influence of wind stress and ambient flow on a high...
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Influence of Wind Stress and Ambient Flow on a High Discharge River Plume
I. Garc�a Berdeal, B.M. Hickey and M. Kawase
School of Oceanography Box 357940, University of Washington, Seattle, WA 98195-7940
Abstract
The response of a high discharge river plume to an alongshore ambient flow and wind
forcing is studied with a three-dimensional numerical model. The study extends prior model
studies of plumes by including (1) a very large volume discharge (14,000 m3 s-1, about twice the
maximum used in other models), (2) ambient flow in a direction opposite to that of the
propagation of coastally trapped waves and (3) a sequence of wind direction reversals. The
magnitude of the ambient flow, wind stress, estuary width and river outflow are based on typical
values for the Columbia River on the Washington coast. The model results challenge two
longstanding notions about the Columbia plume: first, that the plume orientation is in a relatively
stable southwest position in summer – with average discharge conditions (7000 m3 s-1) a
summertime downwelling event can erode the southwestward plume and advect it to the north of
the river mouth over several days. Second, the plume is not always uni-directional; branches can
occur both upstream and downstream of the river mouth simultaneously. The model also
provides an explanation for the observation that the plume rarely tends southward during the
winter season – in contrast to summer conditions, the rotational tendency of the plume and the
ambient flow are in the same direction, so that wind stress must be be significant (> 1.4 dynes
cm-2 for at least 2 days) to reverse the plume direction. Distinct anticyclonic freshwater pools
form in modeled plumes both north and south of the river mouth under steady forcing conditions
when ambient flow is present. The scale of modeled pools is consistent with features observed in
the Columbia plume.
1. Introduction
The plume from the Columbia River is a dominant feature in the hydrography of the U.S.
West Coast. The Columbia River discharge varies between 3000 and 17,000 m3 s-1 over a typical
year (Hickey et al., 1998) and accounts for 77% of the coastal drainage on the U.S. West Coast.
The largest outflows occur during spring due to snowmelt (May-June) and during winter storms
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due to rainfall. The plume can extend as far north as the Strait of Juan de Fuca (47°N) in winter
and as far south as 40°N in summer (Fig. 1). The seaward extent of the plume can be as large as
400 km (Barnes et al., 1972). The Columbia River plume therefore affects a vast area of the
coastal ocean, including the coastal estuaries in the Pacific Northwest (Hickey et al., 1999), not
only by reducing salinity, but also by changing the distribution of other water properties such as
nutrients. The plume plays an important role in the transport of dissolved and particulate matter,
phyto- and zooplankton, larvae, contaminants, etc. (Barnes et al., 1972; Grimes and Kingsford,
1996).
Winds and ambient coastal flow both play important roles in determining the
characteristics of buoyant plumes. The seasonal cycle of wind in this region is determined by the
alternation of atmospheric pressure systems over the North Pacific. During winter the Aleutian
Low results in northward winds along the coast; in summer, the North Pacific High results in
southward seasonal mean winds (Barnes et al., 1972; Hickey, 1989). Superimposed on this
seasonal mean are fluctuations with time scales of 2-10 days (Hickey, 1989). In the winter, these
episodes have a predominantly northward alongshore wind stress (“downwelling-favorable”)
with a magnitude typically ranging between 0.5 dyne cm-2 and 3 dynes cm-2, reaching 4-5 dynes
cm-2 during severe storms. Episodes of southward alongshore wind stress (“upwelling-
favorable”) during winter rarely exceed 1 dyne cm-2 and are usually about 0.5 dyne cm-2 (Hickey
et al., 1998). The latter are associated with good weather in the region. In contrast, in summer,
northward and southward wind stress events are comparable in magnitude (~ 0.5 dyne cm-2).
Mean coastal currents off Washington and Oregon also exhibit a strong seasonal cycle
(Hickey, 1989). In fall and winter the monthly mean flow is northward; during spring and
summer the surface (upper 50 m) coastal waters flow southward, although deeper layers may
flow northward. The seasonal mean currents have typical amplitudes of 5-20 cm s-1. Fluctuations
in the coastal currents are strongly wind-driven in all seasons, with forcing being more local in
winter, more remote in summer (Hickey, 1989). Typical fluctuations are ~10-50 cm s-1.
Both in situ hydrographic data (Hickey et al., 1998; Barnes et al., 1972) and satellite-
derived data (Fiedler and Laurs, 1990) show that the average position of the Columbia River
plume also varies with season. During the winter when the prevailing winds and coastal currents
are northward the plume from the Columbia River is usually observed north of the river mouth.
During periods of strong northward winds the plume “hugs” the coast. Under lighter northward
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or southward wind events the plume “relaxes” to a west to northwest position (mean winter
position) (Hickey et al., 1998) as seen in the sea surface temperature (SST) satellite image shown
in Figure 1a. When the weather systems change after the transition to spring conditions and the
prevailing winds and coastal currents turn southward, the plume generally adopts a
southwestward orientation (mean summer position) as seen in the coastal zone color scanner
(CZCS) image shown in Figure 1b.
In summer, episodes of inclement weather (when the winds turn northward) result in a
plume with a northward "winter" orientation. Fiedler and Laurs (1990) describe an event with
northward wind stress of 0.5 dynes cm-2 for about 5 days in July 1979. Following this episode
CZCS data show the plume hugging the coast north of the river mouth as in winter. These
summer plume reversals, although not often seen in satellite images due to the cloud cover that
invariably accompanies bad weather, may be relatively common. For example, in the summer of
1998 several reversals were detected in the salinity signature of Willapa Bay, an estuary 75 km
north of the Columbia River (Hickey et al., 1999).
In this paper we describe a series of numerical experiments designed to better understand
the response of a high discharge river plume to varying wind forcing and coastal currents, and in
particular, the processes involved in direction reversals of such a river plume. A number of
authors have previously addressed the dynamics of lower discharge buoyant plumes using
numerical models. Chao (1986) modeled an estuary and coastal ocean to describe the basic three-
dimensional structure of an unforced river plume as a function of prescribed vertical mixing and
bottom stress. He later explored the influence of bottom slope on the shelf and in the estuary on
plume structure. He also classified plumes as supercritical or subcritical according to an
empirical Froude number (Chao 1988a). Chao (1988b) investigated the effect of wind on pre-
existing estuarine plumes in a coupled shelf-estuary system and again the influence of bottom
slope. He found that a sloping bottom reduced the offshore extent of the plume. Oey and Mellor
(1993) introduced a turbulence closure scheme to calculate the vertical mixing coefficients in
their unforced, flat bottom estuarine plume model. Kourafalou et al. (1996a and 1996b) studied
the influence of wind on a pre-existing plume and made a simulation with realistic wind stress
for an individual source and for a “line source” of freshwater. Fennel and Mutzke (1997) used a
stratified non-tidal coastal ocean but flat bottom slope in their model to study the dynamics of a
river plume with wind forcing. They found that with a stratified ocean, a secondary bulge
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develops downstream. A classification of river plumes as surface or bottom-advected based on
the vertical structure was given by Yankovsky and Chapman (1997). Fong (1998) and Fong and
Geyer (2001) studied the effect of winds and downstream ambient flow on a river plume with an
average discharge of 1500 m3 s-1 and a sloping shelf. In particular, these papers addressed
advection and mixing of a surface-trapped plume during an upwelling wind event. Garvine
(1999) investigated the dependence of the alongshelf penetration of an unforced buoyant coastal
discharge on parameters such as bottom slope, background diffusivity, tidal amplitude and river
discharge. In a recent paper Xing and Davies (1999) explore the horizontal spreading and
vertical mixing of a buoyant plume with a discharge of 2000 m3 s-1 as a function of turbulence
closure scheme, wind direction and bottom slope.
The present study extends this research in three important areas by including (1) a very
large volume discharge (about twice the maximum used in other models); (2) ambient flow in a
direction opposite to that of the propagation of coastally trapped waves; and (3) a sequence of
wind direction reversals. The magnitude of the ambient flow, wind stress, estuary width and river
outflow are based on typical values for the Columbia River and the Washington coast. The
horizontal and vertical resolutions are among the finest used in previous studies to ensure that all
pertinent features are adequately resolved.
2. Numerical Model
2.1. Description of the model
The numerical model used in the study is ECOM3d, a three-dimensional, sigma
coordinate, hydrostatic, primitive equation model derived from the Princeton Ocean Model
(Blumberg and Mellor, 1987). Since this model has been widely used, we refer the reader to
Kourafalou (1996a) or Fong (1998) for a more thorough description of the model details. We
focus here only on the details specific to our study.
The model domain is rectangular (100 x 200 grid cells of size 1.5 km x 2 km, with finer
resolution in the cross-shore direction) with a coastal wall on the eastern side and three open
boundaries (Fig. 2a). Freshwater at 10°C is introduced uniformly throughout the top half of the
water column into the two grid cells at the head of an estuary, located at y = 120 km for winter
runs and y = 200 km for summer runs. The estuary is 4 km wide, 10 km long and 20 m deep. An
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estuary is included to generate an estuarine circulation that inputs not only freshwater but also
momentum to the coastal ocean. Discharge rate is kept constant throughout a model run although
discharge rate is varied for different experiments. The coastal ocean is initialized with a
homogeneous temperature of 10°C and a salinity of 33 psu.
The 22 sigma layers in the vertical fall on Chebyshev collocation points so as to resolve
the surface and bottom boundary layers as well as the surface-trapped density plume (Fig. 2b).
This results in a vertical resolution better than 1.5 m near the surface across the entire domain.
The bottom topography is a uniform slope α = 2x10-3. This slope is roughly that of the
Washington shelf and does not include the shelf break and continental slope. The reasons for not
having more realistic bottom topography are two-fold: first, we are trying to resolve a surface-
trapped plume that thins out in the offshore direction; the sigma levels follow the opposite
trend—inclusion of the continental slope would decrease the near surface resolution by a factor
of at least five. Second, a larger slope (thus, larger offshore depths) would increase the external
wave speed. The time step required to resolve this larger speed would then have to be smaller by
about a factor of three to keep the model numerically stable, therefore significantly increasing
the time it takes to run the model.
The model includes a mode splitting technique for computational efficiency. The external
and internal time steps are 10 seconds and 7 minutes respectively, in compliance with the CFL
criterion. The horizontal mixing coefficients of salt, temperature and momentum are
parameterized using the Smagorinski (1963) formula, while the vertical mixing coefficients are
parameterized using the 2.5-level closure scheme of Mellor and Yamada (1982). The Coriolis
parameter corresponds to a latitude of 46°N for the majority of runs and is kept constant since
the β-effect is negligible for the spatial and temporal scales examined.
The boundary conditions at the sea surface are zero salt and heat fluxes. In experiments
with wind, the surface stress is set by an alongshore wind stress as described by Blumberg and
Mellor (1987). Winds are applied in the alongshore direction and are constant in the cross-shore
direction and, after an initial ramping, in time. At the bottom, the momentum is balanced by a
quadratic bottom stress with a bottom drag coefficient given by the "law of the wall"; salt and
heat fluxes and vertical velocity are zero. The coastal wall boundary is impenetrable,
impermeable and no-slip.
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On the open boundaries, the boundary conditions are such that the bore triggered by the
plume passes through the boundaries. The surface elevation is clamped to zero on the offshore
boundary and radiated on the northern boundary. On the southern boundary the normal external
velocity is set to the specified ambient flow and the surface elevation allowed to adjust
geostrophically to the specified flow. For the tangential external velocities a no-slip condition is
applied. Internal velocities are radiated on all open boundaries following Orlanski (1976).
Temperature and salinity on the open boundaries are relaxed to specified boundary values (those
of the coastal ocean) for inflow, and the existing gradients are advected out of the grid for
outflow. On the northern boundary a sponge layer is implemented over the last 20 km on both
temperature and salinity to absorb the excess river water. For model runs with an ambient flow a
barotropic velocity is imposed at the southern boundary. The model does not include tides since
we will focus on the subtidal response of the buoyant plume to variable wind stress, river
discharge and ambient flow.
2.2. Sensitivity to numerical details
Before proceeding to experiments with variable winds and ambient flows we investigated
the sensitivity of the model to numerical details such as the advection scheme, vertical resolution
and vertical diffusivities of momentum, salt and temperature. In particular, the hydrodynamic
stability of the modeled plume proved to be extremely sensitive to both the advection scheme
and vertical resolution. The spatial structure of the modeled plume proved to be highly sensitive
to vertical diffusivity.
a) Advection scheme and vertical resolution
The use of a centered difference scheme was eliminated as a choice from the outset since
it can lead to negative salinities, especially at the river mouth (Fennel and Mutzke, 1997). Our
next choice was an advection algorithm based on an upwind scheme with an “anti-diffusion”
velocity to correct for the numerical diffusion introduced by the upwind advection scheme
(Smolarkiewicz, 1984; Smolarkiewicz and Clarke, 1986; Smolarkiewicz and Grabowski, 1990).
The resulting scheme is then second order positive definite. We implemented a version with two
consecutive corrective steps (here designated Smolar_2) as well as a computationally more
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demanding version in which the anti-diffusion velocity equivalent to applying an infinite number
of corrective steps is estimated using a recursion relationship (here designated Smolar_r).
Surface salinity contours at 14 days for model runs with different vertical resolutions and
different advection schemes are shown in Figure 3. For all three runs a freshwater discharge rate
of 7000 m3 s-1 is used, and winds and ambient flow are zero. Vertical diffusivities are calculated
by the Mellor-Yamada closure scheme with a background value of 10-6 m2 s-1, and the bottom
slope is 2x10-3. Model runs with 12 layers in the vertical with a higher resolution near the surface
and the Smolar_2 advection scheme exhibited instabilities developing around the fringe of the
plume (Fig. 3a). Employing the same advection scheme, but increasing the vertical resolution to
22 layers (so that the surface layer is 0.6 m thick 50 km offshore instead of 0.74 m) delayed the
appearance and growth rate of those instabilities but did not eliminate them (Fig. 3b). Adequate
vertical resolution of the surface-trapped plume was crucial to the stability of the result for the
Smolar_2 advection scheme. Fong (1998) notes that horizontal resolution is also very important
and that under-resolution in the horizontal can also produce wave-like meanders around the
bulge. However, increasing horizontal resolution (grid cells of size 500 x 500 m) using the
Smolar_2 scheme produced no significant changes in our results (not shown).
Because increasing either vertical or horizontal resolution failed to eliminate model
instabilities, the computationally more demanding Smolar_r advection scheme was implemented,
with the result that bulge instabilities disappeared (Fig. 3c). The Smolar_r scheme also reduced
the offshore extent of the bulge by about 20% while increasing the width of the downshelf plume
to accommodate the additional transport. All runs mentioned hereafter use the Smolar_r
advection scheme and 22 layers in a Chebyshev distribution.
b) Vertical mixing coefficients
The model also proved very sensitive to vertical mixing coefficients for salt and heat (KH)
and for momentum (KM). In general, as mentioned above, a Mellor-Yamada level 2.5 turbulence
closure scheme was used to calculate the vertical mixing coefficients, and a background value of
10 -6 m2 s-1 was employed for both coefficients. However, when this background value (UMOL)
was increased to 10 -4 m2 s-1 (Fig. 4a) and especially to 10-3 m2 s-1 (Fig. 4b), the plume's spatial
structure changed dramatically. Garvine (1999) suggests that the turbulence closure scheme shuts
down for high Richardson numbers such as observed near the front of a river plume, so that
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vertical mixing coefficients revert to the background value set by the user. In fact, holding both
vertical mixing coefficients at a constant value of 10-4 m2 s-1 and 10-3 m2 s-1 instead of using the
closure scheme for the two runs mentioned above yielded virtually identical results (not shown).
The effects of increasing the vertical mixing coefficient were especially noticeable in the
"upshelf" (sensu Garvine, 1999) penetration of the plume as well as in the offshore extent of the
bulge (Fig. 4). The upshelf (here, south of the estuary) intrusion of the freshwater plume in some
numerical models has been briefly addressed by Garvine (1999) and, in more detail, by
McCreary et al. (1997) and Yankovsky (2000). Kourafalou et al. (1996a) attributed the upshelf
intrusion to the sloping bottom. Our results show, however, that for the base case (the unforced
plume with a bottom slope of 2 x 10-3, 22 layers in a Chebyshev distribution, Smolar_r advection
scheme and a turbulence closure scheme to calculate the vertical mixing coefficients with
background diffusivity of 10-6 m2 s-1, shown in Fig. 3c) little upshelf penetration occurs even
though the bottom has a significant slope. If the background vertical diffusivity is increased to
10-4 m2 s-1 (Fig. 4a), more upstream intrusion is noticeable (compare to the base case with a
background of 10-6 m2 s-1). If the diffusivity is further increased to 10-3 m2 s-1, the bulge is
dramatically diminished in size as the plume water is mixed both upshelf and downshelf of the
river mouth. An anticyclonic eddy develops and propagates upshelf (Fig. 4b).
In the absence of bottom slope, some upshelf intrusion still occurs, but there is no
obvious upshelf propagation of an eddy as with a sloping bottom for the same UMOL and the
bulge is again wider (Fig. 4c). This is consistent with previous numerical model results for flat
bottom cases (Oey and Mellor, 1993; Kourafalou, 1996a; Garvine, 1999). Addition of a
downshelf ambient flow also inhibits the upshelf plume penetration as shown in model results
from Yankovsky and Chapman (1997) who purposefully added a downshelf ambient flow of 4
cm s-1 to prevent upshelf penetration. Similarly, when a northward ambient flow of 10 cm s-1 was
added to the case portrayed in Figure 4b (UMOL = 10-3 m2 s-1) the upshelf penetration of the
plume was eliminated (not shown).
Since upshelf propagation of the type noted here has not been reported in observations of
the Columbia River plume, we have elected to use Mellor-Yamada 2.5 with molecular
background viscosity for our model study (Fig. 3c). However, we note that the choice of vertical
mixing coefficients (or of a background value if using Mellor-Yamada) is clearly non-trivial,
suggesting that model coefficients, configurations and turbulence closure schemes (as shown by
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Xing and Davies, 1999) be carefully examined before making model to model or model to data
comparisons.
3. Results
In Section 3.1 plumes are first allowed to develop for about 13 days with ambient shelf
flow. Northward ambient flow simulates winter conditions over the Washington shelf; southward
ambient flow simulates summer conditions. The river discharge is 7000 m3 s-1, the long-term
annual average for the Columbia River. In order to illustrate the response of plume orientation
and surface structure to realistic wind reversals (Sec. 3.1a) these pre-existing plumes formed
with a coastal ambient flow were subjected to 6 days of downwelling-favorable wind stress,
followed by 6 days of upwelling-favorable wind. The magnitudes of the ambient flow and wind
stress are 10 cm s-1 and 0.5 dynes cm-2, respectively. To illustrate plume vertical structure (Sec.
3.1b) the pre-existing plumes formed with the northward and southward ambient flows are
subjected to either several days of upwelling wind stress or several days of downwelling wind
stress. For those cases, wind stress of both 0.5 and 1.4 dynes cm-2 are used. The effect of wind
stress magnitude and direction on freshwater transport are discussed in more detail in Section
3.2. In Section 3.3, where we examine the formation of freshwater pools, discharge rate and
ambient flow are also varied.
3.1. Response to wind stress and ambient flow
a) Plume surface structure
The base case consists of an unforced plume; i.e., freshwater discharges into the coastal
ocean which is at rest (Fig. 3c). The plume structure consists of an anticyclonic bulge off the
mouth of the estuary and a coastal current that propagates as a bore in the same direction as
coastal-trapped waves, as described by others for lower discharge volume cases (Kourafalou,
1996a; Fong, 1998). As Fong (1998) points out, this is a non-steady problem in the sense that the
bulge keeps growing without limit due to the fact that the coastal current is unable to
immediately transport such a large river discharge. Some authors (Garvine, 1987; Kourafalou,
1996a) have classified these plumes as supercritical by analogy with hydraulic theory.
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With the addition of an ambient flow in the downshelf direction (northward in this case)
the problem becomes quasi-steady (Fong, 1998). The bulge is advected to the north with the
ambient flow and its offshore extent reaches a limit as the transport in the coastal current is
increased by the ambient flow (Fig. 5a). The maximum offshore extent of the fresher water
occurs several kilometers downstream of the river mouth. We have extended Fong’s study to
include an ambient flow in the opposite direction. In this case some of the freshwater of the
bulge off the mouth of the estuary is advected upshelf (southward) to form an elongated bulge;
however, a downshelf coastal current is still observed (Fig. 6a).
For northward ambient flow (the winter case) with the onset of downwelling-favorable
winds the pre-existing freshwater plume is pushed onshore against the coast (Fig. 5b) so that by
the sixth day of this wind event the freshwater is trapped in a very narrow region adjacent to the
coast (Fig. 5c). With the onset of subsequent upwelling-favorable winds the plume moves
offshore (Fig. 5d). By the end of this upwelling wind event the plume adopts a northwestward
orientation with a northward downshelf tail ~60-100 km offshore (Fig. 5f) reminiscent of the
satellite-derived SST image from winter 1991 (Fig. 1a).
For southward ambient flow (the summer case) the south-southwestward oriented plume
moves onshore at the onset of downwelling-favorable winds so that freshwater plumes are found
both north and south of the river mouth (Figs. 6b and 6c). Both north and south of the river
mouth the freshwater is transported northward in a narrow band next to the coast. By the end of
six days of downwelling winds, the plume resembles the “winter” plume hugging the coast
although a small remnant of freshwater from the southwestward plume is still observed south of
the river mouth (Fig. 6d). In the next episode of upwelling winds the freshwater, including the
remnant, is carried offshore (Fig. 6e) and after six days the plume is in a predominantly
southwest “summer” position (Fig. 6f) reminiscent of the summer ocean color image in Figure
1b. However, because of the recent downwelling, a northward tending “residual” tail remains
approximately 60-80 km offshore north of the river mouth.
The velocity field associated with the low salinity structures seen in Figures 5 and 6 is
highly three-dimensional. For example, the surface velocity field associated with plumes under
northward and southward ambient flow conditions is shown in Figure 7. For these examples, in
which plumes have been allowed to develop for 28 days, distinct pools of low salinity are
observed for ambient flow in both directions and strong geostrophic flows have developed
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around the light pools. Such pools can also be seen in the shorter model runs of Figures 5 and 6.
Pool formation and structure will be discussed in more detail in Section 3.3. For northward
ambient flow conditions, the plume reinforces the ambient flow producing a northward jet at its
outer edge where the density front is strongest. Flow is weak along the axis of the plume and a
southward jet is observed near the coast on the shoreward side of the plume (Fig. 7a). For
southward ambient flow, at locations south of the river mouth the southward ambient flow
seaward of the plume reverses to a narrow northward jet at the edge of the plume. Flow is weak
along the plume axis and a strong southward jet is observed on the coastal side of the plume.
North of the river mouth a northward coastal jet occurs with maximum velocities near the coast;
the flow reverses to the ambient direction within about 20 km of the coast (Fig. 7b).
The three-dimensional velocity structure becomes even more complex when wind stress
forcing is added. However, for the standard 0.5 dynes cm-2 forcing used in most of the model
runs, the effect of wind forcing is confined primarily to the top and bottom frictional layers (see
next subsection). This flow is too weak to reverse the ambient flow at the surface although
direction reversals can occur for higher wind stress. Geostrophic wind-driven flows develop only
with the larger stress (see next subsection), but these can reverse the ambient flow and add
substantial complexity to the velocity field.
b) Vertical plume structure
Cross-shelf sections of salinity and east-west and north-south velocity components 40 km
north or south of the river mouth for northward or southward ambient flow conditions,
respectively, are displayed in Figures 8a-c. Results are shown for the base case of no wind, as
well as 3 days after the onset of either downwelling or upwelling-favorable winds of magnitude
0.5 dynes cm-2. In Figures 9a-c the vertical structure obtained with the standard wind stress is
compared with that for greater wind stress (1.4 vs. 0.5 dynes cm-2).
Results show that the plumes are strongly surface trapped with respect to salinity (Fig.
8a). Plume depth is shallow (<10-15 m) whether in the absence of winds or with the standard
wind forcing of 0.5 dynes cm-2. Thus, plumes do not make bottom contact at this location for this
relatively weak wind stress. Under conditions of either no winds or upwelling-favorable winds,
plumes are generally deeper for northward ambient flows than for southward ambient flows and
stratification is weaker. However, this is not the case for downwelling winds (Fig. 8a, compare
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middle panels). Although stratification is weaker for northward tending plumes, surface salinity
is usually several psu lower. Plumes deepen and stratification decreases as wind stress increases
for both upwelling and downwelling winds (Fig. 9a), likely due to increased vertical mixing.
The cross-shelf salinity sections also clearly demonstrate the onshore and offshore
movement of the plumes in response to wind stress. For example, the leading edge of the plume
with either northward or southward ambient flows moves onshore almost 30 km after three days
of downwelling and offshore about 60 km after 3 days of upwelling with a wind stress of 0.5
dynes cm-2 in each case (compare location of seaward front in left three panels in Fig. 8a). The
movement across the shelf increases to about 40 km onshore and 100 km offshore with a wind
stress almost three times as great (Fig. 9a).
One of the important questions with respect to buoyant plumes is the manner and extent
to which they modify the regional circulation. We are interested in the magnitudes of velocities
in plume-affected regions in comparison to the more chronic wind-driven velocities as well as
whether a plume significantly affects flow beneath it. To explore these issues in detail we present
velocity on vertical cross-shelf transects (Figs. 8b, c and 9b, c) as well as time series at locations
inside and outside the plume in the surface layer and in the interior, i.e., outside surface and
bottom boundary layers (Fig. 10). For the cross-shelf component of flow, results are shown for
the entire water column so that surface and bottom Ekman layers are captured (Fig. 8b). Details
in the upper 20 m are shown in Figure 9b.
Cross-shelf velocity sections illustrate the presence of bottom Ekman layers in opposite
directions for the oppositely directed ambient flows across the entire shelf (Fig. 8b). During
wind-driven episodes, a surface Ekman layer is also visible, with weak velocities in the upper
~5-10 m. The onshore or offshore flow in the direction of surface Ekman transport is more than
an order of magnitude greater within the plume in most cases. For example, frictional velocities
of about 2.5 cm s-1 occur outside the plume in contrast with about 10 or 50 cm s-1 inside the
plume for a wind stress of 0.5 dynes cm-2, with the larger velocities during upwelling. Note that
for greater downwelling wind stress under northward ambient flow conditions, surface velocities
are reduced in the plume near the coast, likely because the plume is closer to the coastal wall
(Fig. 9c, lower left). A classic upwelling pattern of cross-shelf flow—offshore at the surface and
onshore in the bottom boundary layer—is observed near the coastal wall for both directions of
ambient flow with the modest wind stress of 0.5 dynes cm-2. In the northward ambient flow case,
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onshore flow beneath the plume can occur because alongshore flow reverses to southward near
the coast once the plume separates from the coast (Fig. 8b, lower left). For downwelling
conditions, on the other hand, the return flow is not purely confined to the bottom boundary layer
(Fig. 8b, middle panels), unlike the classic downwelling pattern. Reversal of the bottom
boundary layer cross-shelf flow across the entire shelf would only be expected in cases where
wind stress is sufficiently large to reverse the direction of the alongshore ambient flow all across
the shelf.
Alongshelf velocities greater than ambient are largely confined to the upper 10 m of the
water column, indicating that plume related currents are essentially surface trapped (Fig. 8c). The
magnitude of velocities in the plume is several times ambient. In general, plume velocities are
greater for northward ambient flow than for southward ambient flow (~40 vs. 10 cm s-1) except
during upwelling conditions. For the unforced case with both ambient flow directions and for the
upwelling case with northward ambient flow, counterflow due to the geostrophic flow around the
plume is observed—on the coastal side of the plume for northward ambient flow and on the
seaward side of the plume for southward ambient flow (see plan view velocity maps in Fig. 7 and
related discussion). For a wind stress of 0.5 dynes cm-2 wind-driven alongshelf flow adds or
subtracts (depending on wind and ambient current directions) about 5 cm s-1 to the flow field, but
only in the upper 5 m or less (Fig. 8c). When wind stress increases both the magnitude and depth
of influence of the wind-driven frictional flow increase (Fig. 9c, lower panels).
To separate contributions to the alongshelf velocity from buoyancy forcing, wind forcing
and ambient flow, time series of velocity near the surface and in the interior are compared at sites
in the coastal current within (“nearshore”) and outside (“offshore”) the plume (Fig. 10).
Measurement depths are the surface grid point and either 22 m or 85 m in bottom depths of 36
and 140 m at nearshore and offshore sites, respectively, about 140 km downstream of the river
mouth (see locations in Figure 2). Note that surface measurement depths are within the surface
Ekman layer whereas the deeper measurement depths are well outside the bottom Ekman layer.
The heavy lines in the second row of figures display model results for runs with an ambient flow
but without a plume—a “control” case. These data illustrate that nearshore flow is about 3 cm s-1
below ambient both at the surface and in the interior even in the absence of a plume. This
decrease is due to frictional drag on the coastal wall. Thus, in every case we can expect a slight
frictional reduction of the nearshore velocity in comparison to that farther offshore.
14
The time series show that the majority of the variance occurs in the nearshore surface
layers and that this variance increases when ambient flows or wind driving are added to the
forcing. In contrast to the surface layers, the plume appears to have little effect on the interior
velocity field—offshore and nearshore time series are virtually (with the small deficit due to
frictional effects nearshore as mentioned above). In the absence of wind driving or ambient flow
(top row) alongshelf currents of about 40 cm s-1 are generated by the freshwater plume at this
location 140 km from the river mouth. The total velocity increases by the value of the ambient
flow when ambient flow is added (second row). When wind stress is added to the pre-existing
plumes formed with ambient flow at day 13.3, velocities decrease in the weaker wind case and
then increase dramatically when the buoyancy from the bulge region reaches the measurement
site (third row). When this freshwater passes the velocities return to levels attained in the absence
of wind forcing. The rapid increase is due primarily to the increasing lateral density
gradient—hence geostrophic flow—as the freshwater is moved onshore in the surface Ekman
layer (see Fig. 8a). The increase occurs sooner and is greater (up to 115 cm s-1 above ambient)
with greater wind stress (compare the 1.4 dynes cm-2 case with the 0.5 dynes cm-2 case in Figure
10) .
Wind-driven contributions to the variance are evident in the surface layer offshore of the
plume as a slight increase (~5 cm s-1) over the ambient flow that remains constant over the 3 days
shown (Fig. 10, third row, left; note level of dashed line relative to arrow). This increase is not
observed in the interior (third row, right; dashed line), an indication that the flow is entirely
frictional. For greater stress, a velocity increase with time in both the interior (bottom right,
dashed line) and surface layer outside the plume (bottom left, dashed line) suggests that this
increase (10 cm s-1 over 2 days) is geostrophic rather than frictional.
3.2. Effect of wind stress magnitude on freshwater transport
To study the mechanisms responsible for the advection of freshwater as a function of
applied wind stress, the freshwater transport, Q, was calculated across a rectangular control
volume enclosing a region off the river mouth (shown in Fig. 2a) normalized by the river
discharge. Thus,
15
S SS
u n dsest
amb
amb= −
∫∫1
' • '
where Qest is the river discharge, S is the salinity, Samb is the background salinity (33 psu in our
case), u' is the total velocity (for the “total transport”) or the geostrophic velocity obtained from
the pressure field (for the “geostrophic transport”), and n' is the unit vector normal to the surface
of the control volume with a surface element ds (= dxdz or dydz, depending on the transect
chosen). The sides of the control volume were located 80 km north of the estuary (northern
transect), 40 km south (southern transect) and 50 km west (western transect). The control volume
was chosen so that it framed the bulge in the base case at the time at which the winds are added
in the different experiments. The total transport as well as the transport due to geostrophic flow
through each element were obtained as a function of time. The calculations were performed for
both northward and southward ambient flows of 10 cm s-1 and for several wind stress
magnitudes. All runs were spun-up with the average river discharge (7000 m3 s-1) and ambient
flow for 13.6 days, after which a uniform alongshore wind stress (either upwelling or
downwelling) was applied. The run with the lowest wind stress (τ = 0.5 dynes cm-2) had a
duration of almost 6 days; the run with τ = 1.4 dynes cm-2 had a duration of about 3 days; and the
highest wind stress run (τ = 3 dynes cm-2) terminated after about one day due to a violation of the
CFL criterion.
Results show that downwelling winds enhance northward transport of freshwater across
the northern transect by as much as a factor of ten over the plume formed under no wind
conditions for northward ambient flow, and a factor of five for southward ambient flow (Fig. 11,
compare two top panels). In general, northward and westward transports are much greater for
northward ambient flow (top two left panels) than for southward ambient flow (top two right
panels). The transport increases immediately when wind stress is applied, with a more rapid rate
of increase for higher stress. The transport peaks in less than 1.75 days in all cases shown, with
shorter times associated with higher stress. The peak in transport occurs when the primary
freshwater bulge passes the transect. Note that the maximum occurs somewhat earlier here than
in the velocity time series in Figure 10 due to the closer proximity of the transect to the river
mouth. The discussion in the last section demonstrates that the onset of downwelling-favorable
wind stress is accompanied by large flows in the surface Ekman layer which transport the
freshwater toward shore. The increased cross-shelf density gradients generate enhanced
16
alongshelf flow which produces the transport peak across the northern transect in Figure 11
(upper left). After the bulge of freshwater passes, transports decrease almost to their pre-wind
levels. However, the ongoing Ekman transport confines the freshwater near the coast so that
geostrophic alongshelf currents and hence total transports remain higher than in the no wind
case. Comparison between total transport and geostrophic transport through the northern transect
shows that the transport is primarily geostrophic (Fig. 11). Small but significant differences are
observed between total and geostrophic transport across this transect and also, at times, across
the southern transect. However, the differences disappear once the bulge passes the transect. This
indicates that the ageostrophic flow is due to non-linear advection in the bulge area rather than to
near surface wind-driven frictional flow. Frictional flow is clearly inefficient at driving transport
in the alongshelf direction.
On the other hand, frictional ageostrophic flow is the dominant transport mechanism for
cross-shelf flow. For both northward and southward ambient flow conditions, cross-shelf
transport of freshwater through the western transect occurs only under upwelling conditions (Fig.
11, middle panels; cases with zero transport are not shown). For both northward and southward
ambient flows, the cross-shelf ageostrophic transport moves about as much freshwater as the
alongshelf, primarily geostrophic transport.
Our results have shown that a plume generated under a constant ambient flow will tend in
the direction of the ambient flow (Fig. 7). An important question with respect to plume dynamics
is under what wind conditions the direction of a plume can be reversed. Freshwater transports
show that with northward ambient flow conditions only strong and persistent upwelling winds
generate significant freshwater transport across a transect 40 km south of the river (Fig. 11,
bottom left). The transport must be sufficient to overcome the natural tendency of the plume to
turn northward as well as the northward ambient flow. For our particular model configuration,
such an event required a wind stress of over 1.4 dynes cm-2 lasting longer than 2 days. With
southward ambient flow, on the other hand, the freshwater transport is easily reversed with the
weakest wind stress (Fig. 11, top and bottom right panels).
For northward ambient flow twice as strong, freshwater transports are very similar to the
case with the ambient flow shown in Figure 11 except that the coastal current transports nearly
double the amount of freshwater (as noted also by Fong, 1998). Maximum transport for
downwelling winds, although the same in magnitude, is achieved sooner than with a weaker
17
ambient flow (not shown). For upwelling winds with stronger northward ambient flow, more
freshwater is transported through the northern transect and less through the western transect than
for lower ambient flow (not shown).
3.3. Freshwater pool formation
As mentioned previously, the structure of the plume differs remarkably when an ambient
flow is added to a freshwater discharge. The most outstanding result, apart from the deformation
of the bulge, is the formation of distinct freshwater pools that detach from the bulge and are
advected with the ambient flow (Fig. 7). These pools all have anticyclonic motion, producing
counterflows adjacent to the coast (for northward ambient flow; Fig. 7a) or in the region offshore
of the coast (for southward ambient flow; Fig. 7b). Oey and Mellor (1993) described the
formation and detachment of freshwater pools in their plume model with no ambient flow.
However, Fong (1998) attributed the features in their model to instabilities around the fringe of
the plume resulting from lack of horizontal resolution. More recently, Yankovsky (2000)
described the periodic shedding of anticyclones in the presence of a weak downshelf ambient
flow. As in the present model Yankovsky (2000) has a sloping bottom (exponential) and constant
discharge.
For a river discharge of 7000 m3 s-1, larger, more energetic pools containing fresher water
at a given time are formed under northward ambient flow conditions than under southward
ambient flow conditions of the same magnitude (compare Figs. 7a and 7b). Also, we note that
pools produced with southward ambient flow conditions are located further offshore than pools
produced under northward flow conditions. Along-plume salinity sections about 15 km from the
coast illustrate differences in depth structure of the plume and its pools formed under ambient
flows of the same magnitude but opposite directions (Fig. 12). In particular, the pools formed
under northward ambient flow conditions are fresher than those formed with southward ambient
flows. They also have a greater thickness, although weaker stratification, at a given time after
formation than pools formed under southward flow conditions. This is due to the fact that with
northward ambient flow the freshwater transport is composed of the buoyancy-induced coastal
current and the ambient flow; on the other hand, for southward ambient flow, part of the
freshwater is transported northward by the coastal current.
18
The rate of formation and spatial structure of the fresh pools could be affected by the
strength and direction of the ambient flow as well as by river discharge rate. To investigate the
characteristics of the pools in more detail fifteen experiments were performed with a variety of
discharge rates and ambient flows. Results indicate that formation characteristics differ between
northward and southward ambient flow cases. For northward ambient flow the rate of pool
formation depends primarily on the magnitude of the ambient flow. For example, with an
ambient flow of 4 cm s-1, one pool is formed with a variety of discharge rates (compare Figs. 13a
and 13b); with an ambient flow of 10 cm s-1, three pools are formed with a variety of discharge
rates (compare Figs. 7a and 13c).
For southward ambient flow pool formation rate is primarily determined by the
magnitude of the ambient flow as it was for northward ambient flow. However, different
formation regimes were identified for low and high discharge rates. For a discharge rate of 7,000
m3 s-1 pools form within the thin upshelf elongation of the bulge (Fig. 7b). In contrast, for a
discharge rate of 14,000 m3 s-1 the whole bulge detaches to generate a distinct pool (Fig. 13d). In
this case the discharge rate is sufficiently large to rapidly form another bulge about to detach
from the river mouth at 28 days (Fig. 13d). Pools formed in this manner are larger, deeper and
have stronger velocities than their lower discharge counterparts.
In contrast to the rate of pool formation, the cross-shore scale of the pools appears to be a
function of both river discharge rate and ambient flow—pools are wider with greater discharge
and with lower ambient flow (compare examples in Figs. 7 and 13). Typical pool scales are
about 10-30 km. A parameter analysis of the spatial scale, L, of the freshwater pools shows that
pool width depends on the characteristic velocity of the pools, U, as well as the Coriolis
parameter, f, and estuary width. The model runs used to determine the scaling are listed in
Table 1. All runs have the same northward ambient flow (10 cm s-1). Southward ambient flow
runs were excluded because of the extra variable that the two different pool formation regimes
introduces. The velocity scale was measured as the average of the magnitude of the velocity
within the largest pool (the one that was first formed) at about 28 days. The length scale was
measured as the distance between the maximum and minimum alongshore velocity along a
cross-shore transect through the center of the largest pool at about 28 days. The length scale was
also measured from the salinity field (as the radius of the 32 psu contour comprising the pool)
with analogous results. Results show that for the same ambient flow and discharge rate pool
19
scale decreases significantly with latitude, e.g., from 30 km at 20˚N to 15 km at 60˚N (Table 1).
The width scale of the pools also decreases significantly with increasing estuary width. In
general, pool width scales as U/f (Fig. 14). The near linear relationship between the scale of the
pools and U/f shows that the pools formed in the different model runs all have a similar Rossby
number, U/fL. Values range between 0.3 and 0.5, with a best linear least-square fit of 0.41. This
shows that although rotation is dominant, nonlinear advection of momentum is significant within
the pools.
Preliminary calculations of the form drag on isopycnal surfaces within the pools suggest
that for a northward ambient flow the form drag differentially accelerates the fluid in the
horizontal to reduce the pre-existing horizontal shear (not shown). Thus the pools are formed as a
result of barotropic instabilities, gaining energy from the lateral shear. For southward ambient
flow the instabilities are baroclinic, gaining energy from the vertical shear. A complete analysis
of the formation of the anticyclonic pools is a subject of ongoing research and is beyond the
scope of this paper.
4. Summary and Discussion
A numerical model was used to study the factors affecting the spatial structure and
variability of a high discharge buoyant plume over a sloping shelf. Response of the plume to
ambient flows (both northward and southward), periods of wind reversals and a variety of
freshwater discharge rates were examined. The model parameters are based on the Columbia
River plume and its oceanographic environment, and, in spite of being a somewhat idealized
model (no continental slope and no stratification in the coastal ocean), the model appears to
capture much of the reported seasonal behavior of the Columbia River plume. The model has
also distinguished features hitherto unreported in the literature—separating pools with both
directions of ambient flow and a “dual-mode” plume structure (i.e., branches both upstream and
downstream of the river mouth) in the summer season.
Various numerical details were found to affect model results. In particular, a fine vertical
resolution of the surface-trapped plume along with the advection scheme Smolar_2 proved
critical to avoiding instabilities around the fringe of the plume’s bulge. These instabilities were
completely eliminated by employing a recursive version of this advection scheme (Smolar_r).
The choice of vertical mixing coefficients (or a background value if calculating coefficients with
20
the Mellor-Yamada 2.5 turbulence closure scheme) had a strong influence on the upshelf
penetration of the plume. The degree of penetration increases as the vertical mixing coefficient
increases. Some penetration occurs even when the bottom is flat, although the propagation of an
eddy-like feature derived from the bulge was observed only with a sloping bottom.
The model plume's response to winds is very rapid (several hours) as is the case for the
Columbia River plume, which responds to winds in a matter of 3-6 hours (Hickey et al., 1998).
The plume is moved onshore during periods of downwelling wind and offshore during periods of
upwelling wind, regardless of the direction of the ambient flow typically northward in winter and
southward in summer off the Washington coast. Both alongshelf velocity and freshwater
transport increase by as much as a factor of 10 for a brief period following the onset of wind
stress when the low salinity water in the bulge moves onshore, increasing lateral gradients and
hence alongshelf geostrophic flow. Once the bulge water has been transported through the area,
transports and velocities return almost to their pre-wind levels for weak wind stress, although
transport remains higher than in the no wind case due to the onshore trapping of the continuous
supply of light water by the Ekman transport. Transport increases with increasing wind stress;
with higher stress an alongshelf geostrophic wind-driven component adds to the total flow and
enhances the alongshelf transport.
Plume-related velocities are highly three dimensional, with counterflows occurring
frequently as a result of near-geostrophic transport around features of lower salinity water as well
as the competing effects of the ambient flow and the plume. Plume-induced velocities are
generally confined to the near surface region of lower salinity, as observed in the Columbia
plume (Hickey et al., 1998). Both the width and depth of the plumes during the winter
simulations are similar to those shown in Hickey et al. (1998); namely, for the majority of the
freshwater, 5-20 km width and 10-40 m depth for downwelling and ~70-100 km width and less
than 10 m depth for upwelling.
The model results challenge longstanding notions about the Columbia plume: first, that
the plume orientation is in a relatively stable southwest position in summer (see e.g., Barnes et
al., 1972; Hickey, 1989). The model results show that with average discharge conditions (7,000
m3 s-1) a summertime downwelling event of typical magnitude and duration can erode and advect
away the bulk of the southwestward plume to the north of the river mouth over several days. The
surface Ekman transport first pushes the southwestward tending plume of freshwater against the
21
coast; once there, the geostrophic flow associated primarily with the lateral density gradients
transports the plume northward until it reaches almost a typical “winter downwelling” position.
Only a weak plume remnant is left off the coast south of the river mouth. The return to upwelling
conditions moves the plume offshore north of the river mouth as it does in winter with northward
ambient flow conditions, but the southward ambient flow directs the newly formed bulge region
south-southwest as opposed to north-northwest in winter. A plume originating from a larger
discharge event (e.g., 14,000 m3 s-1) would be expected to have higher stratification and a larger
volume and hence would be more difficult to mix or displace. The presence of ambient
stratification, which was not included in our model, might also inhibit erosion of plume water by
limiting vertical mixing.
A second traditional notion of the Columbia plume is that the plume is only oriented
southwest in summer (Barnes et al., 1972; Hickey, 1989). The model results show that even
when the plume tends southwest due to the ambient southward flow, a narrow plume hugs the
coast north of the river mouth. Thus, the plume frequently has both northward and southward
branches at the same time (Fig. 7b). Careful inspection of available observations show that this
does indeed appear to be the case. In every available survey, light water is observed in summer
off the Washington coast—over the mid to outer shelf during upwelling events and next to the
coast during downwelling events (e.g., Hermann et al., 1989, Figs. 6.7b and 6.7c; Horner et al.,
2000). The presence of this buoyant coastal current is also consistent with the mean northward
flow that has been reported in this region in summer near the coast (Hickey, 1989). This
phenomenon has been overlooked in previous studies—the presence of light water was usually
attributed to an isolated newly emerging plume rather than a persistent plume as suggested by the
model results.
Observations of the Columbia plume in winter showed that in spite of periods of
persistent upwelling the plume never changed direction from generally north-northwestward to
southwestward (Hickey et al., 1998). The model results suggest that the difficulty in reversing
the plume direction in winter is due in part to the northward direction of the mean ambient flow,
which is in the same direction as the natural rotational tendency of the plume. For the model’s
winter conditions the plume develops substantial reversals, ones that reach the measurement
section 40 km south of the river mouth only for southward wind stress greater than 1.4 dynes
cm-2 blowing for at least two days. Such strong upwelling wind events in the winter are rare.
22
Another important result from the model is the demonstration that the addition of an
ambient flow to the river plume model elongates the freshwater bulge in the direction of the
ambient flow leading to the generation of distinct freshwater anticyclonic pools that detach from
the bulge. Such pools have been observed in both northward and southward tending plumes from
the Columbia. In particular, winter observations revealed a strong counterflow next to the coast
downstream of the mouth consistent with such pool formation (Hickey et al., 1998). For very
large discharges and southward ambient flow conditions typical of summer in the Pacific
Northwest (14,000 m3 s-1) plumes are more likely to form detached eddies. Distinct low salinity
pools have been observed in the southwest tending Columbia plume (e.g., Barnes et al., 1972;
Fiedler and Laurs, 1990; Hickey 1989) and have sometimes been attributed to tidal flows (see
Fig. 1b). Our model results provide another possible mechanism for pool formation, one that
does not depend on a time-variable source.
The rate at which pools form is a function of the strength of the ambient flow in either
direction but not the river discharge rate. For example, for northward ambient flow conditions,
only one pool formed with an ambient flow of 4 cm s-1; three pools formed with an ambient flow
of 10 cm s-1 for a variety of discharge rates. For southward ambient flow, the structure of the
pools does vary with discharge rate. Low discharge rates produce thin, weakly stratified pools;
large discharge rates result in more vigorous, deeper and more stratified pools because the entire
bulge can completely detach from the river mouth. The size of the pools depends not only on the
magnitude of the ambient flow, but also on discharge rate, width of the estuary mouth and
latitude.
River plumes are highly important for distribution of sediment as well as for
phytoplankton growth and transport, larval transport and movement of juvenile fish. A high
volume river plume such as we model here can impact thousands of square kilometers of a
coastal region. The plume affects stratification, provides fronts that may act as lateral boundaries
and induces local currents that can be several times the strictly wind-driven flow. The presence
of a plume enhances cross-shelf movement of suspended and dissolved material by an order of
magnitude over that in a region of wind-driven transport alone. This model has taken an
important step in examining the variability of such plumes in realistic conditions of ambient flow
and changeable wind driving. However, several questions remain. For example, what are the
formation mechanisms for the anticyclonic pools that form with the ambient flows; how would
23
ambient stratification and realistic bottom slope affect plume structure and variability; what are
the respective roles of mixing and advection in distributing freshwater? These and other
questions are the subject of our continuing research.
Acknowledgements
We would like to thank Alan Blumberg for making the numerical code available to us
and Derek Fong, Rich Signell and John Klinck for their assistance with the model
implementation. This work was funded in part by grants to B. Hickey (the Pacific Northwest
Coastal Ecosystem Regional Research program, a National Oceanic and Atmospheric
Administration Coastal Ocean Program grant #NA960PO238), Washington Sea Grant (grant
#NA76RG0119 and NA76RG0119 AM08) and the National Science Foundation (grant
#OCE968186). Ms. García Berdeal was funded primarily by a fellowship from the Fundación
Pedro Barrié de la Maza, A Coruña (Spain).
24
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27
Table 1. Parameter values for the model runs used to study the length scale L of the freshwaterpools. Q is the river discharge, f is the Coriolis parameter, w is the width of the estuary and U isthe scale of the velocity within the pools. Each run was made for 28 days. Ambient flow wasnorthward at10 cm s-1 for each case.
Model Run Q (m3 s-1) f (s-1) x104 w (km) U (m s-1) L (km)B4 1500 1.046 4 0.5 10B5 7000 1.046 4 0.8 20B6 14000 1.046 4 0.8 25C1 7000 0.497 4 0.6 30C2 7000 1.260 4 0.7 18C3 7000 1.046 14 0.6 15
28
Figure Captions
Figure 1. (a) SST image of the Washington-Oregon coast from 23 February 1991, illustrating
the Columbia River plume during an upwelling-favorable wind event in winter. (b) CZCS image
from 24 May 1982 illustrating the Columbia River plume during peak river flow in early summer
with southward winds (adapted from Fiedler and Laurs, 1990).
Figure 2. (a) Model domain and horizontal resolution in the x-y plane. Location of the estuary is
y=120 km for winter runs and y=280 km for summer runs. Symbols denote locations for data
used in time series in Figure 10. The rectangular region marked in the figure indicates the control
volume used in the freshwater transport calculations in Section 3.2. (b) Model domain and
resolution in the x-z plane. Dots denote the center of the grids.
Figure 3. Model sensitivity to vertical resolution and advection scheme. Surface salinity (psu)
contours at t=14 days for (a) 12 layers in the vertical and Smolar_2, (b) 25 layers in the vertical
and Smolar_2, (c) 22 layers in the vertical and Smolar_r. For all three runs a freshwater
discharge rate of 7000 m3 s-1 is used, the diffusivities are calculated by the Mellor-Yamada
closure scheme with a background value of 10-6 m3 s-1 and the bottom slope is 2x10-3. Contours
are drawn from 31 to 13 psu in units of 3.
Figure 4. Model sensitivity to vertical mixing coefficients and bottom slope. Surface salinity
(psu) contours at t=14 days for a background vertical mixing of (a) 10-4 m2 s-1 and bottom slope
of 2 x 10-3, (b) 10-3 m2 s-1 and a bottom slope of 2 x 10-3, and (c) 10-3 m2 s-1 with a flat bottom. The
freshwater discharge rate is 7000 m3 s-1 and winds and ambient flow are zero. Contours are
drawn from 32 to 12 psu in units of 2.
Figure 5. Evolution of surface salinity (psu) for northward ambient flow conditions in response
to 6 days of downwelling-favorable winds followed by 6 days of upwelling-favorable winds at
(a) 13 days, (b) 15 days, (c) 19 days, (d) 21 days, (e) 22 days and (f) 25 days with a northward
ambient flow of 10 cm s-1. Winds change direction after 19 days immediately after (c). The
distance between tick marks is 20 km.
29
Figure 6. Evolution of surface salinity (psu) for southward ambient flow conditions in response
to 6 days of downwelling-favorable winds, followed by 6 days of upwelling-favorable winds at
(a) 13 days, (b) 15 days, (c) 16 days, (d) 19 days, (e) 21 days and (f) 25 days with a southward
ambient flow of 10 cm s-1. Winds change direction after 19 days immediately after (d). The
distance between tick marks is 20 km.
Figure 7. Surface salinity (psu) contours and surface velocity vectors (m s-1) at t = 28 days for
(a) northward ambient flow of 10 cm s-1 and (b) southward ambient flow of 10 cm s-1. River
discharge for both cases is 7000 m3 s-1.
Figure 8a. Salinity contours at 2 psu intervals for a cross-shore section 40 km north of the river
mouth for northward ambient flow conditions (left panels) and 40 km south of the river mouth
for southward ambient flow conditions (right panels). Results are shown for ambient flow only
(top panels), after 13.3 days of ambient flow and 3 days of downwelling winds (middle panels),
and after 13.3 days of ambient flow and 3 days of upwelling winds (bottom panels).
Figure 8b. Cross-shelf velocity structure (m s-1) corresponding to panels in Figure 8a. Offshore
flow is shaded. Note that to show the bottom boundary layer, the vertical sale differs from that
used in Figures 8a and 8c. To aid visualization of this model “snapshot” data were smoothed
with a 5-7 point binomial filter. Contours are drawn at 0.0 and +/- 0.05, 0.1, 0.3, 0.5 and 0.7 m
s-1. Dashed contour levels fall between those in the list. In this figure only contour maxima are
labeled.
Figure 8c. Alongshelf velocity structure (m s-1) corresponding to panels in Figures 8a and 8b.
Southward flow is shaded. To aid visualization of this model “snapshot” data were smoothed
with a 5-7 point binomial filter. Contours are drawn at 0.0 and +/- 0.1, 0.2, 0.4, 0.6, and 0.8 m s-1.
Dashed contour levels fall between those in the list. Ambient flow is 0.1 m s-1.
Figure 9a, 9b, 9c. Comparison of (a) salinity, (b) cross-shelf velocity and (c) alongshelf
velocity for two different values of downwelling-favorable wind stress, applied for 3 days
following 13.3 days of ambient flow. Contour intervals, smoothing and shading are as in Figure
30
8. Dramatic structure in the velocity fields near the left margin are strictly numerical and are due
to the presence of the boundary at 150 km.
Figure 10. Time series of velocity at sites within the plume (nearshore) and outside the plume
(offshore) for surface and interior flow during northward ambient flow. Locations are shown in
Figure 2. The sites are in 36 and 140 m bottom depths; the measurement depths are the surface
grid point and 22 or 85 m, the latter depth being well above the bottom boundary layer. Heavy
lines and dashes show results with an ambient flow but no plume. Wind was applied after 13.3
days of forcing with ambient flow (data near the end of the second row). The initial spike before
day 14 in the bottom two left panels is a transient response to the onset of wind forcing and can
be ignored in the context of the discussion. Arrows on the side of the panels indicate ambient
flow magnitude. Note halving of vertical scale in bottom 2 rows.
Figure 11. Total freshwater transport (heavy lines) and geostrophic transport (faint lines) across
northern (N), western (W) or southern (S) transects for northward (left panels) and southward
(right panels) ambient flows of 10 cm s-1 and either downwelling or upwelling-favorable wind
stress. The magnitude of the wind stress (in dynes cm-2) is indicated next to the corresponding
curve. The zero winds case is labeled as “0.0”. Note change in y-axis scale for transport across
the southern transect in bottom two panels.
Figure 12. Along-plume salinity structure15 or 18 km from the coast with ambient flows in both
northward and southward directions but with no winds applied. River discharge rate is 7000 m3
s-1. To aid visualization of this model “snapshot” data were smoothed with a 5 point binomial
filter.
Figure 13. Surface salinity (psu) contours and surface velocity vectors (m s-1) at t = 28 days for
selected runs with various discharge rates and ambient flows.
Figure 14. Relationship between the characteristic length scale (L) of the freshwater pools and
the velocity scale of the pools (U) divided by the Coriolis parameter (f). The straight line shows
31
the linear, least squares fit. The inverse of the slope (the Rossby number) is 0.41 (r2 = 0.96;
correlations exceeding 0.75 are significant at the 95% level).
_ 4
6o N
4
6o N -
47o N
- 125o W
124
o W
48o N
-
45o N
-
(a)
(b)
Figu
re 1
125
o W12
4o W
120 100 80 60 40 20 0 0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
x (km)
y (k
m)
Plan view
120 100 80 60 40 20 0 −300
−200
−100
0
x (km)
z (m
)
Section (x−z)(a) (b)
x
Figure 2
x
120 80 40 0
80
120
160
200
240
280
x (km)
y (k
m)
31
25
19 13
Smolar_2
12 layers
t=14 d
120 80 40 0 x (km)
3125
19
13
Smolar_2
22 layers
t=14 d
120 80 40 0 x (km)
3125 19
13
Smolar_r
22 layers
t=14 d
a) b) c)
Figure 3
120 80 40 0
80
120
160
200
240
280
x (km)
y (k
m)
3228
24
UMOL=10−4 m2 s−1
α=2 x 10−3
t=14 d
120 80 40 0 x (km)
32
28
UMOL=10−3 m2 s−1
α=2 x 10−3
t=14 d
120 80 40 0 x (km)
32
28
24
UMOL=10−3 m2 s−1
α=0
t=14 d
a) b) c)
Figure 4
(a) No wind (b) Downwelling (c) Downwelling
(d) Upwelling (e) Upwelling (f) Upwelling
Northward ambient flow
t = 13 days t = 15 days t = 19 days
t = 21 days t = 22 days t = 25 days
40 km
Figure 5
Southward ambient flow
(a) No wind (b) Downwelling (c) Downwelling
(d) Downwelling (e) Upwelling (f) Upwelling
t = 13 days t = 15 days t = 16 days
t = 19 days t = 21 days t = 25 days
40 km
Figure 6
(a)
Nor
thw
ard
ambi
ent f
low
, no
win
ds
(b)
Sout
hwar
d am
bien
t flo
w, n
o w
inds
Q =
700
0 m
3 s-1, v
amb=
10
cm s
-1
Q =
700
0 m
3 s-1
, , v am
b= -
10 c
m s
-1
x (k
m)
x (k
m)
1
.0 m
s-1
1.
0 m
s-1
t = 2
8 da
ys
t =
28
days
1
20
80
40
1
20
80
40
-
40 -
40
0
0
4
0
40
80
80
1
20 1
20
1
60 1
60
y (km)
y (km)
Fig
ure
7
−20
−15
−10
−5
0
z(m
)
Northward flow, no wind
32
28
24
20
32.75
t=13.3 d
Southward flow, no wind
32
2824
32.75
t=13.3 d
−20
−15
−10
−5
0
z(m
)
Northward flow, downwelling, τ = 0.5
3228
24
32.75
t=16.4 d
Southward flow, downwelling, τ = 0.5
32
32.75
t=16.4 d
120 100 80 60 40 20 −20
−15
−10
−5
0
x(km)
z(m
)
Northward flow, upwelling, τ = −0.5
32
28
32.75
t=16.4 d
120 100 80 60 40 20 x(km)
Southward flow, upwelling, τ = −0.5
32
2832.75
t=16.4 d
28
24 24
~33.0
~33.0 ~33.0
~33.0 ~33.0
Figure 8a
~33.0
z(m
)
t=13.3 d
−300
−250
−200
−150
−100
−50
0
t=13.3 d
z(m
)
t=16.4 d
−300
−250
−200
−150
−100
−50
0
t=16.4 d
x(km)
t=16.4 d
140 120 100 80 60 40 20 x(km)
z(m
)
t=16.4 d
0
140 120 100 80 60 40 20 −300
−250
−200
−150
−100
−50
0
−0.1 −0.05
0.1 0.1
−0.5 −0.3
Northward flow, no wind Southward flow, no wind
Northward flow, downwelling, τ = 0.5 Southward flow, downwelling, τ = 0.5
Northward flow, upwelling, τ = −0.5 Southward flow, upwelling, τ = −0.5
Figure 8b
z(m
)
Northward flow, no wind
0.10.2 0.4
0
0.6
t=13.3 d
−20
−15
−10
−5
0Southward flow, no wind
0−0.1
−0.05
t=13.3 d
z(m
)
Northward flow, downwelling, τ = 0.5
0.1
0.20.4
0.15
t=16.4 d
−20
−15
−10
−5
0Southward flow, downwelling, τ = 0.5
0
0.1
−0.075
−0.05
t=16.4 d
x (km)
z(m
)
Northward flow, upwelling, τ = −0.5
0
−0.1−0.2
0.2
0.1
0.1
0.1
t=16.4 d
120 100 80 60 40 20 −20
−15
−10
−5
0
x (km)
Southward flow, upwelling, τ = −0.5
−0.
1
−0.2−0.1 −0.15
t=16.4 d
120 100 80 60 40 20
−0.1 −0.2
−0.4
Figure 8c
−20
−15
−10
−5
0
z(m
)
Northward flow, downwelling, τ = 0.5
3228
2432.75
t=16.4 d
140 120 100 80 60 40 20 −20
−15
−10
−5
0
x(km)
z(m
)
Northward flow, downwelling, τ = 1.4
322832.75
t=16.4 d
Northward flow, upwelling, τ = −0.5
32
28
32.75
t=16.4 d
140 120 100 80 60 40 20 x(km)
Northward flow, upwelling, τ = −1.4
32
28
32.75
t=16.4 d
~33.0
24 24
~33.0
~33.0 ~33.0
Figure 9a
z(m
)
Northward flow, downwelling, τ = 0.5
0.050.1
0
0.025
t=16.4 d
−20
−15
−10
−5
0
x(km)
z(m
)
Northward flow, downwelling, τ = 1.4
0.05
0.06
0.02
5t=16.4 d
140 120 100 80 60 40 20 −20
−15
−10
−5
0
Northward flow, upwelling, τ = −0.5
−0.05
−0.1−0.3
0
0
−0.025
t=16.4 d
x(km)
Northward flow, upwelling, τ = −1.4
−0.
05
−0.1−0
.3
−0.5−0.3
00
0
−0.0
25
t=16.4 d
140 120 100 80 60 40 20
0.05
−0.1
−0.5
−0.1
Figure 9b
z(m
)
Northward flow, downwelling, τ = 0.5
0.1
0.20.4
0.15
t=16.4 d
−20
−15
−10
−5
0
x (km)
z(m
)
Northward flow, downwelling, τ = 1.40.4
0.3
0.2
0.2
t=16.4 d
140 120 100 80 60 40 20 −20
−15
−10
−5
0
Northward flow, upwelling, τ = −0.5
0.1
0.1
0.2
0.1 0
−0.1
t=16.4 d
x (km)
Northward flow, upwelling, τ = −1.4
0−
0.1−0.2
0.10.2
0.1
0 0
0.1
t=16.4 d
140 120 100 80 60 40 20
−0.05
−0.2
Figure 9c
0 5 10 15
0
0.2
0.4
0.6v
(m s
−1 )
0 5 10 15
0
0.2
0.4
0.6
0 5 10 15
0
0.2
0.4
0.6
v (m
s−
1 )
0 5 10 15
0
0.2
0.4
0.6
14 16 18
0
0.4
0.8
1.2
v (m
s−
1 )
14 16 18
0
0.4
0.8
1.2
14 16 18 0
0.4
0.8
1.2
time (days)
v (m
s−
1 )
14 16 18 0
0.4
0.8
1.2
time (days)
Uamb
=0
Uamb
=10
Uamb
=10
Uamb
=10
SURFACE
nearshore
offshore τ = 0
τ = 0
τ = 0.5
τ = 1.4
no plume
INTERIOR
Figure 10
12 14 16 18 200
2
4
Northward ambient flow
Nor
mal
ized
FW
Tra
ns.
12 14 16 18 20
−4
−2
0
Nor
mal
ized
FW
Tra
ns.
12 14 16 18 20−0.1
−0.05
0
time (days)
Nor
mal
ized
FW
Tra
ns.
12 14 16 18 200
2
4
Southward ambient flow
12 14 16 18 20
−4
−2
0
12 14 16 18 20
−1
0
1
time (days)
N
W
S
downwelling
downwelling upwelling
upwelling
0.0
3.0
1.4
0.5
1.4
0.5
3.0
1.4
0.5 1.4
0.5
3.0
1.4 0.5
1.4 0.5
0.0
0.0
0.0
0.0
0.0
Figure 11
N
W
S
downwelling
upwelling
z(m
)
Northward flow, no wind
33
32
28 2420
16
32.75
15 km offshoret=28 d
−80 −40 0 40 80 120 160 200−35
−30
−25
−20
−15
−10
−5
0
Distance from mouth (km)
z(m
)
Southward flow, no wind
33
3228
24 16
32.75
18 km offshoret=28 d
−160 −120 −80 −40 0 40 80 120 −35
−30
−25
−20
−15
−10
−5
0
Figure 12
1.00 m s-1 1.00 m s-1
1.00 m s-1 1.00 m s-1
(a) Q = 1500 m3 s-1, vamb
= 4 cm s-1 (b) Q = 7000 m3 s-1, vamb
= 4 cm s-1
(c) Q = 14,000 m3 s-1, vamb
= 10 cm s-1 (d) Q = 14,000 m3 s-1, vamb
= -10 cm s-1
0 0
40 40
80 80
120 120
160 160
-40 -40
120 80 40 120 80 40 x (km) x (km)
y (
km)
y (
km)
y (
km)
y (
km)
120 80 40 x (km)
120 80 40 x (km)
-40
0
40
80
120
160 80
40
0
-40
-80
-120
Figure 13
0 5 10 150
5
10
15
20
25
30
35
U/f (km)
L (k
m)
Figure 14