A three-dimensional transport model for the middle atmosphere
Abstract
In this paper we describe fundamental properties of an 'off-line' three-dimensional transport model, that is, a model which uses prescribed rather than predicted winds. The model is currently used primarily for studying problems of the middle atmosphere because we have not (yet) incorporated a formulation for the convective transport of trace species, a prerequisite for many tropospheric problems. The off-line model is simpler and less expensive than a model which predicts the wind and mass evolution (an 'on-line' model), but it is more complex than the two-dimensional (2-D) zonally averaged transport models often used in the study of chemistry and transport in the middle atmosphere. It thus serves as a model of intermediate complexity and can fill a useful niche for the study of transport and chemistry. We compare simulations of four tracers, released in the lower stratosphere, in both the on- and off-line models to document the difference resulting from differences in modeling the same problem with this intermediate model. These differences identify the price to be paid in going to a cheaper and simpler calculation. The off-line model transports a tracer in three dimensions. For this reason, it requires fewer approximations than 2-D transport model, which must parameterize the effects of mixing by transient and zonally asymmetric wind features. We compare simulations of the off-line model with simulations of a 2-D model for two problems. First, we compare 2-D and three-dimensional (3-D) models by simulating the emission of an NO(x)-like tracer by a fleet of high-speed aircraft. The off-line model is then used to simulate the transport of C-14 and to contrast its simulation properties to that of the host of 2-D models which participated in an identical simulation in a recent NASA model intercomparison. The off-line model is shown to be somewhat sensitive to the sampling strategy for off-line winds. Simulations with daily averaged winds are in very good qualitative agreement but are less diffusive than when driven with instantaneous winds sampled at half-hour intervals. Simulations with the off-line and 2-D models are quite similar in the middle and upper stratosphere but behave quite differently in the lower stratosphere, where the 3-D model has a substantially more vigorous circulation. The off-line model is quite realistic in its simulation of C-14. While there are still systematic differences between the 3-D calculation and the observations, the differences seem to be substantially reduced when compared with the body of 2-D simulations documented in the above mentioned NASA intercomparison, particularly at 31 deg N.
A three-dimensional transport model for the middle atmosphere
Jeffrey A. Nittrouer,1 Mead A. Allison,2 and Richard Campanella3
Received 8 March 2007; revised 12 March 2008; accepted 9 April 2008; published 23 July 2008.
[1] New methods of data collection and processing are developed to provide quantitative,
reach-scale measurements of bedform transport mass within the tidally influenced
Mississippi River. A multibeam swath profiler was used to collect daily bathymetry over a
range of water discharges, and bed elevation changes induced by dune migration are
measured. These values are coupled with bulk physical properties of the bed sediment to
constrain mass flux, and annual bedform transport is estimated at 2.2 106 metric tons
(MT). The total annual sand flux from the Mississippi River, calculated by combining
measured bedform transport rates and suspended sediment flux, is estimated to be 20
106 MT. Survey data also provide information about the spatial distribution of dunes
across the channel bottom. Straight reach segments are commonly mantled by dunes for
the entire cross section, while bends are typically areas of focused scour devoid of
bedforms. Presumably, any sediments associated with migrating dunes are propelled into
suspension within bends before redepositing in the subsequent straight reach. Movement
via suspension is therefore an important component for the downriver transport of bed
materials in the lower Mississippi River.
Citation: Nittrouer, J. A., M. A. Allison, and R. Campanella (2008), Bedform transport rates for the lowermost Mississippi River,
J. Geophys. Res., 113, F03004, doi:10.1029/2007JF000795.
1. Introduction
[2] Sediment transport studies within the world’s major
fluvial systems have primarily examined the flux of sus-
pended materials because this component often represents
the majority of particulates reaching the oceans [Milliman
and Meade, 1983]. However, many large river channels are
sand bedded in their final, relatively low gradient reach near
the land-ocean interface and quantitative bed load measure-
ments are difficult to acquire owing to dynamic conditions
near the bed-water interface. Observations are further com-
plicated near the river outlet by the occurrence of tides and
estuarine circulation, whose signals perturb data collection of
sediment motion and water discharge. Sand and associated
bed materials (e.g., flocs and particulate organics) therefore
represent an under-measured sediment component within
fluvial systems.
[3] Fluvial sand flux and deposition patterns are primarily
responsible for setting channel morphology of lowland
sand-bedded rivers. At the river outlet, sediment supply to
the delta serves to build and maintain coastal land forms
[Fisk, 1961; Coleman and Wright, 1975; Coleman et al.,
1998]. Sand deposits are important because they provide a
stable substrate for coastal wetlands, such as marshes and
mangroves [Kulp et al., 2005], and promote the growth of
barrier islands and mainland beaches [Stone and McBride,
1998]. River and deltaic sands often contain a significant
fraction of large (>1 mm) organic carbon, and make for
important oil and gas reservoirs because of their interfinger-
ing with organic-rich mud facies [Bianchi et al., 2007].
[4] Assessments of sand transport are important for
coastal restoration efforts. Sediment starvation (due to river
channel confinement within artificial levees) and base level
rise (rapid regional subsidence coupled with eustatic sea
level rise) over the past century have promoted wetland
deterioration in the Mississippi River delta. This issue is
potentially mitigated through restoration efforts that seek to
distribute sediment-laden river water to surrounding wet-
lands, and mine the channel bottom for sand [Britsch and
Kemp, 1990; Penland et al., 1990, 1992; Turner, 1997; Day
et al., 2000]. These efforts are facilitated by quantitative
measurements of sand and sediment transport.
[5] The primary objective of the present study is to
measure the component of sediment flux associated with
the downriver migration of dunes. Four study areas were
examined along the final 150 km reach of the Mississippi
River. Data were collected with multibeam (swath) bathy-
metric sonar over a range of water discharges, and analyzed
tomeasure bed elevation changes induced by dunemigration.
We utilizeChurch’s [2006] definition for bedmaterials in this
study: those sediments (mineral or organic) corresponding to
the coarser portion of river sediments, which may move
either as classic bed load (i.e., rolling, sliding, saltating), or
as near-bed suspension. Bedform sediment flux is the
1Department of Geological Sciences, Jackson School of Geosciences,
University of Texas, Austin, Texas, USA.
2Institute for Geophysics, Jackson School of Geosciences, University of
Texas, Austin, Texas, USA.
3Center for Bioenvironmental Research, Tulane University, New
Orleans, Louisiana, USA.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2007JF000795$09.00
F03004
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, F03004, doi:10.1029/2007JF000795, 2008
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ing dune forms by way of lee face sedimentation.
2. Methods for Measuring Bed Material Flux in
Sand Bed Rivers
[6] Mass flux estimates for bed sediment remain poorly
constrained within large river channels because of temporal
and spatial limitations of existing observational methods,
and a lack of consensus in what constitutes bed load and
suspended load transport, particularly for the size class of
particles that readily transition between the bed and the
water column [Gomez, 1991]. The latter arises because of
limited measurements within large, sand bed rivers that
distinguish between sediment grains that move as ‘‘true’’
bed load, and those that intermittently move as suspended
load for downstream distances greater than a single dune
wavelength.
[7] Bed load flux has traditionally been measured using
basket and pressure-difference point samplers, which are
deployed to the sediment-water interface to collect rolling
and saltating grains. Although sampler designs have been
modified to minimize impact on natural flow (e.g., the
Helley-Smith sampler, Emmett [1980], and Hubbell et al.
[1981]), their intrusive nature necessitates a calibration for
sampler efficiency [Engel and Lau, 1980]. In large rivers,
point samplers are temporally limited because collection
capacity is often reached before turbulence-induced bed
sediment flux variabilities can be resolved. Further, point
measurements are spatially restricted, requiring interpola-
tion between sample locations when determining across-
and down-channel transport rates [Gomez, 1991].
[8] Nonintrusive acoustic measurements are a more effec-
tive means for measuring bed material transport. The dune-
tracking technique uses single-line bathymetry data to
quantify bed load transport over spatial scales of meters to
kilometers, by coupling dune geometries and translation
lengths from repeated surveys [Simons et al., 1965, Engel
and Lau, 1980, 1981; Kostaschuk et al., 1989; Harbor,
1998; Ten Brinke et al., 1999; Wilbers and Ten Brinke,
2003]. This method is limited, however, by its two-dimen-
sional nature, requiring accurate reoccupation of transect
lines. Additionally, bedform geometry and dimensions must
remain stable over the period of observation, such that
dunes remain identifiable, and shape deformation does not
compose a significant portion of the translating mass
[McElroy and Mohrig, 2006]. Because of these potential
errors, formulations will often utilize empirically derived
bed load discharge coefficients, which account for grains
carried more than one bedform wavelength, bed load-to-
suspended load exchanges, and unbalanced yields resulting
from accelerating or decelerating fluid flow.
[9] Recent studies have used acoustic Doppler current
profilers (ADCP) to assess bed sediment velocities, and
constrain sediment flux [Rennie et al., 2002; Kostaschuk et
al., 2005; Villard et al., 2005]. Resolution of the system is
dependent on fixed instrument frequency, and physical
characteristics of bed sediments, such as porosity, grain
size, and depth of the mobile layer. The latter parameters
must be known accurately to constrain rates [Kostaschuk et
al., 2005]. The technique may generate ambiguous results
because of the difficulties in resolving suspended sediment
velocities from the underlying mobile bed sediment, and to
the preferential selection of the coarser material in transit.
For error reduction, the ADCP system may require bed
monitoring in a fixed position for survey periods greater
than 30 minutes, and this is a difficult task in commercially
active rivers [Rennie et al., 2002].
[10] Abraham and Pratt [2002] and Abraham and
Hendrickson [2003] introduced a new method to assess
bedform transport utilizing multibeam bathymetric map-
ping. Their study used repeated surveys to measure dune
migration and compare spatial patterns of bed accretion and
erosion. Sediment mass transport is calculated by convert-
ing volume changes with measured sediment density. The
processing techniques of Abraham and Pratt [2002] limit
measurements to an assessment of mass change per unit
width, and therefore do not provide downstream, width-
adjusted sediment loads.
[11] The present study improves the use and data pro-
cessing techniques of multibeam mapping to assess sedi-
ment transport. The three-dimensional calculations avoid
the need to adjust for spatial bedform variability when
measuring across-channel sediment flux, as is necessary
when employing the dune tracking method. Our technique
covers the entire channel at four river reaches; each reach
measuring several kilometers in length, and separated from
each other by distances of 150 kilometers.
3. Setting
[12] The Mississippi River has the world’s third largest
drainage basin, extending over 45% of the contiguous
United States and adjacent areas of Canada (Figure 1a),
and ranks seventh worldwide in both annual sediment and
water discharge [Meade, 1996]. The Mississippi River
channel in Louisiana is sinuous above river kilometer
(RK) 130, before its final, relatively straight, course to the
Gulf of Mexico. Since 1930, the channel has been held in
place below RK 250 by the construction of federally
maintained artificial levees, hence modern morphology for
the lowermost river is a reflection of prelevee channel
planform, subsequently modified by incision into relict
fluvio-deltaic strata. Limited accretion and erosion contin-
ues along banklines inside the artificial levees, and ephem-
eral muds are commonly deposited from suspension in
shallow (<20 m water depth) bank areas during periods of
low water discharge [Galler, 2004]. Below Baton Rouge,
Louisiana (RK 370), the Mississippi River channel incises
into seaward dipping, highly consolidated fluvio-deltaic
strata that range from Pleistocene age upstream to
<1000 years old near the Gulf of Mexico [Stanley et al.,
1996]. Below RK 164, channel bed sediment is primarily
fine to medium sand. Ranges for dune wavelengths and
heights are 10–40 m and 0.5–3 m, respectively, and vary
with water discharge [Allison and Nittrouer, 2004].
[13] Meteorology within the Mississippi River catchment
drives water discharge, which typically is at minimum during
late summer and autumn months (July–November) and at
maximum between midwinter and late spring (January–
May) [Bratkovich et al., 1994]. Water discharge measure-
ments for the lower Mississippi River are taken from the
United States Army Corps of Engineers (USACE) monitor-
ing station at Tarbert Landing, MS, (RK 492). No contin-
F03004 NITTROUER ET AL.: MULTIBEAM DATA AND SEDIMENT FLUX
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