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weathered and absorbed amounts and the oil age. The oil
slick at time t is defined by the volume distribution mapped
onto a Cartesian grid of points for all parcels. The oil volume
in the cells of the grid are found by summing the particles for
all parcels. Thus, the dependent variable field of the oil spill
model is a volume distribution denoted by -V(x;,t), with
associated attributes.
DATA ASSIMILATION
Satellite image data are assimilated into the model as a
redundant boundary condition at the sea surface. The
following parameters and their data sources are presently
used in the model:
Sensor Parameter Dependent Variable
AVHRR SST T(x; t)
SeaSonde surface current ui(x; 0, i=1,2
HF radar ;
SAR surface slicks V(x; t)
Surface Layer Temperature
The ascending NOAA-14 AVHRR "quicklook" reference
images are screened daily for cloud-free conditions exceeding
about 40% of the model domain and, for those images
meeting this criterion, the level 1b data file is downloaded to
a workstation via a DirecPC satellite data link. These image
data are then navigated and processed to a set of single-band
radiance image files mapped onto a georeferenced conic
projection. A cloud mask is generated for the image by
flagging all pixels which meet either low-temperature or high-
brightness criteria, and a land mask is created by binarizing
the optical-NIR (near-infrared) difference image at a suitable
threshold level. The navigated radiance images are used to
compute sea-surface temperature fields starting with the
McLain et al. (1985) MCSST algorithm, incorporating
Kidwell's (1995) correction for the satellite zenith angle, with
NOAA's standard coefficients. — The MCSST algorithm
provides an estimate of the skin temperature of the ocean; the
bulk temperature for the upper layer of the model is
calculated using the regression equation:
Tbulk = 0.816 MCSST + 2.419 °C ©)
based on 175 observations from ocean buoys in the model
domain.
These fields have a resolution of approximately 1.1 km and
are generally spatially intermittent. They are resampled to
the model grid (5 km on the shelf and 1 km in the strait) and
filtered to remove unrealistic values close to land and cloud
edges. The resampled field provides the calibrated T(x; t) for
assimilation. A computationally efficient nudging scheme
(Ghil and Malanotte-Rizzole, 1991) is used to assimilate the
surface layer field. This nudging scheme is based on a
Gaussian weighting function raised to a power, centered at
the image time with a period of +3 h. The function has a
value of 1 at the image time, resulting in replacement of the
modelled value with the image value. When the power
applied to the function is increased, the time over which the
image data modifies the modelled field is reduced; a power of
5 was found to give reasonable results over the continental
shelf.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998
Surface Current
The SeaSonde is a compact ground wave radar system for
mapping surface currents based on a frequency-modulated,
continuous-wave (FMCW) signal format (Hodgins, 1995).
Transmit frequencies of 12.5 and 25 MHz are typically used
in coastal applications. At 12.5 MHz, the SeaSonde has a
range resolution of 2.556 km over 31 range cells, giving a
theoretical range of 79.2 km. The system utilizes two or
more radar sites each separated by 25 to 35 km along the
coast. À radar site consists of the transmit/receive hardware,
a data acquisition computer, compact cross-stick or air-loop
receive antennas and a monopole transmit antenna. One
radar site provides a measurement of the radial velocity field
within the radar's field-of-view. The radial current
components vi(¢;) around each range ring are derived from
the Doppler shi of the Bragg peaks in the sea echo spectra.
Directions $; associated with each radial current are found
using a least squares direction finding algorithm (Lipa and
Barrick, 1983). Typically, 15 Doppler spectra are averaged
to provide one hourly estimate of vi(#;) and the standard
deviation Óv of the speed. The azimutfial resolution of the
radial currents is 5?. Barrick et al. (1974) have shown that
the current sensed by the radar backscatter represents an
average over a depth proportional to the radar wavelength.
This depth is approximately 0.95 m for a carrier frequency of
12.5 MHz; thus, HF radars measure a near-surface current
that is a reasonable approximation for the upper layer current
in the circulation model.
The radial current maps from two or more sites are then used
to calculate the total current field u;(x;,t) by combining radial
currents on the uniformly spaced Cartesian model grid. A
circular cell is defined around each grid point encompassing
one or more radial components from each radar site. The
radial velocity at the grid point is calculated as a weighted
average of the radial components for one site contained in the
circle. The weights incorporate the distance (weighted
inversely) from the grid point to a contributing radial, and the
standard deviation óv for each v;(¢;). Radial components
from each site are combined by vector addition to give the
total current magnitude and direction, and estimates of the
error in speed (ôr) and direction (60). The current errors are
spatially dependent. Confidence in the observed current, as
reflected by dr and 90, is highest near the centre of the
coverage area between the radars, where radar performance
is best, and lowest toward the edges of the coverage area.
The larger separation between radial currents with increasing
range, combined with poorer radar performance at large
range, and increased triangulation error in the vector addition
(Leise, 1984), accounts for the lower confidence around the
limits of coverage. These characteristics lead to surface
current measurements that are slightly noisier than one
expects from conventional current meter data. In order to
take these error characteristics in account, the data
assimilation scheme adopted for u;(x;,t) blends the observed
field with the modelled field at centre time of the
measurement using a spatially-dependent weighting function
of the form:
u;(x;.t)a = K u;(x;,t})p + (1-K) u;(x;,0M (10)
where K is a weight, and subscripts A, O and M represent
Assimilated, Observed and Modelled currents. A variable €
is defined as the ratio of the area of the tip of the current
vector that is allowed to vary with r + 8r and © + 80 to the
area of the annular ring segment defined by r + ôrmax And ©
+ S0max- The weight K is defined as 0.75(1-e). The factor
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