Geoscience Reference
In-Depth Information
Analogous expressions can be found for the purpose of calculating oceanic angular
momentum (OAM). For example, the OAM matter terms follow from Eqs. (
51
) and
(
54
)if
p
s
is substituted by
g
H
, where
H
represents the total height of the oceanic
column and a constant density for seawater is used. Such variations inOAMare partly
due to the effect of tidal displacements of water mass (Dehant and de Viron
2002
),
but are certainly also created by thermohaline processes and the oceanic response
to atmospheric surface winds and pressure fluctuations (Wahr
1982
). Whereas mod-
eling wind-induced oceanic motion is a more complex problem, the pressure-based
reaction on time scales longer than 5d (Wunsch and Stammer
1997
) can be eas-
ily taken into account by reverting to the IB (inverted barometer) model, see e.g.
Munk and MacDonald (
1960
). This hypothesis is valid in deep water for most cases,
whereas the response of shallow water requires separate treatment, refer to Wunsch
and Stammer (
1997
) for a brief discussion. The IB model supposes the ocean surface
to readjust to the spatial variation of atmospheric pressure, i.e. water is depressed (or
lifted) by a local pressure increase (or decrease). Such a near-surface compensation
of pressure variations implies that the bottom pressure at the bathymetry is constant
in space but changes with time (de Viron and Dehant
1999
). Hence, for the purpose
of studying Earth rotation variations, the IB correction at a specific epoch consists
of building the mean atmospheric pressure across the oceans
ρ
1
O
p
o
=
¯
p
o
d
O
and adopting for each above-ocean data point the resulting value
p
o
in place of
the actual surface pressure
p
s
in Eq. (
51
). As noted in Wahr (
1982
), this approach
makes the oceanic contribution to
¯
p
i
compensate the corresponding contribution
from the atmospheric portion above the oceans, so that in total the amplitude of
the AAM matter term is reduced. At daily and subdaily time scales, though, the IB
correction worsens the agreement of AAM functions with geodetic data (Brzezi nski
et al.
2002
) and needs to be replaced by a sophisticated model that describes the
dynamical response of the oceans to high-frequency atmospheric wind and pressure
forcing.
We close this section with a brief investigation of axial AAM at the annual fre-
quency. The significant dependency of this quantity on the strength and distribution
of zonal winds
u
χ
is highlighted on the basis of monthly means of cli-
matological data that have been generated by the ECMWF (European Centre for
Medium-Range Weather Forecasts) within a 40-year reanalysis effort. Figure
5
dis-
plays the climatology of zonal winds, averaged over the full range of longitude and
expressed as latitude-pressure cross-sections. From the available fields of
u
(
p
,φ,λ)
at
monthly intervals, two mean fields have been extracted—one covering the period of
December/January/February (labeled as
boreal winter
) and another one representing
the average of wind speeds in June/July/August (
austral winter
). Data above the iso-
baric level of 10hPa are neglected due to the small amount of total mass above that
level (
(
p
,φ)
1% of the total). This fact ensures that the contribution of upper atmospheric
winds to relative angular momentum is small. Both hemispheres feature similar
≈
