Arya S.P.S. Introduction to Micrometeorology
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198 13 Marine Atmospheric Boundary
Layer
ture becomes clear when one considers the thermodynamic energy bal-
ance at the
sea
surface. A simplified version of this was briefly discussed
in
Chapter
1.
Radiation balance near the
sea
surface is greatly complicated by the
fact that the solar radiation received at the surface can penetrate to con-
siderable depths
of
water
and the shortwave reflectivity (albedo) of the
surface is quite sensitive to solar altitude (see Munn, 1966,Chap. 18).The
longwave radiation from the atmosphere is essentially absorbed by a very
thin surface film of
water
which also gives out radiation to the atmo-
sphere, depending on the surface temperature. The net longwave radia-
tion depends on the presence of clouds and fog; it may vary with height
above the surface due to absorption and emission by water vapor.
It
is the
most important source of energy to the atmosphere.
A major
component
of the energy balance at the sea surface is the latent
heat
of
evaporation
(Hi),
which is usually an order of magnitude larger
than the sensible heat flux. Evaporation from ocean surfaces is not only
the major source
of
water in the atmosphere, but it is also an important
source of energy (made available at the time of condensation) that drives
the atmosphere.
It
occurs most of the time, day and night.
The direct or sensible heat exchange
(H)
between the atmosphere and
ocean is usually much smaller than the latent heat and radiative ex-
changes.
It
depends to a large
extent
on the
air-sea
temperature differ-
ence
(T
IO
-
T
s
) ,
which typically remains within ± I K
over
most open seas
and oceans. During briefepisodes of cold air outbreaks
over
warmer seas,
oceans, and
ocean
currents, however,
air-sea
temperature differences
can
easily exceed 5 K. The sensible heat flux from the sea surface to the
atmosphere becomes a significant
part
of
the energy balance during such
episodes. In extreme cases,
air-sea
temperature differences of 25-30 K
have
been
observed
(e.g., at the beginning of a severe cold air outbreak
over
the
warm
GulfStream, near Cape Hatteras, during the 1986Genesis
of Atlantic
Lows
Experiment), with the most spectacular signs (e.g., sea
smoke, steam devils, and
water
spouts) of intense convection. Under
such conditions, both the direct
and
latent heat fluxes become very large
and nearly
of
the same
order
of magnitude [B =
H/H
L
~
0(1)].
The most uncertain
part
of the energy balance at the sea surface is the
heat exchange
H G through the motions in water. Some of it is by turbulent
transfer and mixing, which depends on the temperature difference across
the oceanic mixed layer. Near-surface currents can also transport heat in
the horizontal direction, and upwelling and downwelling motions trans-
port in the vertical direction. In
order
to get around the difficulty of
measuring or estimating
H
G
and also to account for the penetration of
solar radiation through the depth of the mixed layer, it is found more
13.1 Sea-Surface Characteristics 199
convenient to consider the energy balance of the whole mixed layer
(13.1)
in which the
rate
of
heat
storage
I:!.H
s
200 13 Marine Atmospheric Boundary Layer
surface temperature depend on the latitude, season, and the prevalent
weather conditions at the location of interest. The diurnal range,
AT
s
=
T
smax
-
T
smin
,
is found to decrease with increasing latitude, wind speed,
and cloudiness.
The
typical values of
AT
s
are
O.soC
in the tropics,
O.25°C
in midlatitudes,
and
less than O.loC in high-latitude regions. Similar varia-
tions in
T; during the course of a day also occur intermittently when major
storms pass through the area.
For
example, a marked rise of sea-surface
temperature usually occurs during the approach of a tropical storm, hurri-
cane, or typhoon; it is followed by a similar fall in the surface temperature
after the passage
of
the storm center.
13.1.2
SURFACE
WAVES
The
most
interesting and fascinating aspect of the sea surface is its
endless, unceasing, up and down movement in the form of
waves-a
succession of humps and hollows in ever-changing patterns. Sea-surface
waves are generated by atmospheric winds, astronomical causes (e.g.,
high and low tides), seismic disturbances, and, on a small scale, by pass-
ing ships and boats.
The
most common and persistent of these are wind-
generated waves. The short waves generated and maintained by local
winds are called seas, while long waves generated elsewhere and propa-
gated into the region of interest are called swells. The former are attenu-
ated rapidly as the local winds subside, while the latter continue even
during long periods of near-calm conditions, because they are generated
by distant forces and do not dissipate easily. Surface waves are also
classified according to water depth (e.g., shallow-water and deep-water
waves) and also on the basis of the governing force (e.g., gravity waves
and capillary waves).
A regular (periodic) wave propagating at a constant velocity C
w
can be
characterized by its height
H (vertical distance between a trough and the
following crest), wave period
T (the time elapsed between the passage of
two successive crests or troughs past a fixed observer), and wavelength
L
(the horizontal distance between the adjacent crests or troughs at any
instant). Alternatively, one
can
use the wave frequency n =
T-I
(the
number of waves
per
unit time) or the wave number K = L
-I
(the number
of waves
per
unit length).
For
our
simple wave form, these are interre-
lated as
K =
nl
C;
C;
=
LIT
The
ratio
HI
L is called the wave steepness, which is only about half the
angle from horizontal made by a line from trough to crest.
13.1 Sea-Surface Characteristics 201
Wind-generated ocean-surface waves are quite irregular, nearly cha-
otic, and three dimensional. Successive waves differ markedly in height,
period, speed, and direction of propagation. Using the simplest statistics,
one
can
determine from a record of surface elevation (7)) the mean wave
height
it, the root-mean-square of surface elevation (J"11' or the significant
wave height
fl
ll3
(defined as the mean of the one-third highest waves in a
record), as well as the corresponding wave period. These average wave
characteristics are essentially determined by large (dominant) waves and
are
not
very sensitive to the hierarchy of smaller but steeper waves and
wavelets that ride on the large waves.
More
sophisticated statistical analyses of an irregular wave field as-
sume the field to be composed of a large number of elementary sinusoidal
waves of different frequencies and wave numbers, and sort out the rela-
tive contribution of each to the total variance of surface elevation. A plot
of the
component
variance versus frequency (or wave number) is called
spectrum.
The
peak
in spectrum gives a clear-cut indication of which
frequency (or
wave
number) waves are most dominant in a given wave
field.
For
illustrative purposes some observed wave spectra are shown in
Fig. 13.1, indicating a strong dependence of wave spectrum on fetch
(distance from the shore) along wind.
0.10
0.08
0
0.06
'"
en
N
E
c:
0.04
-
-e-
0.02
0.01
0
3
4
n(red
sec")
Fig. 13.1 A sequence of wave frequency spectra measured at increasing fetch (from 9.5
to 80 km) during the
JONSWAP
Experiment. [From Phillips (1977); after Hasselmann et al.
(1973).]
(13.2)
202
13 Marine Atmospheric Boundary Layer
When a light breeze starts blowing on a calm sea surface, the immediate
first response of the water surface is the appearance of small, ruffled
patches called
eat's
paws. This is in response to the small-scale turbu-
lence, particularly pressure fluctuations, in the immediate vicinity of the
surface. Then, small wavelets only a few millimeters in height and a few
centimeters in wavelength appear. These tiny wavelets are quite steep
and wrinkle the
sea
surface much more than larger waves do. Because
this wrinkling is mainly resisted by surface tension associated with the
capillary effect on liquids, such waves are called capillary waves (gravity
is negligible in comparison to surface tension as a restoring force).
If
the
breeze that initiated the capillary waves dies out, the waves also disap-
pear
quickly and the
sea
surface becomes smooth and glasslike again.
However, if
the
breeze
continues to blow, the capillary waves grow in
height, as well as in wavelength, until they reach a wavelength of 17.2
mm, corresponding to a theoretical minimum wave speed of 0.231
ill
sec-I.
For
surface waves
of
larger wavelength, the gravity force becomes
significant and even the dominant restoring force, so that such waves are
called surface gravity waves. Unlike capillary waves, gravity waves do
not dissipate easily,
even
long after the wind dies out, but continue to
propagatefor long distances from the region
oftheir
genesis. Thus, seas at
one place eventually become swells at other places.
The
sea
state
at any location and time depends on the strength and
duration of winds, the fetch or distance
over
which winds blow in a
coherent or persistent manner, and the strength and direction of surface
currents. In coastal
and
shallow continental shelf waters, the wave field
also depends on
such
factors as
water
depth, bottom slope, and the orien-
tation of the coastline in relation to wind direction. The actual mecha-
nisms and processes of generation, growth, and breaking of wind waves
are too complex to be covered here. Essentially, they involve transfers of
momentum and kinetic energy from the atmospheric surface layer to the
oceanic surface layer.
During persistent stormy weather conditions
over
open oceans, waves
can grow to spectacular and frightening dimensions. Observers have re-
corded waves of
over
20 and even 30 m in height! But, more frequently
encountered seas have significant heights of less than 2 m and wave
periods of less than 10sec. The wavelength and phase speed of an elemen-
tary component gravity wave are related to the wave period as
L =
(g/21T)
12
C
w
=
(g/21T)
T
13.2 Momentum Transfer to the Sea Surface 203
However, these relations do not hold for the average properties of a
complex interference
pattern
of
waves arising from the superposition of a
number of elementary sinusoidal waves.
It
may not be very sensible even
to talk
about
wave speed of such a nonconservative pattern, in which no
individual wave
crest
can
be followed long enough, because it loses its
identity. Swell is more nearly a two-dimensional, regular, and periodic
wave whose wavelength, period, and speed are approximately related
by Eq. (13.2).
The
period of swell may range from several seconds to
minutes.
13.2
MOMENTUM
TRANSFER
TO
THE
SEA
SURFACE
The transfer of momentum from the atmosphere to the ocean at their
interface is
of
considerable importance to meteorologists, as well as to
physical oceanographers. A
part
of this momentum goes into the genera-
tion
of
surface waves, while the remaining portion is responsible for set-
ting up drift currents and turbulence in the upper layers of the ocean. The
relative partitioning
of
momentum between these different modes of mo-
tion in
water
depends on such factors as the stage of wave growth, dura-
tion and fetch of winds, etc., and is
not
easy to determine. But the total
momentum exchange
can
be determined from measurements in the atmo-
spheric surface layer, well above the level of highest wave crests.
Air flow in the lowest layer of direct wave influence is rather complex
and is not easily measured or theoretically predicted. Above a few signifi-
cant
wave heights, however, the mean flow becomes essentially horizon-
tal and unidirectional. In this so-called fully developed surface layer, the
"law
of the
wall"
similarity (the logarithmic wind-profile law) is valid
under neutral conditions and the
Monin-Obukhov
similarity relations are
applicable under more general stratified conditions. First, we consider the
neutral or adiabatic case in order to clearly bring out the influence of
the dynamic
water
surface, as distinguished from that
of
the rigid land
surface.
When one considers extending the
"law
of the wall" similarity to air
flow
over
a moving
water
surface, the effects of both the surface drift
current and surface waves should be taken into account. The surface
current, which is typically
3-5%
of the wind speed at 10 m, but can be
much stronger in certain regions (e.g., the Gulf Stream, Kuroshio, and
other
ocean
currents),
can
easily be taken into account by considering the
air motion relative to
that
of surface
water
(V
=
U«
- V
w
) . The influence
of moving surface waves on mean wind profile in the surface layer is much
204 13 Marine Atmospheric Boundary Layer
more difficult to discern. However, the assumptions of stationarity and
horizontal homogeneity implied in the surface layer and PBL similarity
theories
are
much
better
satisfied
over
large lake and ocean surfaces, as
compared to
most
land surfaces.
13.2.1
SEA-SURFACE
ROUGHNESS
Wind-profile measurements from fixed towers in shallow coastal waters
and from stable floating buoys (ships are not suitable for this, as they
present
too
much of an obstruction to the air flow)
over
open oceans do
show the validity
ofthe
logarithmic law [Eq. (10.6)] under neutral stability
conditions. However, the roughness parameter
(zo) determined from the
same is found to be related to both the wind and wave fields in a rather
complex manner and
can
vary
over
a very wide range (say, 10-
6
- I
0-
2
m).
There have been a number of semiempirical and theoretical attempts at
relating
Zo
to the friction velocity, as well as to the average height, the
phase speed, and the stage of development of surface waves. The simplest
and still the most widely used relationship is that proposed by Charnock
(1955) on the basis of dimensional arguments
Zo
= a
(uVg)
(13.3)
where a is an empirical constant. The basic assumptions implied in
Charnock's
hypothesis (zois uniquely determined by u; and g) are that the
winds
are
blowing steadily and long enough for the wave field to be in
complete equilibrium with the wind field, independent of fetch, and that
the surface is aerodynamically rough.
Individual estimates of
Zo
plotted as a function of
uV
g invariably show
large scatter, because they usually pertain to different fetches and differ-
ent
stages of wave development and also because of large errors in the
experimental determination of
zo. However, when the available data sets
are block averaged, a definite trend of
zo increasing in proportion to
uV
g
does emerge. Figure 13.2 shows such block-averaged data compiled from
some 33 experimental sets of wind profile and drag data (Wu,
1980). Note
that
Charnock's
formula [Eq. (13.3)] is verified, particularly for large
values of
Zo
and
u~/g,
and a = 0.018.
The simple
state
of affairs assumed in Charnock's hypothesis rarely
exists
over
lakes and oceans. More frequently, the wave field is not in
equilibrium with local winds,
but
depends on the strength, fetch, and time
history of the wind field. At low wind speeds, the surface can also become
aerodynamically smooth, or be in a transitional regime between smooth
and rough. A comprehensive treatment of sea-surface roughness at
different development stages of wind-generated waves is given by
13.2 Momentum Transfer to the Sea Surface 205
IO°,----
rrr:
-r---
.....
-r----.--,r------.
10.
1
5
o
s
o
s
,zo
u~/g
=0=0.0185
o
o
s
5
10
1
10-
1
10-4.L-
__
~-L..-.--_:_-.L-..---:-_1.-----.J
10-
2
10°
u;/g(cm)
Fig. 13.2 Observed roughness parameter of sea surface as a function of
u~/g
compared
with Charnock's (1955) formula. [After Wu (1980).]
Kitaigorodski (1970). The fundamental parameter indicating the stage of
wave development, in his theory, is the ratio
Cdu«, where Cois the phase
speed of the most dominant (corresponding to the peak in the wave-height
spectrum) waves.
It
is shown that in the initial stage of wave development
(very small
Co/u*), the characteristic roughness height h
o
is proportional
to
U'''I)' while in the equilibrium stage
of
wave development h
o
is propor-
tional to
uVg,as implied by
Charnock's
formula [Eq. (13.3)]. In a broad
intermediate range of
Co/u*, however, h
o
is shown to depend on both
U'''I)
and Co/u*.
Furthermore,
on the basis of analogy with the aerodynamic
roughness
of
a rigid surface, 20 is assumed proportional to h
o
for a com-
pletely rough surface, proportionalto
vlu;
for an aerodynamically smooth
surface,
and
a function
of
both h
o
and
vlu
; in the transitionally smooth or
rough regime. Kitaigorodski has suggested plausible expressions for the
roughness
parameter
for the various combinations of roughness and wave
regimes, some
of
them involving still unknown empirical constants or
functions. In his matrix,
Charnock's
formula falls in one corner, corre-
sponding to the aerodynamically rough, fully developed (equilibrium)
wave regime.
206 13 Marine Atmospheric Boundary Layer
If, for the sake
of
convenience and
other
practical reasons, Charnock's
formula is used, irrespective
of
the wave development stage, one should
expect
a = gzol
u~
to be a function
of
at least Col
u*,
if not any other
parameter. Only in the asymptotic limit
of
Cdu;
~
00,
a may approach a
constant
value. This explains why empirically determined values of a by
different investigators range from 0.01 to 0.08. Owing to the lack of simul-
taneous
data
on zo
and
sea
state,
the function a(Colu*) has not been well
established,
but
observations indicate that a = 0.015-0.020 for the later
(final) stages
of
wave
development.
For
early stages of wave develop-
ment, the following semiempirical formula suggested by Kitaigorodski
(1970)
can
be recommended:
zo
=
0.12H
exp(-kColu*),
for
Colu*:s
20 (13.4)
where
H =
(27T)1I2(T'1
is the mean wave height. The use
ofEq.
(13.4) would
require,
of
course, detailed wave-height measurements. An experimental
verification
of
Eq. (13.4) is shown in Fig. 13.3, which also demonstrates
the large
scatter
in the individual estimates
of
zo.
10
1,-----------
---.
•
10 I
•
•
•
.;
...
..
.
•••
't •
.
~
..
...
;', .
..,
..
;...
. .
..
.
~~.~
.
•:
~J
•••
.
~
..
..
e./·
.:
..
of>
•
.::..
• •
• •
•
•
• •
••••
•
.~
•
• •
10
1
10
2
E
o
0
10
3
N
10
4
•
10
5
.
•
10-
3
10-
2
10
H exp
(-kCo/~
) (em)
Fig. 13.3 Observed roughness parameter of sea surface as a function of the reduced
wave height
H.,
exp(-kColu*)
compared with Eq. (13.4), indicated by the arrow. [After
Kitaigorodski (1970).]
13.2 Momentum Transfer to the Sea Surface 207
At low wind speeds (say U
IO
< 7 m sec
")
and in early stages of wave
development, neither Eq. (13.3) nor (13.4) may be adequate, because the
surface is aerodynamically smooth or incompletely rough. The sea sur-
face appears to be remarkably smooth, before waves start to break. In
fact, the aerodynamic roughness of even a fully developed sea under a
tropical storm is
observed
to be less than that of mown grass. This is
largely due to the fact that waves are generated by and move along with
the wind
and
do not offer as much resistance to the flow as would an
immobile surface with similar shape. There is also strong evidence sug-
gesting
that
sea-surface drag is primarily due to small ripples and wavelets
with
phase
speeds less than the near-surface wind speed, and that large
waves make only a minor contribution to the same.
Different surface roughness regimes mentioned in Section
10.1
are
found to
occur
over
oceans. In the absence of swell, the sea surface is
found to be aerodynamically smooth during calm and weak winds
(U
IO
<
2.5 m sec-I), transitionally rough in moderate winds (2.5
'S
UIO'S
7.5
ill
sec-I), and completely rough in strong winds
(U
IO
> 7.5 m sec-I). The
above criteria should be considered only approximate and limited to fully
developed (equilibrium) wind-generated waves. The data points corre-
sponding to small values of
u~/
g in Fig. 13.2 probably belong to the
transitional roughness regime.
13.2.2
SURFACE
DRAG
COEFFICIENT
The definition and concept of the surface drag coefficient was intro-
duced in Section 10.3.
It
is found to be particularly useful in oceano-
graphic
and
marine meteorological applications to express or parameter-
ize the sea-surface drag in terms of wind speed at a standard height of 10
m
and
the drag coefficient CD referred to that height.
Note
that under
neutral stability conditions,
CD is uniquely related to the roughness pa-
rameter
zothrough Eq. (10.14). Still, most investigators prefer
CD
over zo,
because of the much smaller range
of
variation
of
the former (0.001 <
CD
< 0.003), as compared to the latter (10-
6
< Zo < 10-
2
m) over the oceans,
and also
because
the surface stress is more directly related (proportional)
to
CD, irrespective
of
the wind-profile shape. The drag coefficient can be
determined from measurements of momentum flux and mean wind speed
at only one level (usually 10 m), while a direct estimate of
zo
requires
accurate wind-profile measurements in the surface layer. Both the drag
and wind-profile measurements are quite sensitive to motions of the ob-
servation platform in response to surface waves, as well as to the deflec-
tion of flow around it.
There
has
been
considerable interest in knowing the dependence of
CD