Analytical Description and Vertical Structure of the Atmospheric Boundary Layer - Surface Based Remote Sensing of the Atmospheric Boundary Layer - page 25

reach an equilibrium state between the wind field and the wave field. Therefore, the
maximum wave height is reached usually several hours after the peak wind speed
(Emeis and Türk 2009 ). When the wind wanes, the existing waves have a large iner-
tia and continue to propagate. Thus, on the rear side of a decaying depression, the
wave speed can easily be larger than the wind speed. Now the waves (old waves
in the sense of eq. ( 2.44 )) can drive the air at the lower boundary of the marine
boundary layer, and the sea surface is no longer a sink but a source for atmospheric
momentum.
The large thermal inertia of the water leads to cycles and time scales in the tem-
perature difference between the surface and the air that are not known from any other
terrestrial surfaces. The temperature of the ocean water is dominated by an annual
cycle while a diurnal cycle is near non-existing. This cycle is delayed one to two
months to the annual cycle of the air temperature. Therefore, we usually find water
warmer than the air and an unstably stratified marine boundary layer in late summer,
autumn, and early winter, while colder waters than the air and a stable stratification
of the marine boundary layer prevail in late winter, spring, and early summer. This
mean temperature difference between ocean and atmosphere is modified by cold-air
and warm-air advections coupled to moving atmospheric pressure systems (depres-
sions and anticyclones). If the atmospheric pressure systems do not move too fast,
warm-air advection or cold-air advection over a given part of the ocean surface can
persist for a day or two. This can be considerably longer than the 6-12 hours for
which a given thermal stratification can prevail over land.
The large humidity source of the water frequently leads to upward turbulent
humidity fluxes into the usually unsaturated air above. Due to this, a very low Bowen
ratio (eq. 2.24 ) of about 0.1 (Sempreviva and Gryning 1996 ) is observed in the
marine boundary layer. This leads to a buoyancy ratio (see eq. ( 2.25 )) of about 0.4,
i.e. 30% of the buoyancy of air parcels in the marine boundary layer is produced
by humidity fluxes. Edson et al. ( 2004 ) even say that the humidity flux component
provides more than half of the total buoyancy flux. Thus, the marine surface layer
is often slightly unstable although the potential temperature slightly increases with
height.
While the thermal conditions of the marine boundary layer can be described with
the same parameters that suffice for a description of onshore boundary layers, the
dynamical interaction between the wave and the wind field at least requires the
introduction of two additional parameters: the wave height, h and the wave age,
ξ

. Additionally the water depth, d , has some influence. Waves become higher but
slower when they come to shallower waters near the coast because they are modified
from deep-water waves to shallow-water waves. The wave age is the ratio between
the wave speed c ph of the dominant waves and either the wind speed or the friction
velocity, u . Usually, the wave age is given by (Oost et al. 2000 , 2002 )

∗

c ph
u

ξ = . (2.44)

∗

Employing definition (2.44), ξ< 28 denotes young (growing) waves and ξ> 28

old waves (swells).