Modeling coastal current transport in the Gulf of...

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Deep-Sea Research II 52 (2005) 2430–2449

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Modeling coastal current transport in the Gulf of Maine

Robert D. Hetlanda,�, Richard P. Signellb

aDepartment of Oceanography, Texas A&M University, College Station, TX, USAbNATO/SACLANT Undersea Research Centre, La Spezia, Italy

Accepted 20 June 2005

Available online 30 September 2005

Abstract

A numerical simulation of the circulation in the Gulf of Maine is compared with observations taken during the spring

and summer of 1994, focusing on two distinct coastal current systems. The eastern Maine coastal current is well mixed out

to approximately 50m depth, with the influence of tidal mixing extending to 100m depth. In contrast, the western Maine

coastal current consists mainly of a surface-trapped plume emanating from the Kennebec River. Various methods of

model/data comparison are discussed, ranging from qualitative comparisons of surface temperature and currents to

quantitative measurements of model skill. In particular, one primary metric of comparison is the amount and distribution

of fresh water carried within the coastal current systems. In both coastal current systems, fresh-water flux has an

approximately self-similar structure so that measurements taken at a single mooring location may be extrapolated to

estimate the entire along-shore fresh-water flux. This self-similar structure is shown to be internally consistent within the

model, and results in good model/data comparisons. The model has more skill at predicting fresh-water flux than other

point-to-point surface property comparisons in all cases except surface salinity in the western Maine coastal current. This

suggests fresh-water flux is a robust feature in the model, and a suitable metric for gauging the model ability to reproduce

the broad-scale transport of the Maine coastal current system.

r 2005 Published by Elsevier Ltd.

Keywords: Gulf of Maine; River plumes; Buoyancy driven flow; Numerical model skill

1. Introduction

Numerical models of ocean circulation arebecoming a standard tool in all facets of oceano-graphic research; more and more they are calledupon to act as the foundation for other, non-hydrodynamic models, such as ecosystem or sedi-ment transport models. However, before the circu-lation model can be used effectively, the limitations

e front matter r 2005 Published by Elsevier Ltd.

r2.2005.06.024

ng author. Tel.: +1 979 458 0096;

6331.

ss: [email protected] (R.D. Hetland).

of the model must be clearly stated in order toascertain if using a particular circulation model isappropriate for the overlaid application, and toestimate the errors that may cascade from thehydrodynamic model upward to the overlaidapplication.

Clearly, any numerical model has limitations anderrors. Perhaps the most obvious is the limitationsof grid-scale resolution, as well as a finite domainfor regional-scale models. Errors also may stemfrom systematically over- or underestimating mix-ing, or using biased initial or forcing fields. Despitesuch limitations, researchers have been using

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numerical models successfully for decades. Webelieve that this is not contradictory—models maybe useful despite limitations. If an application isinsensitive to particular errors, a model that hasthose errors may still be skillful with regard to thatapplication. However, it is clear that a model wellsuited for one application may be completelyinappropriate for another. Therefore, estimatingmodel skill, or in particular using skill estimates to‘validate’ a model, makes no sense without referenceto an application.

For example, Bogden et al. (1996) used an inversemodel to estimate the inflow due to remote windforcing along an open boundary. They note thatmodel skill decreases with increasing model com-plexity (e.g., inclusion of the non-linear terms), andattribute the decline in skill to a mismatch in theactual and simulated energetic, small-scale flowfeatures. This result seems to contradict the notionthat a more complete set of physics will result in amore accurate simulation. Another possible inter-pretation of this result is that the spatial scales overwhich the comparison was performed were inap-propriate for the physical processes that the inversemodel was intended to estimate: the broad-scale,wind-driven flow into the domain. The small-scalefeatures were not averaged through a large enoughcovariance structure, and were contaminating theskill estimate.

In this paper, we examine one method of modeldata comparison using a particular definition ofskill. We seek to quantify the ability of a regionalnumerical model of the Gulf of Maine to predict thefresh-water flux (FWF) in the coastal currentsystem. The motivation is to assess the ability ofthe model to provide an adequate hydrodynamicbasis for simulating blooms of Alexandrium fun-

dyense, a toxic dinoflagellate found in the Gulf ofMaine often associated with the buoyancy-drivencoastal current system (e.g., Franks and Anderson,1992). We presume that prediction of the broad-scale features of the buoyancy-driven current, suchas FWF and salinity differences between the coastalcurrent and background waters, will lead directly tobetter predictions of regional A. fundyense out-breaks. Small-scale differences in, for example, theeddy field or frontal position will matter less as longas the broad-scale features are correctly simulated.

The principal phenomenon of interest here is thecoastal response to seasonal discharge of fresh waterassociated with springtime rains and melting snow.This pulse of fresh water enters the various Gulf of

Maine rivers, and eventually sets up a coastallytrapped, buoyancy-driven coastal current system.Because of spatial differences in tidal mixing, theGulf of Maine has two distinct coastal currentsystems: the vertically well-mixed Eastern MaineCoastal Current (EMCC) and the vertically strati-fied Western Maine Coastal Current (WMCC). Acartoon showing the locations of these two systemsis presented in Fig. 1.

The EMCC extends between Grand MananIsland and Penobscot Bay, and is vertically wellmixed by the tides out to approximately 100mdepth (Brooks, 1994; Lynch et al., 1997; Hetland,1997). There is considerable horizontal salinitystratification (a proxy for density stratification),with fresher, lighter waters closer to shore. Thevelocity structure is similar to that proposed byChapman and Lentz (1994), in which a region withstrong, localized horizontal density gradients, com-bined with no flow at the bottom, create a currentwith uniform vertical shear with very small bottomvelocities. However, it is not yet clear if the cross-shore flow, or cross-shore frontal motions areconsistent with the Chapman and Lentz model ofa density front trapped by the bottom boundarylayer. Previous modeling studies suggest that theEMCC is driven by a combination of tidalrectification, fresh-water input from the Saint JohnsRiver, and barotropic flow from the Scotian Shelf(Brooks, 1994; Lynch et al., 1997; Hetland, 1997).

In contrast, the WMCC is a surface-trapped riverplume emanating from the Kennebec and Penobs-cot Rivers. Wind plays a large role in moving theplume on- and offshore during up- and downwellingwind events, and wind is also a primary cause ofmixing in the plume (Fong and Geyer, 2001; Fonget al., 1997).

2. Methods

2.1. Model description

The Regional Ocean Modeling System (ROMS,Haidvogel et al., 2000) was chosen for the numericalsimulations in this study. ROMS uses a curvilinearhorizontal C-grid, and a stretched, terrain-followingvertical coordinate. The model grid size of grid is80� 150� 20; the horizontal grid is shown inFig. 2. The deep waters off the continental slopeare clipped to 800m depth to limit the external/gravity wave speed (e.g., tides).

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70°W 68°W 66°W 64°W 62°W

40°N

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46°N

St.Johns

Merrimack

WMCC

W

Bayof

Fundy

JordanBasin

WilkinsonBasin

GeorgesBank

GeorgesBasin

GrandMananIsland

Fig. 1. Gulf of Maine springtime coastal current circulation between Grand Manan Island and Cape Ann is shown, with major rivers and

bathymetric features indicated. The eastern Maine coastal current (EMCC) extends from Grand Manan Island, following the 100m

isobath. Near Penobscot Bay, there is a bifurcation point, where the EMCC may continue downcoast, or be deflected offshore. The

western Maine coastal current (WMCC) is more affected by the local wind stress, and may be pressed up against the coast during

downwelling winds or extend 50 km or more offshore during upwelling winds. The figure is based loosely on other circulation diagrams by

Bigelow (1927), Brooks (1985), and Lynch et al. (1997).

R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (2005) 2430–24492432

The model is initialized with a regional scaleclimatology created by Lynch et al. (1997), which isalso used to specify the tracer values along the openboundaries during integration. The climatologyonly contains a rudimentary coastal current systemshoreward of the 100m isobath due to scarcity ofobservations in that region. However, after approxi-mately one month of integration, the coastal currentsystem within 100m is well defined because it is sostrongly forced. Water properties deeper than 100mchange on a much longer time scale, and remainfairly steady throughout the integration. Attemptswere made to modify the climatology to betterrepresent the conditions in 1994, but these changesdid not significantly alter the structure of thesimulated coastal current.

The model grid was designed to be large enoughso that the coastal current systems were somewhatinsulated from the boundaries. Lynch et al. (1997)

found that information about the Gulf-scale wind-driven circulation patterns, in particular the baro-tropic flow from the Scotian Shelf, was crucial inreproducing the coastal current system—furthermotivation for a Gulf-wide domain. However, wedid not intend to simulate the entire Gulf of Mainecirculation correctly. For example, we are aware offlaws in the exchange between the deep Gulf basinsand the Atlantic ocean.

The model is forced with spatially uniform windstress and surface heat flux. Values for surfaceforcing were specified using air temperature, airpressure, and wind from the NOAA buoy 44007 (12NM southeast of Portland at 43:53N 70:14W), aconstant relative humidity of 70%, and short-waveradiation from the Woods Hole OceanographicInstitution (41:52N, 70:67W). This idealized repre-sentation of the surface forcing was consideredsufficient to provide reasonable development of

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70oW 68oW 66oW 64oW 62oW

40oN

42oN

44oN

46oN

CCM

JBMCPM

PBM

Fig. 2. The model grid is overlaid on regional isobaths. Also shown are the four mooring locations discussed in the text: from east to west,

the Cape Porpoise mooring (CPM), the Kennebec River mooring (KRM), the Jordon Basin mooring (JBM), and the eastern Maine

coastal current mooring (CCM). The solid lines represent the cross-sections through which the FWF is calculated for the EMCC and

WMCC. The small gray points show the location of hydrographic cross-sections used to compare with model results.

R.D. Hetland, R.P. Signell / Deep-Sea Research II 52 (2005) 2430–2449 2433

seasonal stratification and wind forcing of coastalcurrents along the Maine coast, since the scale ofsynoptic weather systems is relatively large. Forexample, Mountain et al. (1996) showed that short-wave radiation in the Gulf has a correlation scale ofseveral hundred kilometers, and Greenberg et al.(1997) showed that using uniform wind stress withM2 tide explains most of the remote and local windresponse of the Gulf.

Fresh-water discharges are prescribed fromthe four major rivers: the Merrimack, Kennebec-Androscoggin, Penobscot, and St. Johns rivers.Discharges from these rivers were specifiedusing stream gauge data from the USGS1 andfrom Environment Canada2 adjusted to accountfor drainage area downstream of the gauge loca-tions.

1http://www.water.usgs.gov2http://www.ec.gc.ca

Time series of winds and fresh water dischargesare shown in Fig. 3. To place the situation in 1994 incontext to other years, 1994 was very wet, havingone of the highest peak discharges on record, andhad moderate upwelling persisting through most ofthe spring, as shown in the second panel of Fig. 3.

The model includes tides using a Flather bound-ary condition (Flather, 1976) with tidal elevationscalculated from a finite-element tidal model. M2tidal elevation and currents were specified at theopen boundary using the finite-element tidal modelof Lynch and Naimie (1993). Temperature andsalinity were nudged to climatological values alongthe boundary. Surface forcing includes heat ex-change with the atmosphere, and surface windstresses; both varied in time but were spatiallyconstant. The model was initialized with climatolo-gical values of temperature, salinity and flow, andwas integrated from March 19, 1994 through June30, 1994. Model results were averaged over one tidalperiod, and stored.

http://www.water.usgs.gov

http://www.ec.gc.ca

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01-Apr-1994 01-May-1994 01-Jun-1994 01-Jul-1994

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Fig. 3. Wind and river forcing used in the numerical simulation is shown. The upper panel shows the along-shore winds (relative to the

majority of the Maine coast, with positive wind stress, t, rotated 55� to the right of north). The middle panel shows integrated along-shore

wind stress for four different years (see, for example, Blanton and Atkinson, 1983). In this figure, a positive slope represents net upwelling

winds, a negative slope means net downwelling. Winds in 1994 are generally upwelling favorable throughout the spring, punctuated by a

few downwelling events in May. The lower panel shows the fresh-water discharge for the four rivers included in the model simulation.


2.2. Data

2.2.1. Moored measurements

In the Eastern Gulf of Maine two moorings weredeployed. The eastern Maine coastal current moor-ing (CCM) was deployed within the eastern Mainecoastal current at about 100m depth from April 3 toJune 4, 1994. The Jordon Basin mooring (JBM) wasdeployed at the northwestern corner of the JordanBasin at a depth of about 200m from April 2 toMay 7, 1994. Both moorings were equipped withdownward-looking acoustic Doppler current profi-lers and three temperature/salinity sensors spreadover the mooring line; at the CCM, temperature andsalinity were measured at 5, 40, and 80m depth.

Four moorings were deployed in the western Gulfof Maine from February 17 to October 13, 1994field program, but only two are discussed in this

paper. The Cape Porpoise mooring (CPM) de-ployed offshore of Cape Porpoise in approximately50m of water with current meters and temperature/salinity sensors at 5 and 27m depth. The KennebecRiver mooring (KRM) was deployed in about 80mof water offshore of the Kennebec River withcurrent meters and temperature/salinity sensors at5, 27, and 50m depth.

2.2.2. Hydrography

In the eastern Gulf of Maine, a single hydro-graphic cruise was conducted from 26 to 29 April1994. In the western Gulf of Maine, three large-scalehydrographic surveys were conducted throughoutthe spring and summer of 1994, with additionalsurveys conducted along the Cape Porpoise trans-ect. In this paper, the focus is on two transects,shown in Fig. 2, along with the corresponding


transect used from the model for comparison. Wechose these lines because they both cross mooringlocations where time series of along-shore FWF isestimated. Other transects, not shown, also havebeen used in the hydrographic estimates of FWF.

2.2.3. Other data

Advanced Very High Resolution Radiometry(AVHRR) sea-surface temperature images areavailable from the NOAA CoastWatch program.3

Five Satellite tracked drifters were released in theeastern Gulf of Maine during the hydrographiccruise, drogued at either 10 or 40m depth. Thedrogue depth seemed to make very little differencein the behavior of the drifters, in that both types ofdrifter were carried into the coastal current system,and both types were entrained into the Jordan BasinGyre.

2.3. Definitions

2.3.1. Fresh-water flux (FWF)

FWF is calculated by multiplying the fresh-waterfraction, ðs� s0Þ=s0, times the velocity, v, andintegrating over some plane, A, so that

FWF ¼

ZZA

s� s0

s0

� �vdA, (1)

where dA is directed perpendicular to the areathrough which the flux is being calculated, s is thesalinity, and s0 is a reference salinity. The definitionof the reference salinity is not always straightfor-ward, and the particular choices are discussed inmore detail below. In this paper, we are primarilyconcerned with the local FWF, following the fresh-water input into the system from local rivers, so thereference salinity is chosen accordingly.

2.3.2. Model skill

Model skill is defined in this paper as

skill ¼ 1�

PNi¼1ðdi �L½mi�Þ

2

PNi¼1ðdi � ciÞ

2, (2)

where di are the available measurements, and L½mi�

is a row vector of the model results in which mi istransformed by the linear operator L to match themeasurements (see Bennett, 2002), and ci is a vectorof climatological, or background values. The finalterm in the definition of skill can be interpreted themodel error variance normalized by the data

3http://coastwatch.noaa.gov.

variance, where the data variance is relative to theclimatology. Thus, a perfect model (di ¼L½mi�) hasa skill of one, as long as the data contain significantdepartures from the climatology (i.e. the denomi-nator is non-zero). If the model simply returns theinitial best guess of climatology (mi ¼ ci), the skill iszero. Note that an energetic model that disagreeswith the data may have negative skill. Also, becausethe time series are not detrended, differences in themean values will contribute to the error variance,and reduce the skill.

The definition of skill has not been standardized,differing primarily in the denominator of the finalterm. This term represents a proxy for the truevariance of the observed field. Ideally, this numberwould be specified before the skill calculation, andin some cases where long time series are available, agood a priori estimate may be found usingmeasurements outside of the time frame of thenumerical simulation. However, given our relativelyshort, solitary time series, care must be taken inestimating the data variance. We choose to estimatethe variance by referencing the data to theclimatology, as opposed to a data mean. Byreferencing the time series to climatology, we avoidthe possibility that the mean is biased by the strongevents that are apparent in the measurement timeseries. That is, we assume that the climatology is abetter estimate of the true mean state of the systemthan a simple mean of the relatively short timeseries.

3. Results

A variety of model/data comparisons wereperformed. Comparisons between modeled andmeasured properties in the EMCC and WMCCrange from qualitative (sea-surface temperature andsalinity cross-sections) to quantitative (estimates ofmodel skill), and are described below, with eachregion examined separately. Although the focus ofthis paper is quantitative skill assessment, aqualitative understanding of the flow field isimportant in identifying potential weak elementsof the prediction.

3.1. Eastern Maine coastal current (EMCC)

The development of the EMCC in 1994 wasstudied by Hetland (1997), who noted that there wasa transition in the along-shore current strengthassociated with a homogenization of the water

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column on around May 6. The mean along-shorecurrents nearly double after this date, increasingfrom 0.12 to 0:22m s�1. This transition will be afocal point of the analysis below. Both the characterof the flow before and after the event, and thetiming of the transition are important in correctlypredicting the along-shore fresh-water transport.

3.1.1. Sea-surface temperature

Two relatively cloud-free AVHRR images of sea-surface temperature were available on May 3 and 11(Fig. 4), straddling the transition date May 6. OnMay 3, a plume of cold water is seen to be travelingdown the coast from Grand Manan island; the coreof the current is just about to impact a mooringlocated within the coastal current. On May 11, thecold jet has already hit the CCM, and a coldfilament has squirted offshore. The influence of thisfilament is seen in surface currents measured at amooring located on the northern rim of the JordanBasin, as well as in satellite-tracked drifter paths.This filament is discussed in more detail byPettigrew et al. (1998). Comparisons with AVHRRimagery (Fig. 4) show that, although the details aredifferent, the model produces a cold coastal jet withsurface filaments flowing offshore from the EMCCthat is qualitatively similar to what is seen in thesatellite imagery. These jets may be importantmechanism for transporting fresh water from theEMCC offshore, so it is important that numericalsimulations reproduce these features at least statis-tically correct. Because of the non-linear nature ofthe flow, we do not expect to reproduce thesefeatures exactly.

3.1.2. Salinity cross section

The EMCC is well mixed within 50m depth, andthe influence of tidal mixing extends to approxi-mately 100m depth. Observed and modeled salinitycross-sections are shown in Fig. 5. The comparisonshows that the measured extent of tidal mixing frontoccurs at about the same place in the model,approximately 100m depth. However, absolutevalues of salinity are off by a constant value; themodel is approximately 0:2 psu saltier than observa-tions. This is due to an initial condition that is notrepresentative of the true initial state. Climatologi-cal values of salinity may not be representative of aparticular year. Because of the timescales of salinitychanges in the deep basins within the Gulf areseasonal, or longer, errors in the initial conditionwill persist throughout a simulation covering only

one or two seasons. Mountain (2003) shows that theaverage salinity over the Mid-Atlantic Bight canchange by over 1 psu, and similar changes might beexpected in the Gulf of Maine.

3.1.3. Moored salinity and current time series

Point-to-point comparisons of moored salinityand current time series at the CCM are calculatedby finding the nearest grid cell to the measurementlocation. The model results are not averaged overneighboring points because the EMCC jet is fairlynarrow at the mooring location. Using a spatialcovariance structure as a weighted spatial averagemay bias the measurements toward waters that arenot within the EMCC jet.

Comparisons of salinity time series at the CCMare shown in Fig. 6. The comparison indicates thatthe model is much more stratified than observa-tions. Also, while in mid-May, in the observedsalinity time series the water column stratifies andthen mixes (partially) again, the model predicts thatthe water column remains stratified until mid-June(bottom panel in Fig. 6). Much of the variability instratification in the observations most likely has todo with the position of the EMCC front. The watercolumn will stratify as the front moves onshore, anddestratify as the front moves offshore.

There is some evidence in the model that on- andoffshore motions of the EMCC front are respon-sible for changes in stratification at the mooringlocation. Further inshore, at the 50m isobath, themodel does stratify temporarily, then destratifies ina manner similar to the observations (not shown).Here, the peak surface-to-bottom stratification issimilar in magnitude to the observed surface-to-bottom (5–80m) stratification at the CCM (about1:1 psu), but the modeled peak in stratification atthe 50m depth is delayed by 5 days because the flowinshore of the EMCC jet is weaker.

Comparisons of velocity time series (Fig. 7) showthat model results generally are within the envelopeof variability for observations. Measured meansurface currents in the EMCC were 0:16� 0:08;modeled currents over the same time frame are0:18� 0:04. The modeled currents have consistentlymuch less variance than observed currents; bothalong- and cross-shore; observed currents have twoto three times more variance as modeled currentsthroughout the water column (not shown). This is atypical problem with coastal ocean models that donot reproduce the smaller scale turbulent flow fieldoften observed in satellite images. As resolution

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Fig. 4. Modeled surface temperature (upper panels) and AVHRR satellite-derived sea surface temperature images (lower panels) from

May 3 and May 11, 1994 show a cold jet protruding from the EMCC. The jet has not yet developed in the satellite image on May 3. The jet

is most pronounced in both the model and observations on May 11, and is circled in both images. The colormap is arbitrary, chosen to

highlight the features of the flow, with darker colors representing colder water. The AVHRR images also show near-surface moored

current measurements (the straight lines attached to crosshaired circles), and drifter tracks (the curvy lines). The flow at the inshore

mooring on May 3 is 0.09, 0:23m s�1 on May 11. The solid lines in the drifter tracks show two days prior and after the time of the image,

with a circle marking the time of the image; dashed lines continue the tracks to 10 days after the image date. The offshore mooring was cut

between the SST image dates, and the dashed line represents the average flow between May 6 and 7, the last two days of the current record.


increases, these features become part of the simu-lated solution, and the simulated variance becomescloser to the observed variance (e.g., Marchesielloet al., 2003).

In early May, the modeled currents are relativelysteady, and follow the peak measured velocities,indicating that perhaps the EMCC jet is morestationary in the model. Some of the measured

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44 44.1 44.2 44.3 44.4 44.5−200

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Fig. 5. A comparison of measured and modeled salinity structure across the EMCC. The bold isohalines represent the reference salinity

used for calculations of FWF from measurements and the model. The position of the stations, and the line of the cross-section in the

model, is shown in Fig. 2. The data cross-section shows the locations of the hydrographic casts (vertical lines). The model cross-section

shows the cross-shore structure of the mean FWF as determined by the model (shading); the vertical line shows the location of the FWF

profile. The panel to the left shows a comparison of the vertical structure of the predicted and measured FWF at the CCM. Note that the

measured profile is extrapolated from salinity time series at 5, 40, and 80m depth by assuming constant vertical shear and salinity

stratification.


variability may have to do with meandering of jetassociated with the EMCC tidal mixed front;however, there is only slight evidence for this inthe T-S time series (not shown). Another explana-tion is that the flow within the EMCC pulses inresponse to upstream variability; for example, wind-forced continental shelf waves propagating into theregion from the Scotian Shelf.

3.1.4. Fresh-water flux time series

In the model, a time series of FWF was calculatedthrough a plane near the hydrographic cross-section(Fig. 5, located at the bold line in Fig. 2) using areference salinity of 32:6 psu. The reference salinitywas chosen as the isohaline intersecting the 100misobath (i.e., the saltiest water at the CCM location,Fig. 2). The same criterion was also used to set the

reference salinity in the observational estimates ofEMCC FWF, described below, although the actualvalues are different because of differences in theclimatology used to initialize the model and theactual distribution of salinity in 1994. This choice ofreference salinity gave values of FWF similar inmagnitude to the inputs of fresh water from theSt. John River in all cases. The calculation was setup such that salinity values higher than the referencevalue do not contribute to the FWF.

The mean cross-sectional structure of the EMCCFWF is shown in Fig. 5, along a hydrographicsection crossing the CCM position. The modelpredicts that most of the FWF occurs in the upper20m, and is horizontally centered about the CCM.A comparison of the vertical profile of FWF at theCCM location, however, indicates that the model

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Fig. 6. The upper panel shows a time series of salinity measured at three depths and is compared to model predictions. The lower panel

shows the measured and modeled surface-to-bottom salinity difference. Climatological values are also shown in both panels for reference.


over-predicts the local FWF by about a factor of 2(Fig. 5, left panel). Given that the measure-ments show a less-stratified water column at thislocation as compared to that predicted by themodel, and that the model has stronger cross-shore salinity gradients, it seems that the modeledEMCC is narrower than observed. However, in thediscussion section, it is explained how changes inwidth of the EMCC will not significantly alter theFWF.

As a test of the systematic errors in assuming aself-similar structure to arrive at the observedestimates of FWF, the self-similarity of the modeledFWF is examined. We hypothesize that the modeledFWF has a self-similar structure, in that measure-

ments at a single profile of velocity and salinity arerepresentative of the entire FWF carried by theEMCC. That is, an estimate of FWF from a verticalprofile (say, from a mooring) can be used toestimate the entire cross-sectional FWF by multi-plying the profile derived estimate by a constant.FWF calculated across the entire cross-section iscompared to the FWF calculated at the CCMmultiplied by a constant value, 16; 505m2, calcu-lated such that the two FWF time series would havethe same mean. A comparison of the point andentire cross-sectional estimates of FWF is shown inFig. 8. The ratio of FWF calculated from the profilevs. the entire cross-section has a standard deviationof 18% of the mean.

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Fig. 7. Observed and modeled along-shore (upper panel) and cross-shore (lower panel) currents at the EMCC mooring are compared.

Positive currents are upstream (against the Kelvin wave propagation direction) and offshore.

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sec

Fig. 8. Comparison of EMCC FWF calculated from a profile vs. an entire cross-section. The upper panel shows the filtered (one week)

FWF for a single profile and the entire cross-section of the FWF. The profile estimate of FWF was normalized by an area, such that the

mean of both FWF estimates is identical. The bottom panel gives the ratio between these two estimates. A value of one would mean the

two FWF estimates are identical. Higher values indicate that the point estimate is greater, lower values mean that the cross-sectional

estimate is greater.



Observed FWF carried by the EMCC wasestimated from observations by multiplying thevertically integrated profile of FWF at the CCM bythe constant representing the cross-sectional area ofthe FWF calculated above. The results are com-pared with numerical estimates of the FWF inFig. 9. The reference salinity for the observationalestimate is 32.4 (see Fig. 5). FWF was alsoestimated from a number of other cross-sectionstaken during the hydrographic cruise using geos-trophic currents with v ¼ 0 set at the sea floor, andagain using a reference salinity of 32.4. Thehydrographic estimates of FWF agree with boththe FWF estimated from the moored measurementsand calculated from the model.

The model correctly simulates the magnitude andtiming of the boxcar-like response present in theobservational FWF estimates; the model reproducesthe sudden increase in FWF observed on May 6, aswell as the sudden decrease on May 27. Morespecifically, the model has a skill of 0.94 atreproducing the observed FWF estimate for time-scales of 7 days and longer; model skill is discussedin more detail in the discussion section.

3.2. Western Maine Coastal Current (WMCC)

Geyer et al. (2004) discuss observations of theWMCC taken during the spring and early summer

04/01/94 04/15/94 05/01/940

1000

2000

3000

4000

5000

6000

7000

8000

9000

Fres

h w

ater

tran

spor

t (m

3 s-1

)

Fig. 9. Simulated and observed FWF, and ancillary quantities are show

of 1993 and 1994. They hypothesize that the along-shore FWF may be extrapolated from surfacemeasurements at a single mooring, with deepermeasurements upstream to estimate backgroundflow and salinity. Below, this hypothesis is examinedwithin the context of the model.

3.2.1. Salinity cross-sections and near-surface

salinity

Salinity cross-sections and near-surface salinitymeasured during a number of hydrographic cruisesare compared with model results. Salinity cross-sections show that, although there is reasonableagreement below about 5m depth, the modelpredicts fresher and more stratified near-surfacewaters than suggested by the observations. In part,this may be due to the fact that the upper few metersof the water column is not always accuratelymeasured using standard CTD techniques. Also,there is considerable stratification between theupper two cells in the model; the uppermost cellmay be up to 2 psu fresher than the underlying cell.

Maps of surface salinity (Fig. 10) show that themodel predicts a pool of fresh water offshore fromthe Kennebec River estuary that is not present inobservations. This pool comes from river dischargeblown offshore in the early part of the modelsimulation in April. The model does not sufficientlymix this fresh water, resulting in a persistent,

05/15/94 06/01/94 06/15/94

St. Johns river discharge Climatological FWF estimate Coastal Current Mooring FWF estimateROMS FWF estimate Hydro cruise FWF estimate

n for the EMCC. Methods of calculation are explained in the text.

ARTICLE IN PRESS

Fig. 10. The upper panels show observed and modeled cross-sections of salinity along the Cape Porpoise line on May 3 and May 10, the

average date of each cross-section. Lower panels show comparisons of modeled and observed near-surface salinity (at 3m depth) on May 3

and May 11, 1994, the average date of each survey. Observations are indicated by filled circles using the same color scale used to plot the

simulated fields.


surface-trapped pool of fresh water that is stillpresent when downwelling first occurs in earlyMay (see Fig. 3). This persistent stratificationis a well-known problem in the Mellor-

Yamada turbulence closure. In general, mixingin river plumes, which are highly stratified andusually only a few meters thick, is poorly under-stood.


3.2.2. Moored salinity and current time series

Salinity time-series measurements (Fig. 11, lowerpanels) show good agreement between observationsand model predictions after the plume has had timeto develop. Although the waters near the Kennebecoutflow are freshened by the mean presence of theplume in the climatology, a well-defined plume isnot present in the initial condition (climatology),but forms after the model has been started. Thesimulated plume grows to contact the CPM locationin early May. The large increase in FWF occursabout a week after the Kennebec river inflowreaches the CPM. The model remains slightly saltierthan the observations, about 0:5 psu, which is notsurprising given that the background water in the

0

5

10

15

Fres

h w

ater

tran

spor

t (10

3 m3 s

-1)

28

29

30

31

32

33

Plum

e sa

linity

(S p

)

04/01/94 04/15/94 05/01/94 05/1531

31.5

32

32.5

33

Ref

. sal

inity

(S 0

)

Fig. 11. The upper panel shows FWF estimated from salinity and curr

panel shows the measured and modeled plume salinity (CPM, at 5m

reference salinity (KRM, at 50m depth).

model is about 1:0 psu saltier than that measured.Again, this is due to slightly saltier conditions in theclimatology than were present in 1994.

Current time-series observations (Fig. 12) revealthat the model is generally within the envelope ofvariability seen in the observations. Downcoast flow(in the Kelvin wave propagation direction) appearsto be related with onshore flow, as expected for awind-influenced buoyant plume, but this trend isnot statistically significant.

3.2.3. Fresh-water flux time series

Plume cross-sectional area was estimated in themodel by comparing the FWF at a single point tothat calculated over an entire cross-section (Fig. 13).

All upstream riversClimatology Data - Mooring Data - Hydrography Model

Climatology Data - MooringROMS

/94 06/01/94 06/15/94 07/01/94 07/15/94

Climatology Data - MooringROMS

ent observations, and from the model in the WMCC. The center

depth), and the bottom panel shows the measured and modeled


Geyer et al. (2004) used a nearly identical method toextrapolate point measurements of FWF to a cross-sectional estimate of FWF. The cross-sectional area

04/01/94 04/15/94 05/01/94-0.4

-0.2

0

0.2

0.4Sp

eed

(m s

-1)

WMCC mooring

04/01/94 04/15/94 05/01/94-0.4

-0.2

0

0.2

0.4

Spee

d (m

s-1

)

WMCC mooring c

Fig. 12. Observed and modeled along-shore (upper panel) and cross-

compared. Positive currents are upstream (against the Kelvin wave pro

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Fres

h w

ater

flu

x

03/15/94 04/01/94 04/15/94 05/01/90

0.5

1

1.5

2

FWF

poin

t / F

WF

line

Fig. 13. Comparison of WMCC FWF calculated from a profile vs. an e

FWF for each case; the bottom panel gives the ratio between these t

1000m3 s�1. The presentation is identical to that shown in Fig. 8.

of the plume stays nearly constant, and the point-estimate and cross-sectional estimate of FWF agreeto within a factor of 2 when the FWF is high (over

05/15/94 06/01/94 06/15/94

along-shore currents

05/15/94 06/01/94 06/15/94

ross-shore currents

ClimatologyData Model

shore (lower panel) currents at the Cape Porpoise mooring are

pagation direction) and offshore.

Cross-section estimatePoint estimate

4 05/15/94 06/01/94 06/15/94 07/01/94

ntire cross-section. The upper panel shows the filtered (one week)

wo estimates. The ratio is only shown for values of FWF over


1000m3 s�1). The total WMCC FWF (Fig. 11, toppanel) was estimated from observations by extra-polating the point FWF measurement, assuming thesame constant cross-sectional area as calculatedwithin the internal model point/cross-section com-parison.

4. Discussion

4.1. Model skill

Estimates of model skill for various point-to-point surface property comparisons and estimatedFWF are presented in Table 1. Surprisingly, theFWF calculated within the EMCC, a bulk propertyof the flow field, is relatively skillful despite negativeskill in nearly all of the point-to-point comparisons.Skill at estimating the FWF in the WMCC is alsorelatively high, at least for time periods of morethan one week, but here the highest skill is thecomparison between modeled and observed sea-surface salinity.

One explanation for the high skill in predictingFWF is that it depends on the product, orcovariance, of along-shore velocity and salinity.For example, imagine that the velocity and salinityare both oscillatory functions. Simulated time seriesof both these properties could be individually out ofphase with observations, while the product of thetwo time series is in phase. This results in lower skillfor the individual time series, and higher skill for theproduct. This difference in skill might be expected ifsmall-scale eddies are a significant fraction of theFWF.

It is not yet clear that high skill in reproducingFWF will result in better simulations of A.

fundyense or other plankton in the Maine coastalcurrent. Based on the calculations of model skill, we

Table 1

Model skill is calculated for surface values of along-shore

currents and salinity

EMCC WMCC

33h 7 day 33h 7 day

Along-shore surface currents �0.41 0.01 �0.87 �0.74

Cross-shore surface currents �1.06 �0.46 �0.51 0.57

Surface salinity �0.47 �0.36 0.83 0.98

Fresh-water flux 0.52 0.86 0.03 0.66

Time series were filtered with either a tidal filter (33-h cutoff), or a

seven-day boxcar filter to remove weather-band variability.

expect that broad features of A. fundyense bloomscould be simulated with high skill, but the details ofthe population distribution with less skill. This maytranslate into the ability to predict the presence ofA. fundyense regionally, but not the ability topredict the exact location of affected regions alongthe coast.

4.2. Conceptual models of self-similar fresh water

flux

In the model, it is comparatively straightforwardto extract the time series of some large-scale process.In contrast, a point measurement requires aconceptual model of the process to extrapolateinformation at to an entire cross-section. Theconceptual model is essentially a covariance struc-ture based on simple physical processes. Unfortu-nately, skill measured using a conceptual model toextrapolate measurements to a larger scale nowdepends not just on the model’s ability to representthe flow field, but also on the ability of theconceptual model to extrapolate the measurements.When using this method of model assessment, thenumerical model and conceptual model of thecirculation field are tightly linked.

Predictions of FWF may be expected to have ahigh skill because fresh water is conserved in themodel calculation. However, there are many poten-tial sources for errors that could degrade the FWFprediction. The primary error in FWF calculationsis the reference salinity, as the fresh-water fraction isdefined relative to this quantity. There may also beerrors in the predicted FWF because of modelerrors. In the case of the EMCC, the model mayover- or under-predict the cross-frontal FWF. Inthe case of the WMCC, too much mixing in themodel may destroy the coherency of the plume, sothat the fresh water of the plume becomes entrainedinto the background flow. The fact that the modelmaintains skill at predicting FWF despite thesecompounding potential errors means that thesimulated dominant dynamical balances integratedover each of the coastal current legs must be mostlycorrect.

More fundamentally, the underlying dynamicsthat cause the two coastal current systems to be self-similar must be understood in order to quantify theerrors in the assumption, as well as to predict if andwhen the assumption will break down. The causesof self-similar FWF, distinct in each leg of thecoastal-current system, are discussed below.


4.2.1. EMCC

The EMCC is a bottom-trapped flow, controlledin part by topography and tidal mixing. As noted byYankovsky and Chapman (1997), the transportcarried by a bottom-trapped front, at its equilibriumposition across the shelf, is dependent only on theheight of the front and the density difference acrossthe front. The transport is carried within the frontalregion, rather than across the entire shelf, similar tothe FWF shown in Fig. 5. This simple model may bemodified to examine the fresh-water transportcarried by the EMCC. Suppose the EMCC maybe characterized as a discrete front of height H andwidth W with a density difference, Dr, and anassociated salinity difference, DS, across the front(see Fig. 14). Assume the cross-shore densitygradients are constant, so that the vertical shearwill also be constant. Similar to Yankovsky andChapman, it will be assumed that the front ispositioned such that the flow near the bottom isessentially zero. The fresh water carried by this frontwill be

FWFEMCC �

Z 0

�H

Z W

0

us0 � s

s0

� �dxdz

¼g0H2

4f

Ds

s0¼

gbH2

4f r0

Ds2

s0, ð3Þ

where g0 � gDr=r0 is the reduced gravity. There is aquadratic relationship between FWF and the

(ρο−∆ρ)

(So-∆S)

v(z)

W

H

Fig. 14. A diagram of the EMCC front based on the conceptual model

(1997). Note that the isopycnals do not extend from the bottom to th

Yankovsky and Chapman model will still be valid with arbitrary ver

responsible for the bottom-trapped jet (Chapman, 2000). The assumptio

constant (or constantly proportional) across the width of the jet. Com

salinity difference cross the front if a linear relation-ship between salinity and density is assumed(Dr ¼ bDs).

Note that the total FWF does not depend on thewidth of the front. The FWF is modulated by thecross-shore position (in particular, the local depthH) and the near-shore salinity (assuming theoffshore salinity remains relatively constant). How-ever, the local FWF measured at a point will dependon the width of the front; halving the frontal widthwill double the local FWF. Thus, the measuredFWF at any point within the EMCC front will beproportional to the total, integrated EMCC FWFas long as the front maintains its geometry andposition over the shelf. Extrapolating point mea-surements of FWF to estimates of total along-shoreFWF is equivalent to assuming that the frontmaintains a constant width throughout the analysisperiod.

Chapman (2000) extends the basic theory pro-posed by Yankovsky and Chapman (1997) toinclude ambient vertical stratification. Ambientvertical stratification acts to reduce the trappingisobath, but the solution is qualitatively similar.Chapman’s results suggest that the reference densityto use is that near the base of the front, in a similarposition to the reference salinity used in this paperto estimate the FWF.

The fact that the observed frontal width is widerthan the modeled frontal width will not affect the

(ρo)

(So)

of a bottom-trapped front described by Yankovsky and Chapman

e surface, but rather veer into the stratified offshore waters. The

tical stratification superimposed on the horizontal stratification

n of self-similar FWF requires that the vertical structure remains

pare with Fig. 5.


extrapolated estimated of FWF as long as both theobserved and modeled frontal width remains con-stant. The good agreement between the modeledtotal FWF and the FWF extrapolated from mooredmeasurements suggests that both the real andsimulated EMCC width are indeed approximatelyconstant, unless there are compensating errors intemporal variations of the FWF and frontal width.

Moreover, because the FWF relies on the productof the velocity and salinity anomaly, the observedand modeled FWF may be the same even if thesalinity and velocity time series differ. An analogyto this would be getting the turbulent flux of aproperty correct without correctly reproducing theeddy field. To correctly simulate the effect of theeddy field, the statistics of turbulent field must bereproduced or the turbulent flux may be parameter-ized. In the case of FWF, the details of the frontalposition and small-scale energetic features mayincorrect. However, we reproduce these featuresstatistically in a way that, on average, they create aFWF similar to the observed FWF. This mayexplain why the model had relatively high skill inpredicting FWF despite the lower skill in predictingeither salinity or along-shore velocity.

4.2.2. WMCC

The WMCC is a surface-trapped plume that isstrongly influenced by the local along-shore windstress. The plume may be stretched offshore, to the

(ρο−∆ρ)

(ρο)

(So-∆S)

(So)

WdownwelledWupwe

Vdownwelled

Fig. 15. A diagram of the WMCC front shows how the plume is mov

assumption of self-similar FWF requires that the velocity within the plu

constant (i.e., HdownwelledWdownwelled ¼ HupwelledWupwelled). Compare wit

point where it may loose contact with the coast,during upwelling winds; during downwelling, theplume is pressed up against the coast (see Fig. 15).The along-shore fresh water transport is similarlyinfluenced by the local along-shore wind stress:downcoast transport of fresh water is generallyenhanced during downwelling and suppressed dur-ing upwelling. The correlation between along-shorewinds and FWF is given by the regressionFWF ¼ 3:5� 103–6:8� 104t (r2 ¼ 0:44), where po-sitive t is an upwelling wind stress. The regressionimplies that in the absence of wind, the FWF is stillaround 3500m3 s�1, and an upwelling wind stress of0:5� 10�4 m2 s�2 will block downcoast transport offresh water.

For energetic flows within the plume, with a meanspeed of 0:30m s�1 or more and salinities between24 and 28 psu, the flow was moderately slab-like: thestandard deviation about the mean flow speed in theplume was 30–40%. For less energetic flows, thestandard deviation was 40–60% of the mean flowspeed, owing to stronger advection of momentumand tracers in the plume that break the Ekmanbalance between wind stress and surface layer flow.The stronger flow events are associated to strongwind events, indicating that the wind-driven plumeis generally slab-like.

The largest potential for error in the self-similarassumption will be when there are no measurementswithin the plume. Because the plume changes

Vupwelled

Hdownwelled

lled

Hupwelled

ed on- and off-shore by downwelling and upwelling winds. The

me is constant throughout the cross-sectional area, which remains

h Fig. 10.


position, it may be shifted such that the mea-surement point is no longer within the plume.Fortunately, it appears from the surface-salinitymeasurements that this rarely happened at theCPM; the salinity is almost always fresherthan climatological values in April, May, and June(Fig. 11).

5. Conclusions

A numerical simulation of the Gulf of Mainecoastal current system in 1994 was compared withmeasurements. Results suggest that the model mustnot necessarily be skillful at reproducing small-scalevariability to be skillful at reproducing large-scale,integrative circulation features.

Small-scale, energetic features were responsiblefor poor point-by-point comparisons. Some of thisvariability was reproduced within the model. How-ever, the energetic features are non-linear, and donot correlate between the model and observations,degrading the skill of point-by-point comparisons.However, the covariance between salinity andvelocity resulted in relatively high skill at reprodu-cing the along-shore FWF. Preliminary studiessuggest that this is true for other years, as well.

Central to the high FWF skill was the assumptionthat coastal current transport is self-similar for boththe EMCC and WMCC, that is point measurementsof FWF may be extrapolated to estimate the entirealong-shore FWF by multiplying by a constantcross-sectional area. This assumption was internallyconsistent within the model, as well as otherestimates of FWF.

Acknowledgments

This work was funded by NOAA GrantNA960P0099 and by the USGS Coastal and MarineGeology Program. This is contribution number 145from the ECOHAB program. The authors wouldlike to thank Rocky Geyer, Dennis McGillicuddy,and Charlie Stock for stimulating discussions andhelpful suggestions.

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