, E. L.: A relationship between the aerodynamic and physical
roughness of winter sea ice, Q. J. Roy. Meteor. Soc., 137, 927–943, 2011.Andreas, E. L., Tucker, W. B., and Ackley, S. F.: Atmospheric boundary-layer
modification, drag coefficient, and surface heat flux in the Antarctic
marginal ice zone, J. Geophys. Res.-Oceans, 89, 649–661,
10.1029/JC089iC01p00649, 1984.Andreas, E. L., Horst, T. W., Grachev, A. A., Persson, P. O. G., Fairall, C.
W., Guest, P. S., and Jordan, R. E.: Parametrizing turbulent exchange over
summer sea ice and the marginal ice zone, Q. J. Roy. Meteor. Soc., 136,
927–943, 10.1002/qj.618, 2010.Arya, S. P. S.: Contribution of form drag on pressure ridges to the air
stress on Arctic ice, J. Geophys. Res., 78, 7092–7099,
10.1029/JC078i030p07092, 1973.Arya, S. P. S.: A drag partition theory for determining the large-scale
roughness parameter and wind stress on the Arctic pack ice, J. Geophys.
Res., 80, 3447–3454, 10.1029/JC080i024p03447, 1975.Banke, E. G. and Smith, S. D.: Wind stress over ice and over water in the
Beaufort Sea, J. Geophys. Res., 76, 7368–7374,
10.1029/JC076i030p07368, 1971.Beljaars, A. C. M. and Holtslag, A. A. M.: Flux parameterization over land
surfaces for atmospheric models, J. Appl. Meteorol., 30, 327–341,
10.1175/1520-0450(1991)030<0327:FPOLSF>2.0.CO;2, 1991.Bidlot, J.-R., Keeley S., and Mogensen, K.: Towards the Inclusion of Sea Ice
Attenuation in an Operational Wave Model. Proceedings of the 22nd IAHR
International Symposium on ICE 2014 (IAHR-ICE 2014), available at:
http://rpsonline.com.sg/iahr-ice14/html/org.html, 2014.Birnbaum, G. and Lüpkes C.: A new parameterization of surface drag in
the marginal sea ice zone, Tellus 54A, 107–123,
10.1034/j.1600-0870.2002.00243.x, 2002.Castellani, G., Lüpkes, C., Hendricks, S., and Gerdes, R.: Variability
of Arctic sea-ice topography and its impact on the atmospheric surface drag,
J. Geophys. Res.-Oceans, 119, 6743–6762, 10.1002/2013JC009712, 2014.Claussen, M.: Area-averaging of surface fluxes in a neutrally stratified,
horizontally inhomogeneous atmospheric boundary layer, Atmos. Environ., 24A,
1349–1360, 1990.Cook, P. A. and Renfrew, I. A.: Aircraft-based observations of air–sea
turbulent fluxes around the British Isles, Q. J. Roy. Meteor.
Soc., 141, 139–152, 10.1002/qj.2345, 2015.
Curry, J. A. and Webster, P. J.: Thermodynamics of atmospheres and oceans, Academic Press, 65, 471 pp., Elsevier, New York, 1999.Dyer, A. J.: A review of flux-profile relationships, Bound.-Lay.
Meteorol., 7, 363–372, 10.1007/BF00240838, 1974.ECMWF: Working Group Report: ECMWF-WWRP/THORPEX Polar Prediction
Workshop, available at:
http://www.ecmwf.int/sites/default/files/elibrary/2013/13913-ecmwf-wwrpthorpex-workshop-polar-prediction-working-groups-report.pdf) (last access: 10 March 2004),
2013.Fairall, C. W., Bradley, E. F., Godfrey, J. S., Wick, G. A., Edson, J. B.,
and Young, G. S.: Cool-skin and warm-layer effects on sea surface
temperature, J. Geophys. Res.-Oceans, 101, 1295–1308,
10.1029/95JC03190, 1996.Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A., and Edson, J.
B.: Bulk parameterization of air-sea fluxes: Updates and verification for
the COARE algorithm, J. Climate, 16, 571–591,
10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2,
2003.Fiedler, E. K., Lachlan-Cope, T. A., Renfrew, I. A., and King, J. C.:
Convective heat transfer over thin ice covered coastal polynyas, J. Geophys.
Res., 115, C10051, 10.1029/2009JC005797, 2010.French, J. R., Drennan, W. M., Zhang, J. A., and Black, P. G.: Turbulent
fluxes in the hurricane boundary layer. Part I: Momentum flux, J. Atmos.
Sci., 64, 1089–1102, 10.1175/JAS3887.1, 2007.Garbrecht, T., Lüpkes, C., Augstein, E., and Wamser, C.: The influence
of a sea ice ridge on the low level air flow, J. Geophys. Res., 104,
24499–24507, 10.1029/1999JD900488, 1999.Garbrecht, T., Lüpkes, C., Hartmann, J., and Wolff, M.: Atmospheric drag
coefficients over sea ice – validation of a parameterisation concept,
Tellus A, 54, 205–219, 10.1034/j.1600-0870.2002.01253.x, 2002.Garman, K. E., Hill, K. A., Wyss, P., Carlsen, M., Zimmerman, J. R., Stirm,
B. H., Carney, T. Q., Santini, R., and Shepson, P. B.: An Airborne and Wind
Tunnel Evaluation of a Wind Turbulence Measurement System for Aircraft-Based
Flux Measurements, J. Atmos. Ocean Tech., 23, 1696–1708,
10.1175/JTECH1940.1, 2006.Guest, P. S. and Davidson, K. L.: The effect of observed ice conditions on
the drag coefficient in the summer East Greenland Sea marginal ice zone, J.
Geophys. Res. Oceans (1978–2012), 92, 6943–6954,
10.1029/JC092iC07p06943, 1987.Hanssen-Bauer, I. and Gjessing, Y. T.: Observations and model calculations
of aerodynamic drag on sea ice in the Fram Strait, Tellus 40A, 151–161,
10.1111/j.1600-0870.1988.tb00413.x, 1988.
Hartmann, J., Kottmeier, C., and Wamser, C.: Radiation and Eddy Flux Experiment 1991: (REFLEX I), Berichte zur Polarforschung (Reports on Polar Research), 105, 1992.Hartmann, J., Kottmeier, C., Wamser, C., and Augstein, E.: Aircraft measured
atmospheric momentum, heat and radiation fluxes over Arctic sea ice, in: The polar oceans and their role in shaping the global environment,
443–454, 10.1029/GM085p0443, 1994.Hines, K. M., Bromwich, D. H., Bai, L., Bitz, C. M., Powers, J. G., and
Manning, K. W.: Sea Ice Enhancements to Polar WRF, Mon. Weather Rev.,
143, 2363–2385, 10.1175/MWR-D-14-00344.1, 2015.Hunke, E. C, Lipscomb, W. H., Turner, A. K., Jeffery, N., and Elliott, S.:
CICE: the Los Alamos Sea Ice Model documentation and software user's manual,
Version 5.1, 116 pp., available at: http://oceans11.lanl.gov/trac/CICE (last access: 29 January 2016),
2015.Johannessen, O. M. and Foster, L. A.: A note on the topographically
controlled oceanic polar front in the Barents Sea, J. Geophys. Res.-Oceans, 83,
4567–4571, 10.1029/JC083iC09p04567, 1978.King, J. C., Lachlan-Cope, T. A., Ladkin, R. S., Weiss, A.: Airborne
measurements in the stable boundary layer over the Larsen Ice Shelf,
Antarctica, Bound.-Lay. Meteorol., 127, 413–428,
10.1007/s10546-008-9271-4, 2008.Kohout, A. L., Williams, M. J. M., Dean, S. M., and Meylan, M. H.:
Storm-induced sea-ice breakup and the implications for ice
extent, Nature, 509, 604–607, 10.1038/nature13262, 2014.
Kottmeier, C., Hartmann, J., and Wamser, C.: Radiation and eddy flux experiment 1993:(REFLEX II). Berichte zur Polarforschung (Reports on Polar Research), 133, 1994.Kwok, R. and Rothrock, D. A.: Decline in Arctic sea ice thickness from
submarine and ICESat records: 1958–2008, Geophys. Res. Lett., 36, L15501,
10.1029/2009GL039035, 2009.Lüpkes, C. and Birnbaum, G.: Surface drag in the Arctic marginal
sea-ice zone: A comparison of different parameterisation concepts, Bound.-Lay. Meteorol., 117, 179–211, 10.1007/s10546-005-1445-8, 2005.Lüpkes, C. and Gryanik, V. M.: A stability-dependent parametrization of
transfer coefficients for momentum and heat over polar sea ice to be used in
climate models, J. Geophys. Res. Atmos., 120, 552–581,
10.1002/2014JD022418, 2015.Lüpkes, C., Gryanik, V. M., Hartmann, J., and Andreas, E. L.: A
parametrization, based on sea ice morphology, of the neutral atmospheric
drag coefficients for weather prediction and climate models, J. Geophys.
Res., 117, D13112, 10.1029/2012JD017630, 2012.Lüpkes, C., Gryanik, V. M., Rösel, A., Birnbaum, G., and Kaleschke,
L.: Effect of sea ice morphology during Arctic summer on atmospheric drag
coefficients used in climate models, Geophys. Res. Lett., 40, 446–451,
10.1002/grl.50081, 2013.Mai, S., Wamser, C., and Kottmeier, C.: Geometric and aerodynamic roughness
of sea ice, Bound.-Lay. Meteorol., 77, 233–248, 10.1007/BF00123526,
1996.Markus, T., Stroeve, J. C., and Miller, J.: Recent changes in Arctic sea ice
melt onset, freezeup, and melt season length, J. Geophys. Res., 114, C12024,
10.1029/2009JC005436, 2009.Miller, P. A., Laxon, S. W., Feltham, D. L., and Cresswell, D. J.:
Optimization of a sea ice model using basinwide observations of Arctic sea
ice thickness, extent, and velocity, J. Climate, 19, 1089–1108,
10.1175/JCLI3648.1, 2006.Neale, R. B., Chen, C. C., Gettelman, A., Lauritzen, P. H., Park, S.,
Williamson, D. L., Rasch, P. J., Vavrus, S. J., Taylor, M. A., Collins, W.
D., Zhang, M., and Shian-Jiann, L.: Description of the NCAR Community
Atmospheric Model (CAM 5.0), NCAR technical note, NCAR/TN-486 + STR, 268
pp., 2010.Newman, S. M., Smith, J. A., Glew, M. D., Rogers, S. M., and Taylor, J. P.:
Temperature and salinity dependence of sea surface emissivity in the thermal
infrared, Q. J. Roy. Meteor. Soc., 131, 2539–2557, 10.1256/qj.04.150,
2005.Notz, D.: Challenges in simulating sea ice in Earth System Models, Wiley
Interdiscip, Rev. Clim. Change, 3, 509–526, 10.1002/wcc.189, 2012.Overland, J. E.: Atmospheric boundary layer structure and drag coefficients
over sea ice, J. Geophys. Res.-Oceans, 90, 9029–9049,
10.1029/JC090iC05p09029, 1985.Pellerin, P., Ritchie, H., Saucier, F. J., Roy, F., Desjardins, S., Valin,
M., and Lee, V.: Impact of a two-way coupling between an atmospheric and an
ocean-ice model over the Gulf of St. Lawrence, Mon. Weather Rev., 132,
1379–1398, 10.1175/1520-0493(2004)132<1379:IOATCB>2.0.CO;2, 2004.Petersen, G. N. and Renfrew, I. A.: Aircraft-based observations of air–sea
fluxes over Denmark Strait and the Irminger Sea during high wind speed
conditions, Q. J. Roy. Meteor. Soc., 135, 2030–2045,
10.1002/qj.355, 2009.Rae, J. G. L., Hewitt, H. T., Keen, A. B., Ridley, J. K., Edwards, J. M.,
and Harris, C. M.: A sensitivity study of the sea ice simulation in the
global coupled climate model, HadGEM3, Ocean Model., 74, 60–76,
10.1002/qj.355, 2014.Rae, J. G. L., Hewitt, H. T., Keen, A. B., Ridley, J. K., West,
A. E., Harris, C. M., Hunke, E. C., and Walters, D. N.: Development of the Global Sea Ice 6.0 CICE configuration for the Met Office Global Coupled model, Geosci. Model Dev., 8, 2221–2230, 10.5194/gmd-8-2221-2015,
2015.
Renfrew, I. A., Moore, G. W. K., Guest, P. S., and Bumke, K.: A comparison of surface layer and surface turbulent flux observations over the Labrador Sea with ECMWF
analyses and NCEP reanalyses, J. Phys. Oceanogr., 32, 383–400, 2002.
Renfrew, I. A., Petersen, G. N., Outten, S., Sproson, D., Moore, G. W. K., Hay, C., Ohigashi, T., Zhang, S., Kristjánsson, J. E., Føre, I., Ólafsson, H., Gray, S. L., Irvine, E. A.,
Bovis, K., Brown, P. R. A., Swinbank, R., Haine, T., Lawrence, A., Pickart, R. S., Shapiro, M., and Woolley, A.: The Greenland flow distortion experiment, B. Am. Meteorol. Soc., 89, 1307–1324, 2008.Roy, F., Chevallier, M., Smith, G., Dupont, F., Garric, G., Lemieux, J.-F.,
Lu, Y., and Davidson, F.: Arctic sea ice and freshwater sensitivity to the
treatment of the atmosphere-ice-ocean surface layer, J. Geophys. Res.-Oceans., 120, 4392–4417, 10.1002/2014JC010677,
2015.Schröder, D., Vihma, T., Kerber, A., and Brümmer, B.: On the
parameterisation of Turbulent Surface Fluxes Over Heterogeneous Sea Ice
Surfaces, J. Geophys. Res., 108, 3195 10.1029/2002JC001385, 2003.Smith, G. C., Roy, F., and Brasnett, B.: Evaluation of an operational ice-ocean
analysis and forecasting system for the Gulf of St Lawrence, Q. J. Roy.
Meteor. Soc., 139, 419–433, 10.1002/qj.1982, 2013.Sorteberg, A. and Kvingedal, B.: Atmospheric forcing on the Barents Sea
winter ice extent, J. Climate, 19, 4772–4784, 2006.Stössel, A., Cheon, W.-G., and Vihma, T.: Interactive momentum flux
forcing over sea ice in a global ocean GCM, J. Geophys. Res., 113, C05010,
10.1029/2007JC004173, 2008.Stull, R. B.: An introduction to boundary layer meteorology, Kluwer Academic Publishers, Dordrecht,
10.1007/978-94-009-3027-8, 1988.Tsamados, M., Feltham, D. L., Schroeder, D., Flocco, D., Farrell, S. L.,
Kurtz, N., Laxon, S. L., and Bacon, S.: Impact of Variable Atmospheric and
Oceanic Form Drag on Simulations of Arctic Sea Ice, J. Phys. Oceanogr.,
44, 1329–1353, 10.1175/JPO-D-13-0215.1, 2014.Uttal, T., Curry J. A., McPhee, M. G., Perovich, D. K., Moritz, R. E.,
Maslanik, J. A., Guest, P. S., Stern, H. L., Moore, J. A., Turenne, R.,
Heiberg, A., Serreze, M. C., Wylie, D, P., Persson, P. O. G., Paulson, C.
A., Halle, C., Morison, J. H., Wheeler, P. A., Makshtas, A.,Welch, H.,
Shupe, M. D., Intrieri, J. M., Stamnes, K., Lindsey, R. W., Pinkel, R.,
Pegau, W. S., Stanton, T. P., and Grenfeld, T. C.: Surface Heat Budget of
the Arctic Ocean, B. Am. Meteorol. Soc., 83, 255–275,
10.1175/1520-0477(2002)083<0255:SHBOTA>2.3.CO;2,
2002.Vancoppenolle, M., Bouillon, S., Fichefet, T., Goosse, H., Lecomte, O.,
Morales Maqueda, M. A. and Madec, G.: The Louvain-la-Neuve sea Ice Model
Users Guide, 89 pp., available at: http://www.elic.ucl.ac.be/repomodx/lim/ (last access: 29 January 2016),
2012.Vihma, T.: Subgrid Parameterization of Surface Heat and Momentum Fluxes over
Polar Oceans, J. Geophys. Res., 100, 22625–22646, 10.1029/95JC02498,
1995.
Wadhams, P., Squire, V. A., Goodman, D. J., Cowan, A. M., and Moore, S. C.:
The attenuation rates of ocean waves in the marginal ice zone, J. Geophys.
Res.-Oceans, 93, 6799–6818, 10.1029/JC093iC06p06799, 1988.Weiss, A. I., King, J., Lachlan-Cope, T., and Ladkin, R.: On the effective
aerodynamic and scalar roughness length of Weddell Sea ice, J. Geophys.
Res., 116, D19119, 10.1029/2011JD015949, 2011.Weiss, A. I., King, J. C., Lachlan-Cope, T. A., and Ladkin, R. S.: Albedo of the ice covered Weddell and Bellingshausen Seas, The Cryosphere, 6, 479–491, 10.5194/tc-6-479-2012,
2012.