Effects of small-scale bathymetric roughness on the global
internal wave field
John A. Goff and Brian K. Arbic
Institute for Geophysics,
JJ Pickle Research Campus,
Goff: phone: (512) 471-0476; fax: (512) 471-0999;
email: goff@ig.utexas.edu
Arbic: phone: (512) 471-0472; fax: (512) 471-8844;
email: arbic@ig.utexas.edu
Award Number: N00014-07-1-0792
The small-scale roughness properties of
the seafloor are increasingly being recognized as critical parameters in
determining important processes in physical oceanography. For instance, in situ observations (e.g., Polzin et al., 1997) find that mixing
levels are greatly elevated in regions of rough topography. Gille
et al. (2000) demonstrate that mesoscale eddy energy tends to be lower in areas
where the bottom is rough (suggesting the possibility that dissipation of eddy
energy takes place in such areas), and Egbert and Ray (2003) show that substantial
tidal dissipation occurs in such areas. The dissipation is generally thought to
arise from the breaking of internal waves generated by flows over the rough
seafloor. On the time scales of internal waves, mesoscale eddies and the
general circulation can be regarded as steady, while tides are oscillatory. The
physics of linear internal wave generation is different for these two classes
of motions (e.g.,
A significant dilemma for physical
oceanographers studying these processes is that the kind of bathymetric
resolution required to model these processes over
entire ocean basins are not available, nor will be any time soon. Acoustic
bathymetric data, which can achieve lateral resolutions of 0.1-0.2 km,
presently cover only a few percent of the ocean floor beyond the exclusive
economic zones in coastal areas. A complete swath survey of all the deep oceans
would take ~200 years of ship time at a cost of billions of dollars (Carron et
al., 2001). The most comprehensive determination of bathymetry world-wide is
the Smith and Sandwell (1994; 1997; 2004) model derived from satellite altimetry
data combined with data from ship soundings, but the resolution of this product
is limited to >10 km in the deep ocean.
We seek to resolve this dilemma through a novel approach of relating the
texture of satellite altimeter data to seafloor roughness characteristics. We
will then address issues of importance to the Navy with tide models that
utilize this information, either by directly resolving internal wave generation
over the rough seafloor, or by parameterizing the dissipation of these internal
waves. In particular, we will investigate internal wave generation in a global
baroclinic tide model, and we will investigate the effect of parameterized
dissipation over rough topography in both barotropic and baroclinic global tide
models.
OBJECTIVES
Our main
objectives are to characterize seafloor roughness from satellite altimetry data
and investigate the impact of rough topography on the global internal tide
field. Specific tasks are:
(1) Full
spectral characterization of altimeter noise world-wide and transfer function
for predicting resultant noise in the gravity signal via the processing path.
(2) Advance the
study of the relationship between gravity and abyssal hill fabric.
(3) Generate map
of abyssal hill roughness parameters across the ocean basins.
(4) Determine
the location of dissipation in global baroclinic tide models.
(5) Parameterize
unresolved topographic wave drag in global tide models.
(6) Determine the
impact of better roughness estimates on the resolved generation of internal
tides in a global model.
APPROACH
Satellite
altimetry data and the derived gravitational field (Fig. 1) may make it
possible to infer seafloor statistical parameters over entire ocean basins, and
are the focus of tasks 1-3 noted above. While it is difficult, owing to the
limits of upward continuation of gravity in the deep ocean, for seafloor
features < ~10 km scale to be distinguished individually in the altimetry
data, the aggregate fabric of small-scale features, such as abyssal hill
morphology, can have a quantifiable effect on the gravity fabric (Goff and
Smith, 2003; Goff et al., 2004). Our governing hypothesis, which is partially
confirmed by these prior results, is that an empirical transfer function can be
determined which relates the primary attributes of bathymetric and gravity
roughness (rms height, characteristic horizontal scales, and fabric
orientation) to each other. However, at these limiting scales of altimetry
resolution, process filtering (Smith and Sandwell, 1997), which is necessary to
convert raw altimetry data into coherent gravity field estimates, and data
noise, related both to data uncertainties and oceanographic variability, will
also have a significant effect on gravity fabric. These must be fully accounted
for.
The
Goff and Smith (2003) and Goff (2004) analyses demonstrate clearly the
importance of quantifying altimetry noise (Task 1 above) if we are to extract
abyssal hill roughness properties from the altimetry data set. Altimetric noise
is neither constant nor simple in statistical character. To characterize
noise in the gravity map, we must first characterize noise in the raw altimetry
data, prior to the application of the various filtering and processing steps.
In our analyses, we have devised a means of largely isolating the noise by differencing
nearest-neighbor tracks to remove most static components of the field, and
high-pass filtering to remove larger-scale variations associated with mesoscale
oceanographic circulation. We employ a
covariance analysis to quantify the residual profiles, which are dominated by
noise processes. As demonstrated in last
year’s progress report, we were able to decompose the noise into uncorrelated
and correlated components, the measures of which are closely correlated with
identifiable environmental variables, such as significant wave heights,
rainfall rates, sea ice distribution, and the subtropical jet stream. Sea surface height noise statistical
parameters have been estimated world-wide for both Geosat and ERS1 geodetic
missions. The next step in our approach
is to synthesize the noise process along all the tracks for both missions, and
then to run these synthetic data through the full processing steps for
estimating the global gravity field.
This will provide us with a global estimate of gravity noise
characteristics, which will, in turn, enable us to confidently ascertain the
component of gravity roughness that can be associated with abyssal hill
roughness.
Figure 1. Sun-shaded altimetric gravity field
(Sandwell and Smith, 1997), emphasizing roughness, over a portion of the
Southeast Indian Ridge (yellow) corresponding to a change in ridge morphology:
from an axial high in the west to an axial valley in the east progressing into
the Australian-Antarctic Discordance (AAD), and a corresponding change in
abyssal hill roughness (Goff et al., 1997). The blue dashed line marks a
visually-determined textural boundary off axis. Boxes indicate areas chosen by
Goff and Smith (2003) for gravity texture estimation, which demonstrated that
the quantitative characterization of gravity texture varied in concert with the
abyssal hill roughness.
The approach described
above for obtaining abyssal hill roughness parameters from altimetric gravity
roughness is a time-intensive, multi-year project. In the short term, we need to provide an
interim product under Task 3: a realistic rendering of abyssal hill roughness
to provide input for the ocean modeling parts of our objectives (Tasks 4-6,
which are detailed below). To
provide this information, we generate a prediction of abyssal hill roughness
statistical parameters world-wide via relationships presented by (1) Goff et
al. (1997) for the average statistical properties of abyssal hills as a
function of spreading rate (Figure 2) and direction (Figure 3), and (2) by Webb
and Jordan (2001) for the modification to these roughness parameters as a
function of sediment thickness (Figure 4).
These relationships are constrained by digital maps of paleo-spreading
rate and direction (Meuller et al. 2008), and sediment thickness (Divens, NGDC
webs site). Next, modifying synthetic
abyssal hill topography code presented by Goff and Jordan (1998) to work with
variable strike input, we have generated synthetic abyssal hill roughness
globally on 1-minute and 30-second
grids.
Figure 2. Average abyssal hill properties as a
function of spreading rate (Goff et al., 1997).
The spatial
distribution of dissipation in the ocean is a matter of intense interest in the
oceanographic community, including the Navy. Much of the interest stems from
the suggestion by Munk and Wunsch (1998) that the strength of the meridional
overturning circulation is controlled by ocean mixing. In addition, the general
oceanic circulation in models (e.g., Scott and Marotzke 2002) shows a strong
sensitivity to the spatial distribution (in both the vertical and horizontal
directions) of mixing. Mixing diffusivity k is related to energy dissipation e by the relation k = Ge/N2, where G is an efficiency factor of about 0.2 and
N is the Brunt-Vaisala buoyancy
frequency (Osborn 1980). Since mixing is connected to dissipation,
quantification of mixing in the ocean must consider energy sinks, which balance
energy sources in averages taken globally and over long periods of time.
Quantification of the sources and sinks of energy for the deep ocean has been
studied in earnest in recent years. Wunsch (1998) showed that the winds put
approximately 1 TW of energy into the oceanic general circulation, while Alford
(2001) showed that winds put about 0.5 TW of energy into the near-inertial
internal wave field. The details of how these wind energy inputs are eventually
converted into a dissipation are not yet well known. Tides put a total of 3.5
TW into the ocean, and of this about 2.5 TW is dissipated in coastal areas,
where tidal velocities are much larger, while 1 TW is dissipated in the open
ocean, in regions of rough topography (Egbert and Ray 2003). Although the budget
for tidal energy is understood better than for wind-forced motions, important
questions about the tidal energy cycle remain.
Figure
3. Paleo-ridge azimuths (D. Mueller,
personal communiction) for predicting abyssal hill orientations.
Figure
4. Global sediment thickness
distribution (Divens, NGDC webs site) for predicting modification to
abyssal hill roughness via Webb and
In task 4 we will
use the global baroclinic tide model of Arbic et al. (2004) to examine whether
the dissipation of internal tides generated in the open ocean takes place in
coastal areas, in the abyssal parts of the open ocean, or in the thermocline of
the open ocean. In tasks 5 and 6 we will use the roughness estimates from our
work on tasks 1 to 3 in global tide models. In task 5 we will examine the
difference that a better roughness estimate makes on our parameterizations of
unresolved topographic wave drag, which are used in both barotropic and
baroclinic tide models. In task 6 we will return to global model of the
resolved internal tide field, as in task 4, but this time with better estimates
of seafloor roughness, which will improve the resolution of high baroclinic
modes.
The new
bathymetry for the Global Tidal Model (HYCOM) is to be derived by combining the
latest Smith and Sandwell (1997) bathymetric database (SS) together with an
empirically derived estimate of abyssal hill roughness as described above. Both
products are provided at a resolution of 30 arc seconds. The SS data has been
interpolated onto a 1/12.5 degree HYCOM grid using a radial Blackman filter. The
SS bathymetry also includes a parameter (SID) to identify the source of actual
sounding data used in the preparation of the bathymetric data. We convert this
parameter to a field of 0 and 1 to indicate that the bathymetry is measured
(SID = 1) or estimated from altimetry (SID = 0). The Goff roughness prediction (G) is an
empirically derived estimate of bottom roughness for the worlds
oceans. If the SS data is derived from actual soundings then we do not wish to
alter the bathymetry by adding a roughness parameter. Therefore, in order to
add the Goff roughness parameter which resolves abyssal hill roughness of order
2-10 km, we calculate a weight alpha(x,y)
for each ordinate pair on the 30 arc second grid. alpha
is calculated in the same manner as the HYCOM model bathymetry but with a
filter radius R = 5 km and 10 km. We produce a new bathymetry h_SS_G(x'y') on a 30 arc second grid using:
h_SS_G(x',y') =
SS(x',y') + ( 1 - alpha ) * G(x',y'),
WORK COMPLETED
Goff as
completed analysis of both Geosat and ERS1 altimetry data to provide a world-wide
analysis of altimetry noise at scales < 50 km (i.e., scales that are of
importance to characterizing abyssal hill fabric). Some of these results were detailed in the
previous progress report and will not be repeated here. That work is the topic of a manuscript in
preparation. Goff has since generated a
synthetic noise data set for all the Geosat and ERS1 track lines. These profiles are awaiting full altimetry
processing by collaborators Walter Smith and David Sandwell for eventual estimation
of altimetric gravity noise characteristics.
More significantly, Goff has formulated a preliminary world-wide,
synthetic abyssal hill roughness grid from predictions based on average abyssal
hill characteristics as a function of spreading rate and direction, as well as
modifications by sediment cover. These
grids are now being used by Arbic for tide modeling, and initial results from
that work are expected soon.
Patrick Timko,
a postdoc, has been working full-time on this project
since May 2008. We expect that in the
near-future he will switch over to working half-time on this project, and
half-time on the NRL contract. For the
ONR roughness project, Patrick has learned how to run and analyze
high-resolution HYCOM tide runs, and is nearly finished constructing bathymetries
as described above. We plan in the very
near future to run two-layer versions of HYCOM on both the SS and SS+Goff grids. Once
we get the two-layer model working on both bathymetries, we plan to get a
multi-layer model (say, for instance, a 15-layer model) working on both
bathymetries. We will look for increased
internal wave activity in the runs on the SS+Goff
bathymetry due to the increased roughness.
We expect that the multi-layer runs will exhibit more sensitivity to the
extra roughness, because higher vertical resolution implies the presence of
higher vertical modes, which are more sensitive than low modes to small scales
in the bathymetry. After we do the runs
described above we also plan to run at higher resolution (1/25th degree). We expect at that resolution the goff
roughness will have a more pronounced effect.
RESULTS
A global
predictions of abyssal hill statistical characteristics has been completed
using the approach outlined above. Here
we display plots of rms heights (Figure 5), width scale parameter (Figure 6),
and length scale parameters (Figure 7). Scale
parameters, which define the functional form of the autocovariance function,
are proportional to the inverse of the charactistic width or length. From these predictions we have generated
global synthetic realizations of abyssal hill-scale roughness at both 1-minute
and 30-second resolution. The
IMPACT/APPLICATIONS
Synthetic,
predictive maps of mall-scale seafloor roughness can be used to realistically
“roughen” lower-resolution global bathymetry maps, which can then be
incorporated into oceanographic modeling efforts to predict critical phenomena
such as the generation of internal waves and mixing by both tidal and non-tidal
(i.e., mesoscale eddy) flows.
RELATED PROJECTS
Arbic has a
separate contract with the Stennis branch of the
Naval Research Laboratory to implement global tides in HYCOM. HYCOM is planned to be the next-generation
Navy operational global model. Arbic has
developed a good working relationship with several of the key HYCOM
investigators (e.g. Alan Wallcraft, Joe Metzger,
Harley Hurlbert, Jim Richman, and others). Wallcraft and Arbic
implemented tides into HYCOM, and Wallcraft and Metzger
recently completed a 5-year run of the global 1/12 degree model with
tides. Preliminary results already
indicate important impacts of the tides on the ocean general circulation, and
several analyses and further improvements to the model are planned. The parameterization of topographic wave drag
on both tidal and non-tidal motions in HYCOM is expected to be enhanced by the
bathymetric roughness work done in the current project. In addition, postdoc
Patrick Timko, working with Arbic, has learned to run and analyze HYCOM tidal
simulations, as well as to constuct bathymetric grids
for use in HYCOM. Timko plans to continue to work on both Navy-funded projects,
thus benefitting both projects greatly.
Figure
5. Global prediction of abyssal hill rms
heights.
Figure
6. Global prediction of abyssal hill width
scale parameter
Figure
7. Global prediction of abyssal hill
length scale parameter
Figure
8. Synthetic abyssal hill roughness for
the
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HONORS/AWARDS/PRIZES
Recipient: Dr. John A. Goff, Institute
for Geophysics,