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

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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 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 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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