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A short-term predictive system for surface currents from a rapidly deployed coastal HF radar network

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AUTHOR'S PROOF!
U N C O R R E C T E D P R O O F
1234
A short-term predictive system for surface currents
5
from a rapidly deployed coastal HF radar network
6
Donald Barrick
&
Vicente Fernandez
&
Macu I. Ferrer
&
7
Chad Whelan
&
Øyvind Breivik
8
Received: 12 September 2011 /Accepted: 3 January 2012
9
#
Springer-Verlag 2012
1011
Abstract
In order to address the need for surface trajectory
12
forecasts following deployment of coastal HF radar systems
13
duringemergency-responsesituations(e.g.,searchandrescue,
14
oil spill),a short-termpredictivesystem(STPS)basedononly
15
a few hours data background is presented. First, open-modal
16
analysis (OMA) coefficients are fitted to 1-D surface currents
17
from all available radar stations at each time interval. OMA
18
has the effect of applying a spatial low-pass filter to the data,
19
fills gaps, and can extend coverage to areas where radial
20
vectors are available from a single radar only. Then, a set of
21
temporal modes is fitted to the time series of OMA coeffi-
22
cients,typicallyoverashort12-htrailingperiod.Thesemodes
23
include tidal and inertial harmonics, as well as constant and
24
linear trends. This temporal model is the STPS basis for
25
producing up to a 12-h current vector forecast from which a
26
trajectory forecast can be derived. We show results of this
27
method applied to data gathered during the September 2010
28
rapid-response demonstration in northern Norway. Forecasted
29
coefficients, currents, and trajectories are compared with the
30
same measured quantities, and statistics of skill are assessed
31
employing 16 24-hdatasets. Forecastedand measuredkinetic
32
variances of the OMA coefficients typically agreed to within
33
10
–
15%. In one case where errors were larger, strong wind
34
changes are suspected and examined as the cause. Sudden
35
wind variability is not included properly within the STPS
36
attack we presently employ and will be a subject for future
37
improvement.
38
Keywords
HF radar .Ocean forecasting.Search and
39
rescue.Oil spill
40
1 Introduction
41
HF coastal radars have evolved over the past 40 years into
42
worldwide operational networks that provide real-time data to
43
a variety of end users. Over 450 such radars are operating
44
today, of which about 400 are CODAR SeaSondes®. The
45
primary data products are 2-D surface current vector maps,
46
which require two or more radars with overlapping coverage
47
(Barrick et al. 1977; Lipa and Barrick 1983). In addition to
48
surface currents, secondary outputs include wave parameters
49
(Lipa and Barrick 1986), tsunami detections (Barrick 1979;
50
Lipa et al. 2011
Q1
), and vessel detections (Roarty et al. 2011).
51
The fate of anything floating on the surface, such as vessels
52
adrift or oil/pollutant spills, are highly, if not completely,
53
dependent on surface currents. While the ability of HF radar
54
to provide surface current maps in near real time is of great
55
value, the ability to forecast the currents and, thus, the fate of
56
materialfloatingonthesurfaceisanevenmoreimportanttool.
Responsible Editor: Michel OlagnonThis article is part of the Topical Collection on
Advances in Search and Rescue at Sea
D. Barrick
:
C. Whelan (
*
)CODAR Ocean Sensors,1914 Plymouth Street,Mountain View, CA, USAe-mail: chad@codar.comV. Fernandez
:
M. I. Ferrer Qualitas Remos,C/Toronga, 31,Madrid, SpainØ. Breivik The Norwegian Meteorological Institute,Bergen, NorwayØ. Breivik Geophysical Institute, University of Bergen,Bergen, NorwayOcean DynamicsDOI 10.1007/s10236-012-0521-0
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AUTHOR'S PROOF!
U N C O R R E C T E D P R O O F
57
Efforts to assimilate HF radar-derived currents into coastal
58
ocean models (Breivik and Sætra 2001; Oke et al. 2002;
59
Paduan and Shulman 2004) that can provide forecasts have
60
been successful, but at the current state, full assimilation of
61
surface current maps into hydrodynamic models can be a
62
laborious process that requires archives and other sources of
63
data. Efforts have also been made to use longer time series of
64
surface current maps to make short-term forecasts (Zelenke
65
2005; Frolov et al. 2011). As these efforts to produce surface
66
current model forecasts progressed, the U.S. East Coast be-
67
came populated with a contiguous HF radar ocean monitoring
68
network and the U.S. Coast Guard (USCG) began a program
69
to evaluate SeaSonde data products for use in search and
70
rescue (SAR) operations. Comparisons were performed over
71
many years withself-locating datum markerbuoys (Ullman et
72
al. 2003; O
’
Donnell et al. 2005; Ullman et al. 2006). These
73
evaluations have established conclusively that, in all cases,
74
incorporating radar-derived current fields into short-term pre-
75
dictive systems (STPS) significantly improves SAR capabili-
76
ty, efficacy, and reduces costs of search operations. The STPS
77
methods employed in the USCG SAR operations are Monte
78
Carlo random-walk or random-flight models to forecast the
79
advected drift areas. After nearly a decade of such careful test
80
and evaluation, these methods wereincorporated intothe U.S.
81
Coast Guard operations first beginning 2 years ago for the
82
region from Massachusetts to North Carolina
’
s Cape Hatteras
83
with HF radar surface current data supplied by regions the
84
Mid-Atlantic Regional Association Coastal Ocean Observing
85
System (http//www.maracoos.org). The West Coast is being
86
brought online for SAR operations, from the Mexican border
87
nearly to Canada. Presently, with sparse radar measurements
88
inGulfofMexico,southeasternUSA,Alaska,Hawaii,andthe
89
Caribbean, HF radar in these regions is not included in Coast
90
Guard plans for SAR operations.
91
A similar emergency application with a need for STPS
92
forecasts is oil spill response. SeaSondes have recently been
93
in place and operating for two separate incidents involving
94
spilledoil.Atthetimeofthe2010DeepwaterHorizonincident
95
in the Gulf of Mexico, during which oil spilled continuously
96
for 5 months, as well as during the 2007 Cosco Busan tanker
97
incident in California
’
s San Francisco Bay, SeaSondes mea-
98
sured surface currents in the affected areas in near real time.
99
ThesefortuitousmeasurementsprovedhighlyusefultoNOAA
100
and other groups managing cleanup operations. In fact, four
101
decades ago, it was the motivation of oil spill environmental
102
assessment that led to funding at NOAA under which HF
103
radar/CODAR was developed into a useful current-mapping
104
tool in the early 1970s.
105
Norway has evolved an active offshore oil/gas production
106
industry in their sector of the North Sea and has been a leader
107
inapplicationofthelatestandbesttechnologiestomanagethe
108
inevitable spills that accompany such operations. Although a
109
small network of SeaSondes operate near Fedje, the gateway
110
to the Mongstad refinery, nearly the entire Norwegian coast
111
has no radar coverage and is mostly inaccessible by road and
112
land vehicles. In 2010, with funding from the Norwegian
113
Clean Seas Association for Operating Companies (NOFO;
114
http://www.nofo.no) and Innovation Norway, a rapid-
115
response capability was developed in which a SeaSonde pair
116
could be deployed and provide surface currents within hours
117
of a spill (Kjelaas et al. 2011). This culminated in a month-
118
long exercise in Finnmark during September 2010. Figure 1
119
shows photos of this deployment. The Rapidly Deployable
120
SeaSonde operated in the 13-MHz band, which provided a
121
useful range of about 80 km at 2-km range resolution. Tem-
122
poral resolution for the averaged cross spectra and, therefore,
123
unaveraged radial vector output was 10 min, and the averaged
124
radial vector output interval was 60 min. The Finnmark exer-
125
cise demonstrated that such an approach could provide maps
126
of offshore surface currents quickly during an emergency,
127
therebyofferingimprovedinformationforcleanupoperations.
128
Whereas the USCG and other forecast methods using Sea-
129
Sonde data employed methodologies that relied on a month or
130
moreofhistoric datatoforecasttides andbackground,thiswill
131
not be possible in a rapid deployment to a new area. The
132
challenge, therefore, is to draw upon data collected during
133
the first few hours after radar startup to initialize the STPS
134
forecast method. For example, after 8
–
12 h, enough data
135
should be available to capture the semidiurnal and inertial
136
harmonics, as well as a constant and perhaps linear trend.
137
One might not expect this to be adequate for predictions
138
extending more than an equivalent period into the future.
Fig. 1
Photos of self-contained SeaSonde HF radar being helicopter-deployed in Finnmark region of northern Norway during September 2010, during NOFO emergency-response exercise. Radar antenna ismounted alongside the weatherproof container and portable generator powers the system for up to a week Ocean Dynamics
JrnlID 10236_ArtID 521_Proof# 1 - 10/01/2012
AUTHOR'S PROOF!
U N C O R R E C T E D P R O O F
139
However, this is considered highly useful in directing opera-
140
tions, either for SAR or spill mitigation.
141
It is the purpose of this paper to investigate the utility and
142
accuracy of this concept by selecting 16 24-h periods during
143
the NOFO deployment beginning September 14, 2010, 21:00
144
UTC through September 30, 2010, 22:00 UTC in order to
145
assess the forecast skill of our STPS method. The first 12 h of
146
each period is used as the history/background. The STPS then
147
forecasts currents and derived trajectories ahead for the next
148
12 h. The latter are then compared with actual observations
149
over the second 12 h and statistics of differences calculated to
150
reveal accuracy. In our first attempts here, wind effects are
151
included only to lowest order. A constant wind as well as a
152
linear variation over the 12-h period is in fact included in our
153
STPS model. However, any shorter-period change
—
perhaps
154
due to a frontal passage
—
is not. Expected effects of short-
155
period wind changes are discussed, and a method suggested
156
for dealing with this is proposed.
157
Section 2 describes the open-mode analysis (OMA) spa-
158
tial fitting that is applied to the data every hour to obtain
159
modal coefficients that vary with time. Section 3 derives our
160
STPS temporal modal methodology that is applied to the
161
OMA time-varying coefficients. Following this, Section 4
162
analyzes the forecasted OMA coefficients, current patterns,
163
error statistics, and trajectories with actual measured values
164
based on radar observations with estimations of trajectory
165
displacement differences as a function of time into the future.
166
A case study of short-period wind changes is discussed, and a
167
method suggested for dealing with this is proposed in Sec-
168
tion 5. Finally, a discussion of results is provided in Section 6
169
including additional studies and the possibility of improving
170
predictions by including forecasted winds.
171
2 Open-mode analysis principles and fitting to NOFO
172
currents
173
OMA as advanced by Lekien and Coulliette (2004) is an
174
outgrowth of normal mode analysis (NMA), first introduced
175
for SeaSonde HF radar measurements by Lipphardt et al.
176
(2000). Both are based on representing flow near the surface
177
in terms of a divergence-free stream function and vorticity-
178
free velocity potential. Both the stream function and velocity
179
potential are scalar fields depending on
x
,
y
that are defined
180
within a horizontal domain that roughly describes the radar
181
coverage area:
182
(a)
Stream function: This scalar field satisfies the following
183
Laplace second-orderpartial differentialequation(PDE):
184
r
2
y
x
;
y
ð Þ¼
0
ð
1
Þ
185186
where the Dirichlet condition applies to the boundary, i.e.,
187
y
4
0
0where
4
denotestheboundaryoftheregiontobefitted.
188
(b)
Velocitypotential:This scalar fieldsatisfiesthe following
189
Laplace second-order PDE:
190
r
2
f
x
;
y
ð Þ¼
0
ð
2
Þ
191192
where the Neumann condition applies to the boundary, i.e.,
193
b
n
r
f
4
¼
0
where
b
n
denotes the unit vector normal to the
194
boundary
4
.
195
(c)
Boundary function: The main departure of OMA by
196
Lekien and Coulliette (2004) from NMA of Lipphardt
197
et al. (2000) has to do with how the open boundary
198
region is treated. A portion of the boundary is
“
closed,
”
199
comprised of relevant coastlines where the Dirichlet and
200
Neumann conditions apply. The remainder is an open
201
boundary where neither of the above conditions can be
202
expected to apply. NMA suggested two somewhat arbi-
203
trary waysto dealwiththe open boundary(including use
204
of data from a model, which may not always be avail-
205
able). In OMA, a third function, and resulting set of
206
modes, was demonstrated that defined a new functional
207
“
boundary
”
field
208
r
2
f
b
x
;
y
ð Þ¼
0
ð
3
Þ
209210
that is to be specified on the open boundary in place of the
211
Neumann condition, i.e., by
b
n
r
f
4
¼
g
f
ð
s
Þ
b
n
u
4
0
,
212
where
4
0
is the open portion of the boundary
4
and
s
213
denotes arc-length distance along the boundary.
214
(d)
Eigenfunction solutions for the three Laplace Eqs. 1, 2,
215
and 3:
216
r
2
y
i
þ
l
y
i
y
i
¼
0;
r
2
f
i
þ
l
f
i
f
i
¼
0;
r
2
f
bi
þ
l
bi
f
bi
¼
0
ð
4
Þ
217218
Here, the subscripted quantities define eigenfunctions, which
219
we call OMA modes. These modes are functions of
x
,
y
; they
220
need to be calculated only once using finite element methods
221
for a given radargeometryandthenstoredfor subsequentuse.
222
The subscripted parameters
1
i
are the eigenvalues
223
corresponding to that respective set of modes; the latter are
224
always positive, usually arranged in ascending order. The
225
lowest-order modes have the largest spatial extent, fitting to
226
the interior of the boundary domain, with the higher modes
227
capturing the finer spatial details of the current variations.
228
(e)
Surface current expansions in terms of eigen modes:
229
Understanding that
x
,
y
are the Cartesian coordinates
230
within the locally planar ocean surface
—
generally rep-
231
resenting east and north, respectively
—
the expression
232
for the surface current vector along these directions in
233
terms of stream function and velocity potential is:
234
u x
;
y
ð Þ¼
r
y
x
;
y
ð Þ
b
z
ð Þþ
r
f
x
;
y
ð Þþ
r
f
b
x
;
y
ð Þ ð
5
Þ
Ocean Dynamics
JrnlID 10236_ArtID 521_Proof# 1 - 10/01/2012
AUTHOR'S PROOF!
U N C O R R E C T E D P R O O F
235236
This can now be written in terms of our eigenfunction modal
237
expansion as:
u x
;
y
;
t
ð Þ¼
X
1
i
¼
1
a
y
i
t
j
r
y
i
x
;
y
ð Þ
b
z
þ
X
1
i
¼
1
a
f
i
t
j
r
f
i
x
;
y
ð Þþ
X
1
i
¼
1
a
bi
t
j
r
f
bi
x
;
y
ð Þ ð
6
Þ
238239
where we now include time of the measurement (e.g., hourly)
240
as
t
j
. Thus, every timeinterval weunderstand that a new set of
241
OMA coefficients,
α
i
, are to be fitted (in a linear least-squares
242
(LS) sense) to the radar-observed current fields. It is these
243
sequential time-dependent mode coefficients that are to be
244
used in the STPS method we develop next (rigorous justifica-
245
tion for the OMA mathematics summarized above is found in
246
Lipphardt et al. (2000) and Lekien and Coulliette (2004))
247
These modes can either be fitted to the 2D vectors where
248
measurements of two or more radars overlap and combined
249
prior to modal analysis or they can be fitted to the 1-D
250
measurements (radial velocities) of individual radar sites in
251
their inherent polar coordinate systems (Kaplan and Lekien
252
2007).We havechosentofit tothe 1-D radialvelocities in our
253
investigation,asithasbeenfoundtobemorerobust.Thethree
254
sets of coefficients in the triple summations above are often
255
referred to as Dirichlet, Neumann, and boundary modes,
256
respectively. Kaplan and Lekien (2007) also show how to
257
calculate errors in the OMA-fitted currents based on errors
258
estimated in the srcinal radial velocities.
259
(f)
Numberofmodestouse:Inthe above modalexpansions,
260
we show an infinite number of terms/modes in the series.
261
In practice, we must terminate each of these series at
262
some upper limit (not necessarily the same for each set
263
of modes). Although one is often tempted to include all
264
consecutive terms inascending order oftheir eigenvalues
265
(which are indexed by subscript
i
), this is not necessarily
266
the best criterion of selecting which modes to retain. A
267
morerobustmeasuremaybethekineticenergycontained
268
in the velocities for each fitted mode for the area of
269
interest, in this case the NOFO coverage region; we
270
examine this further below. Other measures have been
271
studied, such as the scale size of the mode area (Lekien
272
and Gildor 2009), which has led to suggestions of
273
hundreds of modes and series terms. We are somewhat
274
wary of this approach because higher-order terms re-
275
spond to noise, outliers, and gaps in the data, which the
276
OMA concept is meant to filter out. Lekien and Gildor
277
(2009) found, for example, that although many hundred
278
modes appear useful for overall OMA-fitted current
279
maps, divergence and vorticity derived therefrom were
280
unacceptably unstable and noisy when the total mode
281
number exceeded 20 or so; this is a subject that needs
282
further investigation. Experience to date suggests that
283
fewer modes rather than too many may be preferred.
284
2.1 NOFO case study of OMA domain
285
The study area (Finnmark, northern Norway) where we have
286
testedthe STPSmethodologypresentedinthispaper isshown
287
in Fig. 2. For this area, we have defined a fixed domain where
288
modes are computed, shown in Fig. 2, illustrating the open
289
and closed boundaries. Note that the coastline is a natural
290
closed boundary (no normal flow through the shoreline), and
291
we allow flow through the straits between the islands.
292
2.2 Dominant modes fitted to NOFO OMA domain
293
In deciding the construction and the number of modes to be
294
used in the OMA fit to the HF data, one limiting factor is the
295
spatialscalethatistoberesolved,whichshouldbethesameor
296
morecoarseresolutionthanthemeasurementgrid(Lekienand
297
Gildor 2009). In this case, our Cartesian measurement grid
298
spacing was 3 km. Ocean features of 15 km are well resolved
22
o
E
30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’
TarhalsenFruholmen
Longitude
L a t i t u d e
Fig. 2
Domain where the current modes are computed and the surfacecurrents are obtained during the period of the study. The
dashed line
represents the open boundary and the
continuous lines
are the closedlines. The
triangles
represent the two SeaSonde Stations. Tarhalsenstation is the mobile unit shown in Fig. 1 and
Q2
Fruholmen is a fixedstationOcean Dynamics
JrnlID 10236_ArtID 521_Proof# 1 - 10/01/2012
AUTHOR'S PROOF!
U N C O R R E C T E D P R O O F
299
with the actual horizontal measurement grid resolution of
300
3 km for the total currents and with the goal in this study of
301
reproducing the modes with the most inertia the choice was
302
made to analyze modes with spatial scales 15 km or larger.
303
With this configuration, we arrive at a total of 34 modes (7
304
free-divergence, 15 irrotational modes, and 12 boundary
305
modes). In Fig. 3, the two most energetic modes for each type
306
derived from the fit to the radial data are illustrated (see
307
Section 4.1 for a detailed examination of an energy analysis
308
of the modes).
30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’30’
23
o
E
30’
24
o
E
30’
25
o
E
30’45’
71
o
N
15’30’
Neumann mode 2 Neumann mode 1
00.511.522.5300.511.522.53
Dirichlet mode 1 Dirichlet mode 2
00.511.522.5300.511.522.53
Bound mode 7 Bound mode 3
00.511.522.5300.511.522.53
Fig. 3
The two most energeticcurrents modes for each type(see Section 4.1 for a detailedanalysis of the energy of themodes). The
first row
shows theincompressible modes, the
second row
shows theirrotational modes, and the
last row
contains the boundarymodes. The
colorbar
is themagnitude of the velocity incentimeters per secondOcean Dynamics
JrnlID 10236_ArtID 521_Proof# 1 - 10/01/2012

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