Getting
to Know OSCURS, REFM's Ocean Surface Current Simulator
By W. James Ingraham, Jr.
jim.ingraham@noaa.gov
Alaska Fisheries Science Center
Originally published
in the Alaska Fisheries Science Center Quarterly Report, April-May-June,
1997.
The quest for knowledge
about ocean currents in the North Pacific Ocean and Bering Sea has
continued for centuries, with important discoveries made in the 1900s.
Early this century, knowledge came from drift bottle experiments,
flotsam recoveries from beaches, and reported multiple sightings of
drifting derelict ships, which led to the mapping of the dominant
horizontal patterns of permanent ocean currents that form the Subtropic,
Subarctic, and Bering Sea Gyres. More knowledge about the ocean-wide
geostrophic currents in the Subarctic Region came in the mid-1950s when
the first cross-ocean baseline Nansen bottle cast data were collected.
As a result of these salinity-temperature-depth profile data, indirect
calculations of surface flow provided the first seasonal and annual
long-term mean geostrophic current charts for the Subarctic Region from
1955 to 1959. By the mid-1970s, improved technology and navigational
systems brought direct current measurements via satellite-tracked
drifting buoys. Drifter trajectories showed that surface currents caused
by winds can be considerably different from the calculated geostrophic
currents and thus were very important in the calculation of surface
flow.
In the late 1970s
computer modeling scientists at the Alaska Fisheries Science Center's (AFSC)
Resource Ecology and Fisheries Management (REFM) Division began
developing a numerical model to investigate how ocean currents might
have influenced various fish populations in the North Pacific Ocean and
Bering Sea. Atmospheric sea level pressure measurements recorded daily
since 1946 at the U.S. Navy Fleet Numerical Meteorology and Oceanography
Center were used as proxy data to calculate wind and changes in sea
surface currents. This early numerical model set the stage for others to
expand on surface current modeling research and led to the development
of the Ocean Surface Current Simulations (OSCURS) model and its use in
ocean current variability research and fishery applications at the AFSC.
A Tool for
Retrospective Analyses
The OSCURS numerical
model is a research tool that allows oceanographers and fisheries
scientists to perform retrospective analyses of daily ocean surface
currents anywhere in a 90-km ocean-wide grid from Baja California to
China and from 10ºN to the Bering Strait from 1901 to the
present. The movement of ocean waters is an integrated response to
atmospheric forcing and reflects changes in wind climatology on the
ocean. This basic water flow is calibrated by comparing model
trajectories with trajectories measured with satellite-tracked
drifters. The OCSURS model is used to measure the movement of
surface currents over time, as well as the movement of what was in or on
the water. Ocean surface currents affect organisms suspended
in the water column such as fish eggs, small larvae, and plankton, and
may affect their survival by determining their location after a few
months of drift. Even swimming or migrating fish or mammals may
have their destinations significantly offset by currents or annual
variability of currents.
Fig.
1
Given a start location
and date anytime during 1901-present, the OSCURS model converts the
selected daily sea level pressure grid (Fig. 1)
to east-west wind velocity (u,v-wind) components and then u,v-current
grids using empirical functions. Adding the long-term mean
u,v-geostrophic currents then produces the total velocity field from
which the day's 24-hour water movement is calculated, using the velocity
interpolated within the grid at the start point. Continuing this
procedure from the end point of the previous day, daily, to the end date
forms a trajectory progressing from the start point (latitude,
longitude, date).
The key to OSCURS's
usefulness is in determination of the time and location for the
application. Trajectories can be computed for up to a year or more in
several modes: 1) one trajectory from one starting point, 2) several
trajectories from one starting point (as in a diffusion model), 3)
trajectories from a line of starting points, or 4) trajectories from a
grid of starting points. Such calculations can be repeated monthly,
seasonally, or annually to provide time-series data on sea surface
currents for use in fisheries analyses. As an added feature, when
5-day sea level pressure forecast grids are available, 5-day drift into
the future may be estimated.
A Numerical Model
The heart of OSCURS
involves calculating the movement of the ocean's near-sur face mixed
layer which varies seasonally from the surface to a depth of about 10
-30 m in summer and 50-100 m in winter. This mixed layer is
stirred consta ntly by the wind and moves with the momentum of a slab as
it quickly is mixed to its downward density limit at the thermocline or
halocline. Although mixe d layer depth data are not presently an
input for the model, OSCURS computes the daily horizontal u,v-velocity
fields of this mixed layer with experimentally established empirical
functions to get the vertically averaged flow (here called an ocean
surface current). The database consists of 20x44-grid-point
subsets from the U.S. Navy's 63x63-point 360-km northern hemisphere grid
of daily sea level pressures from 1946 to the present (Fig. 1). A recent
improvement to OSCURS has been the addition to the database of
time-interpolated daily sea level pressure grids from 1901 to 1945
calculated from National Center for Atmoshperic Research monthly mean
pressure fields. This addded data extends OSCURS' original analysis
capability of 1946-97 to include nearly a century of data. In OSCURS
each daily sea level pressure grid is interpolated to a finer 90-km
92x180-point grid for subsequent computations. At each grid point,
geostrophic u,v-wind is computed from the pressure gradient, rotated
about 15º to 20º toward lower pressure, and diminished about 20%. Then
ocean u,v-currents are computed at these same grid points, where current
speed (cm/sec) equals 4.8 times the square root of the wind speed
(m/sec), and the angle of deflection to the right of the wind increases
from 22º to 30º as the wind speed increases. Total currents,
therefore, are the sum of these wind-induced ocean currents plus the
long-term mean geostrophic currents (0/2,000 decibars) which were
computed separately on the same grid from the long-term mean ocean
temperature and salinity fields (0-2,000 m). Because OSCURS is intended
for broad-scale use, it is sufficient to include in the calculations
only the two main forcing components of surface flow: wind and pressure
gradient. Other minor components of flow such as mesoscale eddies and
tides which are not included comprise the error mode that is tuned out
in the overall model calibrations which compare model tracks to measured
drift in the ocean. Tuning was accomplished by adjusting the current
speed coefficient and/or angle of deflection to the right of the wind.
Tuned to Ocean Current
Measurements
Fig.
2
Several different
functions for current speed and angle to the right of the wind were
tested in OSCURS, and the resulting trajectories compared with data
derived from satellite-tracked drifters drogued at 20 m and tracked from
August to December 1979 in the Gulf of Alaska. The best agreement (Fig.
2) was found using the functions described above. In Figure 2,
notice 1) how the model trajectory filled in for the 30 days of missing
location data (straight line of small dots) along the satellite-tracked
drifter track and 2) the especially good daily agreement in the loop
created during the wind event caused by the slow passage of a low
pressure area (see zoom insert). Tuning to the best visual agreement was
accomplished by multiplying the wind current speeds and geostrophic
current speeds by 1.2. This was the initial calibration of OSCURS.
Studies at the
University of British Columbia (UBC) Oceanography Department comparing
OSCURS' trajectories across the North Pacific and trajectories measured
by the World Ocean Circulation Experiment (WOCE) and trajectories
generated by the U.S. Navy Research Laboratory's (NRL) high resolution
model have had mixed results. However, the cases where the models lacked
agreement were primarily due to the passive WOCE drifters becoming
trapped in mesoscale eddies, which neither OSCURS nor the NRL model
reproduce. The UBC Fisheries Centre used OSCURS velocity fields in their
salmon migration model, NerkaSim, because the OSCURS trajectories were
closest to observed drift. OSCURS achieves even a greater accuracy when
it is used for its primary purpose: determining year-to-year
variability.
96 Years of Water
Movement
It is well known that
oceanic subarctic water (north of 42ºN) is more productive than oceanic
subtropic water (south of 42ºN) and that both move eastward in parallel
paths toward the North American continent as part of long-term mean
ocean circulation. The relative amount of each water mass reaching the
coast varies from year to year as atmospheric patterns shift. This
variance is important to coastal fisheries because the condition of the
water affects its basic food production capacity which is eventually
passed to the fish. The driving force for these changes is associated
with the Aleutian Low, a permanent atmospheric feature of the Subarctic
Region in winter, which varies in intensity and eastward extent year to
year. Surface water is forced onshore by the winds, but swings north or
south as the winds and the currents vary in strength, direction, and
location. The abundance of salmon, for example, a near surface swimmer,
has been particularly affected by regime shifts, and OSCURS suggests
substantial changes may occur about every 20 years. With OSCURS we are
able to simulate the variability in surface water quantitatively, year
by year, for the first time.
Fig.
3
Ocean Weather Station P
(PAPA; 50ºN, 145ºW) was chosen as the single starting position for
simulated drifters because of its location within the eastern edge of
the Aleutian Low and the numerous oceanographic observations made there
since the mid-1950s characterizing the subarctic water mass. A plot of
all-winter (December-January-February) drift tracks shows that the
annual trajectory end points of the PAPA-drift distribute in two
groupings, north and south (Fig. 3). In
year-by-year simulations, the latitudes and longitudes of trajectory end
points ranged 1,700 km between 45º- 60ºN and 130º-155ºW. The north
and south groupings of trajectories appeared in both the first (Fig. 3
A) and second (Fig. 3 B) halves of this century. These oscillations are
a continuous natural process that coincide with the warmer-drier or
colder-wetter climate oscillations in the Pacific Northwest. The annual
trajectories shown in Figure 3 appear to jump back and forth irregularly
in time, alternating between north and south extreme modes, staying near
either extreme for a few years, with a few occurring in the middle, near
the theoretical average trajectory.
Fig.
4
To better see the
patterns in annual and decadal variability, the time-series of annual
values of the latitudes at each trajectory end point was plotted (Fig.
4). The fine line which connects the annual values exhibits
short-term variability, but smoothing the end point latitudes with an
equally weighted 5-year running average (dark line) revealed four peaks
averaging 20 years apart (1926, 1940, 1962, 1985) and four troughs 19
years apart (1909, 1932, 1950, 1967 ). Recently, the 5-year average has
begun turning southward and is nearing its long-term mean latitude
(54.4ºN), indicating the onset of the next oscillation (south mode).
This pattern has value as a forecasting tool on a 5-year average scale
because it shows decadal variability as well as strong evidence of an
impending shift in ocean circulation.
Indication that these
oscillations were present prior to the 20th century is found in western
juniper tree-ring data from eastern Oregon. The tree-ring data showed
oscillations similar to those generated by OSCURS and appear to be a
reasonable proxy for the latitude end point data mentioned above. Based
on counting the troughs in the plot of the 5-year running average
tree-ring widths, 34 oscillations with a spectral period of 17 years
have occurred since the time of Columbus. Adding the longest interval
between troughs (31 years) to the last trajectory trough (1967),
indicates that the next trajectory trough should occur about 1998. The
present 30-year interval is, therefore, nearly the longest in half a
millennium. Salmon catches off Alaska and the U.S. west coast have
varied according to the major regime shifts of the mid-1940s and the
mid-1970s, which are reflected in the north-south changes in the
latitude data. From 1976 to the present, salmon catches off Alaska have
remained high relative to those off Washington-Oregon-California. The
opposite is true for the period from the mid-1940s to the mid-1970s. The
data above suggest a regime shift is due again and accordingly a change
in regional salmon catches.
Currents Deflect
Migrating Salmon
Catch allocation of
Pacific salmon between Alaska, Canada, and the U.S. west coast states is
complicated by the annual effects of local currents during the fishes'
spring onshore migration from winter feeding grounds in the central Gulf
of Alaska to their natal streams. The majority of Pacific salmon in the
central Gulf of Alaska head toward the west coast of North America each
May-June-July in a rapid, well directed, and well-timed migration.
Location and timing of their landfall and subsequent coastal migration
routes are very important for management to know in order to determine
season openings and closings and catch allocation. OSCURS was used
initially in cooperative research between the UBC and the REFM Division
to test the hypothesis that the interannual variability of the surface
circulation in the northeast Pacific Ocean affects the latitude of
landfall and migration speed of adult sockeye salmon returning to the
Fraser River, British Columbia. Insight about the Northern Diversion
Rate (NDR), which describes the percentage of the run going north around
Vancouver Island (Canadian waters) or south through Juan de Fuca Strait
(U.S./Canadian waters) enroute to the Fraser River and its many
tributaries is of particular importance in international treaty
negotiations between the United States and Canada.
Fig.
5
Because the exact start
points of the Fraser River sockeye salmon migration home are unknown,
they were entered into OSCURS as 174 smart drifters which were each
moved around passively by the daily varying currents and also given an
active, fixed swimming speed and compass heading from an array of 174
points which covered most of the Gulf of Alaska. Multiple simulations
were performed with different behavior scenarios involving different but
constant swimming speeds, compass orientations, and migration start
dates (1 May and 1 June). One part of the array shown in Figure
5 is a line of start points 1 degree of latitude apart along 150ºW.
To test the effect of interannual variability of currents during May and
June, the OSCURS model was run for the relatively weak circulation year
of 1982 and the relatively strong circulation year of 1983. Results
indicated the latitude of landfall in 1983, compared to that in 1982,
was generally farther to the north, which is consistent with the
stronger circulation in 1983. The difference in latitude of landfall
between 1983 and 1982 increased for slower swimming speeds, more
southward orientations, and earlier migration start dates. The
differences in the latitude of landfall were greater farther south and
had a mean landfall distance of 292 km for the southern areas. These
results were consistent with the hypothesis that the interannual
variability of the surface circulation in the northeast Pacific Ocean
does significantly affect the latitude and timing of landfall in the
spring migration of adult sockeye returning to the Fraser River, British
Columbia. Thus, the effects of Northeast Pacific Ocean currents should
be included in sockeye migration models.
Salmon Show Model
Behavior
In a collaborative
project between the REFM Division and UBC to evaluate alternative
regression models for predicting stock-specific marine production, a
regression-based prediction of run-timing for Frazer River salmon was
developed in which the independent variables were sea surface
temperature and the landward component of the monthly OSCURS' current
vector in the southeastern portion of the Alaska Gyre. For 1995, 1996,
and 1997 the model gave more accurate predictions of the early Stuart
Lake sockeye population run-timing peak than the temperature-based model
did that the Pacific Biological Station had been using. On the last day
of May, June, and July the daily pressure fields were downloaded and the
model was run to update the latest months current index which was
promptly sent to Canada for the model update to estimate the timing of
the peak concentration of sockeye salmon passing Vancouver Island on
their way to the Fraser River.
The UBC Fisheries Centre
has used OSCURS exclusively in the advection aspect of their
bioenergetics and migration model, NerkaSim. Through NerkaSim, which now
appears on World Wide Web site http://www.eos.ubc.ca/salmon/nerkasim
users can produce visual displays of the biophysical environment,
simulate salmon migration, growth and survival processes, and produce
space/time maps of key bioenergetic variables. NerkaSim links
libraries of data on ocean currents, temperatures, zooplankton and fish
stomach contents/fullness with subroutines that calculate vectors of
fish movement, bioenergetic costs of migration, and growth potential.
The area covered is the northeast Pacific Ocean and the eastern Bering
Sea from 30º to 60ºN and 120º to 170ºW. Libraries are
updateable to include specific areas of interest. The ability of
NerkaSim to integrate the effects of spatial environmental patterns with
time-based migration rules is a unique development within the field of
ecological modeling; it serves as a platform to explore hypotheses
concerning migration, growth, and survival processes.
Some interesting results
of the collaborative modelling efforts show that 1) the salmon growth
rate potential appears to be maximized near the center of the Alaska
Gyre, 2) sockeye have the capability of reaching the Fraser River from
anywhere in the northeast Pacific Ocean, 3) the NDR is affected by the
location of the fish at the time they begin homeward migration from the
Gulf of Alaska, 4) oceanic circulation can affect latitude of landfall
but there is no strong relationship between the effects of circulation
and the NDR, and 5) on the average, Fraser River sockeye make 1.5 loops
of the Gulf of Alaska during their 2.5 years of oceanic life, but the
pattern of movement of each year class is different and highly dependent
on the patterns of ocean circulation that it encounters during its
oceanic life.
Larval Drift to Safer
Nursery Areas
The OSCURS model also
has been used to investigate the spatial distribution of the early life
history stages of walleye pollock, the most abundant and one of the most
commercially important species in the Bering Sea. Fish eggs and small
larvae remain suspended in and drift with the near surface water for
atleast the first few months of life before they become active swimmers
that are more independent of the ocean currents. Such is the case with
the early life history stages of walleye pollock. Juvenile pollock
comingle in the same areas adult pollock and are important prey for the
larger pollock, marine mammals, and birds. Resource surveys by the AFSC
have shown that juvenile walleye pollock stay on the mid-shelf after
being transported there early in life. The larger separation between the
young fish on the mid-shelf and the adults near the edge and outer shelf
in years with large year classes has been suggested as a possible
mechanism for greater survival because the young are more likely to
avoid cannibalism by adults. Prevailing wind and current changes during
and after spawning affect the final spatial distribution of juvenile
pollock and may be favorable to their survival. OSCURS was used to
investigate this theory by quantifying the 90-day water drift in the
Bering Sea from 1970 to 1996 for the period immediately after pollock
spawn.
Fig.
6
Spawning typically
ocurrs in late winter in the southeast corner of the Bering Sea, and the
average currents transport the eggs and larvae slowly northward along
the outer shelf and slope. Reflecting what is generally known about the
timing and location of pollock spawning, OSCURS trajectories were
started each year on 15 April 1970-96 at three locations; 1) just north
of Unimak Island (U) on March 1; 2) near Bogoslof Island (B) on April 1;
and 3) near the Pribilof Islands (P) (Fig. 6).
OSCURS trajectories showed that during spawning years which resulted in
small year classes (1970, 1971, and 1987) there was little net northward
and northeastward transport from any of the three spawning locations
(Fig. 6 A), thus leaving the juveniles in the same area as the adults.
On the other hand, during spawning years which resulted in large year
classes (1978, 1982, and 1989) there was strong northeastward transport
onto the shelf from the Unimak area, strong northeastward and northward
water movement from the Bogoslof area, and stronger northward or
northwestward water movement from the Pribilof Islands (Fig. 6 B).
Accidental Debris
Tracker
Although the dispersion
of animals in the water is the primary interest of OSCURS modelers,
unique opportunities have presented themselves since 1990 to analyze
accidental but fortuitous at-sea events beyond the scale of normal
oceanographic science. Investigation of these events has been used to
fine-tune the OSCURS model. Historically, oceanographers throw only a
few hundred drift bottles at a given time and spot in the ocean hoping
for more than the expected 1-2 % recovery rate. The spill of 80,000 Nike
shoes at one spot in mid-ocean in 1990, followed by other spills of
29,000 plastic bathtub toys, and 1,100 logs in 1992 and 1996,
respectively, brought a new feature to OSCURS to simulate the drift and
diffusion trajectories of great numbers of the same or similar floating
objects from one spot in the ocean.
Shoes: Footprints on
the Sea
On 27 May 1990 a storm
caused the container vessel Hansa Carrier to lose overboard five cargo
containers with 80,000 Nike shoes south of the Alaska Peninsula near
48ºN, 161ºW. Reports from beachcombers revealed that the first 200
shoes started arriving at the northern Washington coast around
Thanksgiving 1990, about 6 months after the spill. Beachcomber finds in
January-February 1991 off Vancouver Island and in March 1991 in Queen
Charlotte Sound showed that the aggregate mass of shoes next floated
northward with the winter Davidson Current. The normal spring wind
transition from southerly winds of winter to northerly winds of summer
off the Pacific northwest coast must have occurred at the end of March
1991, because the next batch of recoveries was reported to the south off
Oregon in April and May, indicating that a sharp reversal of currents
had moved the flotilla to the south. It took a tuning coefficient
multiplier of 1.3 (shoes traveling 30% faster than the current) in the
speed equation to make the model trajectories match the recoveries of
1991.
Toys Float `Round the
Pacific
Fig.
7
OSCURS also was used to
investigate the dispersion of 29,000 children's batht ub toys released
from a cargo container that drifted eastward from a mid-ocean s pill at
44ºN, 178ºE on 10 January 1992 to the North American west coast.
Unlike the shoes, the toys arrived farther north and then drifted
northward and westwar d, counterclockwise, around the Subarctic Gyre
(perhaps, in response to El Nino conditions). In Sitka, Alaska, the
Sitka Sentinal newspaper reported that several hundred blue turtles,
yellow ducks, red beavers, and green frogs washed up on Sitka beaches
after 16 November 1992 (Fig. 7). It took a speed
coefficient multiplier of 1.5 (toys travelling 50% faster than the
water) to get the OSCURS trajectories to match the first recovery.
Following the initial landfall, at least 400 more toys were reported
along beaches from Sitka to Kodiak through the summer of 1993, agreeing
with the model trajectories. Beyond Kodiak and after 1993 there were
only a few, sporadic, new reports at Shumagin, Unalaska, and St. Paul
Islands which generally matched the direction of model tracks
southwestward in the Alaskan Stream then northwestward through Unimak
Pass continuing along the edge of the shelf in the Bering Slope Current.
No reports were received from the western Pacific but the model track
continued across and out of the Bering Sea in the southwestward
Kamchatka Current, turned eastward off the Kuril Islands continuing back
to and past the spill site (May 1994) nearly crossing the Pacific by
January 1995. The next year the model was back at Sitka and Kodiak and
the Alaskan Stream where it avoided Unimak Pass going westward to the
end of the Aleutian Islands. After January 1996 it turned northward at
Attu Island and entered the Bering Sea's slower counterclockwise
circulation. After January 1997, the fifth year of the simulation, the
trajectory again left the Bering Sea in the Kamchatka Current, again
turned eastward at 45ºN, almost reaching the spill site at the
conclusion of this 5 y ear update, 31 July 1997. Thus, the model shows
the toys completing the first circumnavigation of the Subarctic Gyre
quickly in 2 years and the second circumnavigation in about 3 years. The
complexity of coastal diffusion is highlighted with two recoveries from
the Washington coast in March-April 1995 that probably came from the
first set of circumnavigators.
1,100 Logs are floating
hazards
On 20 February 1996,
about 1,100 peeled Douglas fir logs were lost overboard by the log
transport vessel Ocean Orchid in the center of the Gulf of Alaska
(52º02ºN, 148º54ºW). These 20-ft long, 1- to 2-ft diameter logs were
potentially hazardous to fishing vessels transiting the Gulf of Alaska.
The trajectories and monthly locations of the drifting logs were
calculated by OSCURS. Fifteen diffusing trajectories estimated that the
logs should have 1) drifted northward from start point in the Alaska
Current, 2) turned southwestward in the Alaskan Stream after reaching
the continental shelf fishing grounds south of Prince William Sound, 3 )
made a right angle turn offshore south of Unimak Island into the
eastward Subarctic Current, 4) completed the first circuit of the Gulf
of Alaska Gyre and turned northward again, 5) reentered the Alaskan
Stream boundary current just off the shelf edge, and 6) near the end of
the model run, turned offshore again ready for completion of the second
circuit of the Gulf of Alaska in a few months. Episodes of onshore winds
could have sent a cluster to shore along the shelf but the model
suggests many could still be found in a broad area within about 200
miles of shore. Although most apparently continue to circulate around
the offshore gyre, one verifiable report came from Unalaska Bay
confirming the westward extension in the Alaskan Stream and passage into
the Bering Sea. The update through July 1997 showed the hazard continues
for fishing vessels transiting the Gulf of Alaska.
Please report any
sightings of shoes, toys, or peeled fir logs on the beach or offshore to
Jim Ingraham (206)526-4241, e-mail jim.ingraham@noaa.gov, to help
fine-tune the OSCURS model. The logs have an identifying plastic tag
with a unique number code (e.g., AH10043) stapled to one end.
OSCURS and the
World Wide Web
Fig.
8
OSCURS' data are
available to other researchers studying surface current variability in
relation to various species of fish and marine mammals inhabiting the
North Pacific Ocean and Bering Sea. Members of REFM's computer modeling
task are working to make OSCURS available through the AFSC web site at
"http://www.refm.noaa.gov/oscurs." Monthly current trajectory
fields for the North Pacific and Bering Sea will be the first
model-derived product (Fig. 8). Other products
will be designed and included when feedback is received from users. The
OSCURS model will be available in early 1998 for users to calculate a
surface drifter trajectory from three chosen inputs: 1) a starting
latitude-longitude location, 2) start date between January 1946 and the
end of last month (pressure fields updated monthly by the first week of
the month), and 3) the number of days in the run (initial limitation 1
year).
Reverse OSCURS (ROSCURS)
A numerical model the
reverse of OSCURS (ROSCURS) is being developed in order to go backwards
in time from a given spot because it is not always easy to pick an
affective start point that drifts to a particular end point. Assuming
the user knows the start point, OSCURS will respond to the question
"Where did the water go in a chosen time interval?" by
returning a series of daily latitude-longitudes forward in time from
start point to end point. If the user is at an end point of particular
interest and wants to know "where the water came from and how long
it took to reach that point at a certain date," ROSCURS is the
appropriate model. For example, ROSCURS could be used if the desired end
point is somewhere at the mouth of the Columbia River on April 15th when
the salmon smolts leave the river and enter the ocean, and the user
wants to know where the ocean water that the fish encounter came from 6
months earlier in order to assess its quality. The ROSCURS
model will be available in 1998. Stay tuned.
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