Sustained observationsof mesoscale and sub-mesoscale surface circulation

off the U.S. West CoastSung Yong Kim†

Eric J. TerrillBruce D. Cornuelle

Scripps Institution of OceanographyLa Jolla, CA 92093 USAsyongkim@mpl.ucsd.edu†

Burt JonesDepartment of Biological SciencesUniversity of Southern California

Los Angeles, CA 90089-0371 USA

Libe WashburnDepartment of Geography/ICESS

University of California, Santa BarbaraSanta Barbara CA 93106-3060 USA

Mark A. MolineBiological Sciences Department

and Center for Coastal Marine SciencesCalifornia Polytechnic State University

San Luis Obispo, CA 93407 USA

Jeffrey D. PaduanDepartment of Oceanography

Naval Postgraduate School, Code OC/PdMonterey, CA 93943 USA

Newell GarfieldGeosciences Department

and Romberg Tiburon Centerfor Environmental Studies

San Francisco State UniversityTiburon, CA 94920 USA

John LargierBodega Marine Laboratory P.O. Box 247

University of California, DavisBodega Bay, CA 94923 USA

Greg CrawfordThe Faculty of Science

and TechnologyVancouver Island University

Nanaimo, BC, V9T 5S5 Canada

P. Michael KosroCollege of Oceanic

and Atmospheric SciencesOregon State University

104 COAS Administration BuildingCorvallis, OR 97331-5503 USA

Abstract—With collaborated research efforts in the regionalcoastal ocean observing systems (SCCOOS, CeNCOOS, andNANOOS) off the U.S. West Coast (USWC), the nearly completedhigh-frequency radar (HFR) network provides an unprecedentedcapability to monitor and understand coastal ocean dynamics andphenomenology through hourly surface current measurements atup to 1 km resolution. The dynamics of the surface currents offthe USWC are governed by tides, winds, Coriolis force, low-frequency pressure gradients (less than 0.4 cycles per day (cpd)),and nonlinear interactions of those forces. The HFR surfacecurrents resolve coastal surface ocean variability continuouslyacross scales from sub-mesoscale to mesoscale (O(1) km toO(1000) km). Their spectra decay with k-2 at high wave number(less than 100 km) in agreement with theoretical sub-mesoscalespectra below the observational limits of present-day satellitealtimeters.

I. MOTIVATION

Ocean mesoscale variability refers to ocean dynamics occur-ring on scales in which the rotation of the Earth is significant.Specifically, mesoscale variability occurs in the regime ofsmall Rossby number, where the Rossby number (R0) isdefined as ζ/fc with ζ and fc being the vertical component ofrelative and planetary vorticity, respectively [e.g., [1], [2], [3],[4]]. Knowledge of mesoscale processes has been acceleratedwith the advent of high-precision satellite altimeters and

radiometers [e.g., [5], [3], [6]] accompanied by theoreticalefforts [e.g., [7], [8], [9]].

On the other hand, sub-mesoscale features in the ocean,frequently observed as filaments, fronts, and eddies, are char-acterized by both O(1) Rossby number and a horizontal scalesmaller than the internal Rossby radius of deformation. Sub-mesoscale processes are important as they contribute to thevertical transport of oceanic tracers, mass, and buoyancy andrectify the mixed layer structure and upper-ocean stratification[e.g., [10], [11], [12], [13], [14], [15]].

Sub-mesoscale process studies have benefited from ideal-ized numerical models and theoretical frameworks [e.g., [13],[14], [15]]. Unfortunately, there have been very limited in-situobservations of these dynamics because they demand high-resolution (hourly in time and km in space) measurements[e.g., [16], [17], [18]]. Surface current measurements in theupper O(1) m depth using high-frequency radar (HFR) havethe potential to resolve surface sub-mesoscale processes (e.g.,fronts, filaments, and eddies) and to elucidate the missing linkbetween offshore and nearshore dynamics [e.g., [19], [20],[21], [22], [18]].

978-1-4577-2091-8/12/$26.00 ©2011 IEEE

II. OVERVIEW

Shore-based HFR has been used to measure currents andwaves at the ocean surface using Bragg scatter return fromtransmitted radio signals and has been developed into anoceanographic observational tool [e.g., [23], [24], [25]]. Op-erational systems provide hourly surface current fields in theupper O(1) m depth with 0.5 to 6 km horizontal resolutionextending from the nearcoast, excluding the surfzone, offshoreto distances of 50 to 150 km depending on choice of radiofrequency [e.g., [26], [27], [28], [29], [22]]. The radial velocitymaps derived by multiple HFRs are combined into the vectorcurrent map on grid points with a targeting resolution. Thebaseline, the straight line between two radar sites, is an areawhere it is not possible to estimate vector solutions from nearlyparallel radial velocities as they weakly constrain the vectorsolutions normal to the baseline.

Use of HFR for oceanographic research of ocean currentsis a rapidly maturing field. Planning efforts are underwayto instrument the entire U.S. coastline to provide a nationalcapability to monitor and observe surface currents in near-real time. The network of HFRs is expected to support bothscientific studies and operational needs, including connectivitystudies, for monitoring and understanding marine protectedareas and larval transport; the tracking of shoreline discharges,impaired water quality and spilled oil; and at sea search andrescue efforts [e.g., [30], [31]].

III. USWC HFR SURFACE CURRENTS

The USWC HFR-derived surface currents are used as aprimary resource in the proposed analysis. The radial velocitymaps derived by 78 HFRs (as of January 2012) on the USWCare optimally interpolated on grid points with 6 km resolutioninto vector current maps and other kinematic and dynamicquantities (e.g., stream function, velocity potential, divergence,vorticity, and deformation rates) as well as their uncertaintyestimates [e.g., [16], [32]]. An example of cascade maps ofobserved surface currents off the USWC (6 km resolution),southern California (6 km resolution), and southern San Diego(1 km resolution) is shown in Figure 1.

All HFRs used in the proposed analysis are commerciallyavailable compact antenna systems (CODAR Ocean Sensors,Palo Alto, California) and are locally calibrated using antennabeam pattern measurements. An isotropic exponential corre-lation function with 10 km decorrelation length scale wasused to objectively map from radials to the vector currentfield, with assumed error and model standard deviations of6 and 40 cm s−1, respectively. The surface current productsdiscussed are insensitive to the choice of model and errorvariances. As a minor note on the data processing, the radialvelocity map from each HFR has its own spatial resolution inthe range and azimuthal directions depending on both radaroperating frequency and sweeping frequency. Since the radialvelocities with higher spatial resolution are likely to producea bias in the vector current map, radial velocity maps are binaveraged to make them comparable in resolution (e.g., 3 to

5 km range and 5◦ azimuthal resolutions) before they areoptimally interpolated.

The uncertainty of HFR surface current measurements hasbeen estimated with independent in-situ observations fromADCPs, radial velocities of multiple HF radars, and GPS-tracked drifters, with typical ranges, respectively, of 5 to 19cm s−1 [e.g., [33], [34], [29]], 5 to 7 cm s−1 [e.g., [35]],and 1 to 10 cm s−1 [e.g., [36]]. In the present analysis,the uncertainty is computed using currents at the uppermostbin of in-situ ADCPs [NDBC buoys 46027, 46011, 46063,and 46053, moorings at Orange County Sanitation District(OCSD), Point Loma Ocean Outfall (PLOO), and InternationalBoundary and Water Commission (IBWC)], located mostly insouthern California. The estimated uncertainty ranges from 4to 12 cm s−1 depending on the depth of the uppermost bin inthe subsurface current observations, geometry of the installedradars, and radar operating frequency. As the uppermost binis near the surface, the root-mean-squares (rms) differencebecomes smaller. The energy spectra of surface and subsurfacecurrents show continuous and smooth energy distribution withdepth.

IV. ENERGY SPECTRA AT MESOSCALE ANDSUBMESOSCALE

As an example of energy spectra at mesoscale and sub-mesoscale, the power spectra of oceanic currents derived fromHFR and ALT are considered in the wave-number (k = 1/L)and frequency (σ = 1/T ) domains (Figure 2) [e.g., [22]].Variance of currents differs with sampling location becauseof regional variations in driving forces and geostrophic com-ponents. HFR surface currents with resolutions of 1 km and6 km are sampled along a zonal grid line off southern SanDiego and in the area between Los Angeles and San Diego,respectively, where there are relatively weak winds. The HFRsurface currents of 20 km resolution on the coastline axis areconstructed to capture the largest spatial scales on the USWC(Figure 2a). On the other hand, the along-track SLAs are takenfrom sloping tracks in the northeastern Pacific (30◦N to 50◦N,114◦W to 133◦W; Figure 2a). To minimize the influence ofmissing observations on the spectrum estimates, a weightedleast-squares fit is used. The HFR surface currents at 20 kmresolution are only available from August to December of2008, so the wave-number spectrum is computed from onlyfive months of data. This selective estimate does not changeoverall results. The errors of power spectrum estimates areshown by the 95% confidence interval (Figures 2b and 2c).

The wave-number spectra of HFR surface currents showa consistent and continuous variance distribution across threedifferent resolutions (1, 6, and 20 km) (Figure 2b). Resolvedscales range from O(1000) km to O(1) km, and the spectradecay with k−2 at high wave-number in agreement withtheoretical sub-mesoscale spectra [e.g., [11], [14]]. While theirspectra can vary with location because of regional variations indriving forces and geostrophic contents, they have a consistentk−2 decay. Moreover, HFR observations resolve variability atscales smaller than about 100 km wavelength, where we think

the noise in satellite ALT-derived currents becomes dominantover oceanic signals [e.g., [37]]. As an example, the wave-number spectra of HFR surface currents in a region (e.g.,southern California) with minimum wind-driven componentsare comparable to the spectra of along-track ALT geostrophiccurrents (Envisat and Jason-1) in the northeastern Pacific(Figure 2a). The mismatch at low wave-number (L > 500km) is probably due to different coverage (e.g., coastal regionsvs. open ocean): HFR surface currents may contain significantvariance of alongshore coastal signals with large wavelength.

Spectra of near-surface currents (upper 60 m depth) inCalCOFI cruises have k−1 and k−2 slopes bent at 150 kmlength scale (L ≈ 150 km). The energy of subsurface currents(below 60 m depth) decreases with depth, in particular, inlow wave-number (L < 150 km), and the remaining varianceappears as a peak. This may result from either horizontal shearor local eddies of currents off southern California, observed at100 to 150 km offshore from the coast, which is a persistentfeature over the season [e.g., [38]]. The CalCOFI currents alsosupport the continuous transition of oceanic scales betweenmesoscale and sub-mesoscale.

In the frequency domain (Figure 2c), the energy at the majortidal constituents, inertial frequency, and diurnal harmonicfrequencies, and their enhanced variance in nearby bands areclearly identified. The energy of these motions decays with afactor between σ−1 and σ−2 at high frequency [e.g., [39]].In the very-low-frequency band (σ < 0.02 cpd, i.e., T > 50days), the coastal surface current spectra closely matches withmesoscale energy.

V. SUMMARY

Sustained observations of mesoscale and submesoscalesurface circulation are examined with high-frequency radar-derived surface currents off the U.S. West Coast. The HFRsurface currents resolve variability of the surface ocean acrossscales from sub-mesoscale to mesoscale [O(1) km to O(1000)km]. For instance, the wave-number spectra of HFR surfacecurrents decay with k−2 at high wave-number (L < 100 km)aligned with spectra reported in the literature of sub-mesoscaleprocesses. Moreover, at low wave-number (L > 100 km), theyare consistent with spectra of cross-track currents estimatedfrom along-track altimeter observations except for energy ofwaves with long wavelength such as coastally trapped waves.

In conclusion, coupled with other ongoing in-situ observa-tional programs and satellite remote sensing missions, surfacecurrent observations are crucial for monitoring ocean vari-ability continuously in time and space by filling the existinggaps of in-situ instruments from offshore to nearshore and canprovide timely input and a fundamental scientific resource tothe management of coastal waters.

ACKNOWLEDGMENT

Data from this report originate from the following uni-versities and research organizations on the USWC: ScrippsInstitution of Oceanography (SIO) at University of California,San Diego, University of Southern California, Marine Science

Institute at University of California, Santa Barbara, Califor-nia Polytechnic State University, Naval Postgraduate School,Romberg Tiburon Center at San Francisco State University,Humboldt State University, Bodega Marine Laboratory at Uni-versity of California, Davis, and Oregon State University. Thethree USWC IOOS regional coastal ocean observing systems– SCCOOS, CeNCOOS, and NANOOS – are acknowledgedfor their continued support and advocacy of HFR currentmeasurements for monitoring the oceans. The coastal winddata and in-situ ADCPs were provided by National DataBuoy Center (NDBC). The altimeter products were producedby SSALTO/DUACS and distributed by AVISO with supportfrom CNES.

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1 km resolution

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6 km resolution7 3015 23

a b

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Fig. 1. An example of the hourly cascade surface current maps observed by an array of high-frequency radar network on (a) the U.S. West Coast, (b)southern California, and (c) southern San Diego. The grid resolutions of surface current maps are 6 km for (a) and (b) and 1 km for (c). The HFR sites areindicated with balloons and their latency in the near-real time status is shown as colors (e.g., green, yellow, red, and gray). About 100 km diameter mesoscalecounter-clockwise eddy appear off Point Arena along with the equatorward wind event off Oregon coast [Figure 1a] and about 15 km counter-clockwisediameter eddy was observed in the Santa Barbara Channel [Figure 1b] .

132°00’ 126°00’ 120°00’ 30°00’

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Fig. 2. (a) Sampling locations of HFR surface currents with three spatial resolutions (1, 6, and 20 km), ALT gridded geostrophic currents (CCAR and AVISO),ALT along-track SSHAs (Envisat and Jason-1), and a CalCOFI cruise track (Line 90) are indicated. The effective coverage of HFR surface currents is denotedby a dark gray curve. (b) and (c): Power spectra of high-frequency radar-derived (HFR; 1, 6, and 20 km resolutions) surface currents and altimeter-derivedgeostrophic currents [ALT; optimally interpolated current products of CCAR (∼25 km resolution) and AVISO (∼33 km resolution) and along-track Envisatand Jason-1] for two years (2007 and 2008) in the wave-number domain [Length scales (L) of 1, 5, 10, 50, 100, 200, 500, and 1000 km are marked] andfrequency domain [Six seasonal harmonics (SA1 to SA6), spring-neap (SN , 14.765-day), lunar fortnightly (LF , 13.661-day), S1, K1, M2, and S2 tidalfrequencies are marked]. The wave-number spectra of shipboard ADCP currents in quarterly CalCOFI cruises (1993 to 2004) in vertical are shown as lightgreen (shallow; at 16 m depth) to dark green (deep, 408 m depth) curves. The auxiliary lines are denoted as k−1, k−5/3, k−2, and k−3 in the wave-numberdomain and σ−1, σ−5/3, σ−2, and σ−3 in the frequency domain. The 95% confidence interval (CI) of individual spectra is indicated. This is partiallyadapted from [22].