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Cold-front-induced flushing of the Louisiana Bays

Zhixuan Feng a,⁎, Chunyan Li a,b

a Department of Oceanography and Coastal Sciences and Coastal Studies Institute, School of the Coast and Environment, Louisiana State University, Baton Rouge, LA 70803, USAb College of Marine Sciences, Shanghai Ocean University, 999 Hucheng Huan Road, Shanghai, 201306, China

a b s t r a c ta r t i c l e i n f o

Article history:Received 7 July 2009Received in revised form 24 May 2010Accepted 27 May 2010Available online 12 June 2010

Keywords:Cold frontsBay flushingSubtidal barotropic oscillationsAlongshore and cross-shore windsLouisiana coast

Water level variations were used to calculate cold-front-induced water exchange fluxes for three Louisianabays. Twenty-nine cold fronts were identified from weather maps between September 2006 and April 2007.Cold front passages cause water to flush out of the bays, with large variability in volume fluxes. Due to thedifferences in water body area and basin geometry, the Atchafalaya/Vermilion Bays have exchange rates anorder of magnitude higher than the Barataria Bay. We identified five largest flushing events which were allassociated with migrating extra-tropical cyclones with frontal orientations perpendicular to the coastline,suggesting that wind direction is an important component in determining the flushing rate. Both alongshoreand cross-shore winds play important roles in bay-shelf water exchange, and northwest winds appeared tobe most effective in flushing the bays. Strong cold fronts may flush more than 40% of the bay waters out ontothe continental shelf within a less than 40-hour period. An analytical model is applied for the cold front windinduced flushing process which reveals that the amplitudes of water level variations induced by alongshoreand cross-shore winds have the same order of magnitude, indicating that they play almost equally importantroles in driving the subtidal water level changes inside the bays.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The Louisiana coastal zone, including the lower deltaic plain,wetlands, estuaries, bays, barrier islands and inner continental shelf,contains 40% of the U.S. coastal and estuarine wetlands (Stone et al.,1997; Penland et al., 1990). However, these systems account for 80%of the nation's coastal erosion and wetland loss due to the combinedeffects of natural processes and anthropogenic activities (Penland etal., 1990). Theworld's second largest zone of coastal hypoxia (oxygen-depleted waters, defined as dissolved oxygen levels less than 2 mg/l)is also on the Louisiana–Texas continental shelf, referred to as the“Dead Zone” (Rabalais et al., 2001; Rabalais et al., 2002). Althoughlocated in a relatively low wave and tidal energy environment in thenorthern Gulf of Mexico, the low-lying deltaic plain is stronglyinfluenced by various coastal processes, of which the subsidence andcombined impacts of occasional tropical cyclones and frequent coldfronts are the most significant (Georgiou et al., 2005).

Cold front passages and associated coastal responses in the northernGulf of Mexico are of particular interest to researchers (e.g., Roberts etal., 1987;Moeller, et al., 1993;Walker and Hammack, 2000; Pepper andStone, 2004). A cold front is the interface or transition zone(25–250 km) between heterogeneous air masses where colder, drier

and denser air is advancing towards warmer, moister and lighter air(Hsu, 1988). Cold fronts are the prevailing regional weather patterns,with a 3- to 7-day interval, along the U.S. Gulf coast between Octoberand April (Chuang and Wiseman, 1983; Hsu, 1988). Compared withoccasional but more violent tropical cyclones (e.g., Li et al., 2009), thelower energy but more frequent cold fronts may drive greatercumulative coastal changes (Roberts et al., 1987; Moeller et al., 1993).

Throughout the past half centuries, great efforts have beenmade toobtain better understandings of estuarine circulations since Pritchard'spioneering work in the Chesapeake Bay (Pritchard, 1952, 1954, 1955).In the recent decades, the wind-induced subtidal oscillations andbarotropic volume transport have been extensively studied in theestuaries of the Atlantic coast as well as the Gulf coast of the UnitedStates (e.g., Wang, 1979; Swenson and Chuang, 1983; Wong andGarvine, 1984; Lee et al., 1990; Valle-Levinson et al., 2001; Wong andValle-Levinson, 2002; Snedden et al., 2007; Salas-Monreal and Valle-Levinson, 2008). For example, Wang (1979) found that in theChesapeake Bay, coastal remote forcing was mainly responsible forthe longer period (N10 days)motionswhile shorter period oscillationsof less than four days were induced by local and longitudinal winds.Valle-Levinson et al. (2001) identified three major scenarios on thewater exchange through the entrance of Chesapeake Bay and alsoindicated that the northeast winds were the most effective in flushingwater out of the bay.Wong and Valle-Levinson (2002) pointed out theseasonality of volume exchange patterns and relative importance oflocal and remote winds, depending on the frequency of wind eventsand the degree of stratification in the estuary. Salas-Monreal andValle-

Journal of Marine Systems 82 (2010) 252–264

⁎ Corresponding author. Present address: Division of Applied Marine Physics,Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL33149, USA. Tel.: +1 305 421 4984.

E-mail address: [email protected] (Z. Feng).

0924-7963/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.jmarsys.2010.05.015

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Levinson (2008) discussed barometric pressure effect and found that itcould account for 1/3 of the total subtidal sea level variations in theChesapeake Bay. In the Delaware Estuary, Wong and Garvine (1984)found that remote wind effect was more important than local windeffect in forcing subtidalwater levelfluctuation based on observations.This conclusion was further confirmed by Garvine's (1985) barotropicmodel, which considered two independent mechanisms: (1) directsetup and set down by local wind stress in the longitudinal direction ofthe estuary, and (2) remote wind action by producing cross-shelfEkman transport over the adjacent shelf.

The responses of the Louisiana estuaries to wind and tidal forcingsdemonstrate major differences from the other coasts, mostly due tothe Mississippi and Atchafalaya Rivers and the associated deltaicfeatures. In general, these estuaries are bar-built, short (tens ofkilometers) and shallow (usually less than 2.5 m), fringed by coastalmarshes and barrier islands with multiple inlets. The unique andcomplex landscape features largely complicate the hydrodynamics.The shorter channels often make the tides appear as diurnal standingwaves (e.g. Lamb, 1932). In contrast, the east coast estuaries are oftenlonger in length with progressive tidal waves, mostly semi-diurnal(e.g. Pritchard, 1952). Another very important difference is thecharacteristics of winter storms. In the Louisiana coast the windsfrom these cold fronts typically have a unique pattern of changes,demonstrated by a sharp change of onshore southerly wind that causewater setup to a cold and strong northerly, northwesterly, or westerlywinds that drive a subsequent set down (Hsu, 1988). This is due to theroughly east–west orientation of the Louisiana coastline, differentfrom the east coast which is basically north–south oriented. Thewind-induced setup and set down processes in the two systems are thusquite different. Swenson and Chuang (1983) inferred that frontalpassages could induce about 50% of the total volume exchange, andthe volume fluxes could be up to six times greater than the tidal prismin the Lake Pontchartrain. Lee et al. (1990) found a predominantwind-induced barotropic volume exchange mode in the CalcasieuLake, Louisiana. Walker and Hammack (2000) demonstrated thatstrong northwest winds during winter storms could flush 30–50% ofwater out of the shallow bays and reduce water level by more than1 m in the Atchafalaya/Vermilion Bay regions. Snedden et al. (2007)concluded that in the Breton Sound, a very shallow (0.7 m) deltaicestuary east of the Mississippi River, the subtidal estuary-shelfexchange was mainly driven by remote wind forcing through coastalEkman convergence while effect from local wind forcing is minimaldue to limited fetch. Li et al. (2008) demonstrated that circular shapedplumes in the Lake Pontchartrain could be expanded northwardunder northerly winds through wind-induced straining and verticalstratification. Li et al. (2010) estimated that near the mouth of WaxLake Outlet, Atchafalaya Bay, half of the water level setup was due tolocal wind stress (50%), the other half due to wave (25%) and lowbarometric pressure (25%), while Coriolis Effect was negligible.

Our research topic is the bay-shelf water exchange during coldfronts, a subject essential for the understanding of land–seainteraction and ecosystem dynamics for better coastal management.For instance, the sediment flushed out of the Atchafalaya Bay is themajor source for the accretion of the Chenier plain to thewest (Kinekeet al., 2006). Also, the annual oyster yields along the Gulf coast arelargely determined by the estuarine salinity (Tuner, 2006).

Tides in this area are microtidal (tidal range is usually less than0.5 m), whilewind-induced subtidal oscillationsmay cause significantwater exchange, especially during strong cold front events. By using insitu observational data, synoptic weather maps and an analyticalmodel, the primary objectives of this study are: (1) to quantify cold-front-induced water exchange between inner shelf and threeLouisiana bay systems: Atchafalaya/Vermilion Bays (AVB), Terre-bonne/Timbalier Bays (TTB), and Barataria Bay (BB) (Fig. 1), and (2) todetermine the relative importance of cross-shore and alongshorewinds in driving subtidal water level variations in the Louisiana Bays.

2. Data and methods

Hourly water level and wind data, from September 2006 to April2007, were obtained from buoys, oil platforms and tide gauges alongthe Louisiana coast (Fig. 1). Note that wind directions are consistentlydescribed following traditional meteorological convention, e.g., northor northerly winds mean that winds originate from geographicalnorth. The 3-hourly United States surface weather maps wereobtained from the archive of NOAA's National Weather ServiceHydrometeorological Prediction Center (www.hpc.ncep.noaa.gov/html/sfc_archive.shtml) to identify the time of cold front passages,type of cold fronts and their orientation relative to the coastline.

Assuming a quasi-steady state of water level in the entire bay andno other major source and sink of water, the volume exchange ratebetween bay and inner shelf was calculated by:

F =dηdt

× A

where F is volume transport per unit time (m3/s), η is water level (m)in the bay, or mean water level if data from two or more stations areused, t is time (s), and A is the area of the bay (m2).

The areas of the bays (dotted areas in Fig. 1) were measured byArcGIS under the projection of WGS UTM1984 Zone 15 N. The areas ofthe AVB, TTB, and BB are 2025.98×106, 892.48×106, and570.11×106 m2, respectively. Here, the total area of BB also includesLittle Lake which is directly connected to BB through some bayous, butother lakes in the upper Barataria Basin are not taken into account. Thevolumes of the bays were also calculated, based on the digital elevationmodel (DEM) bathymetry data (1″ resolution) obtained from NOAA'sNational Ocean Service's (NOS) Estuarine Bathymetry database. Theestimated total volumes of the AVB, TTB, and BB are 3.87×109,1.30×109, and 0.633×109 m3, respectively. The subtidal water ex-change rates were calculated by applying a 40-hour 6th-order Butter-worth low-pass filter.

3. Observational results

Cold fronts have two end-member types: (1) arctic surge, which isless frequent and is one that moves southward and (2) migratingcyclone, which is accompanied by a strong low pressure cell (Robertset al., 1987; Pepper and Stone, 2004). The essential differences are theorientation of the fronts with respect to the east–west Louisianacoastline, and the resultant behavior of thewind-driven surfacewaters(Roberts et al., 1987; Pepper and Stone, 2004). By examining thesurface weather maps, 29 cold front events were identified betweenSeptember 2006 and April 2007, of which only 4 events were arcticsurges, while the remaining 25 were all migrating cyclones (Table 1).For migrating cyclones, they usually move southeastward across theLouisiana coast, so the AVB are the first to be impacted by the coldfronts, followed by the TTB 3–4 h later and the BB after about onemorehour. Arctic surges affect the entire Louisiana coast almost simulta-neously because the orientations of those fronts are typically parallelto the coastline.

Fig. 2 presents the subtidal volume fluxes, calculated from time-series measurements of water level. In general, the curves of subtidalvolume fluxes show similar pattern for all three bays, but withdifferent orders of magnitude. The AVB have the largest fluxamplitude, which is approximately 4–6 times of that of the TTB, andan order of magnitude higher than that of the BB. Such differences canbe explainedby two factors: surface area and geometry of the bays. TheAVBhave the largest area,which is roughly 2.3 and3.6 times of those ofthe TTB and BB, respectively. The AVB also have a much wider openboundary with the Atchafalaya Bay directly opening to the Gulf ofMexico; while both the TTB and BB are largely protected by a chain ofbarrier islands, limiting the amount of bay-shelf water exchange.

253Z. Feng, C. Li / Journal of Marine Systems 82 (2010) 252–264


In general, cold front passages (vertical lines in Fig. 2) coincidewith the timing of the outward flushing of the bays. However, the rateand amount of flushing vary greatly with different cold fronts,depending on their strength and associated wind variability (Fig. 2and Table 1). Typically, cold-front-induced flushing events last for 25

to 45h. Events of durations less than 25h or more than 45h are rare.The variations of subtidal water levels associated with typical coldfront events are similar. At the beginning, the pre-frontal winds fromsouthern quadrants pile up the water masses. Several to more than10h before the frontal passage, with the approaching of the frontal

Fig. 1. The Louisiana coast and observational stations in the northern Gulf of Mexico. The bays involved in the study are indicated with dotted areas. NOAA and LUMCON tidal gaugesare shown with stars and diamonds, and wind measurements are obtained from WAVCIS CSI-3 (solid circle). Davis Pond Freshwater Diversion is illustrated as a solid square. CP:Cypremort Point; LAP: Lawma Amerada Pass; LUML1: LUMCON Marine Center; TAMIL1: Tambour Bay; GISL1: Grand Isle.

Table 1The duration of flushing, total volume transport and percentage of volume for all cold front events in the three bay systems. The five largest flushing events are highlighted with stars.MC: migrating cyclone; AS: arctic surge.

Event Type AVB TTB BB

duration (hr) Volume (m3) Percent (%) duration (hr) Volume (m3) Percent (%) duration (h) Volume (m3) Percent (%)

1 MC 35 7.67×108 19.83 37 1.35×108 10.40 45 5.13×107 8.102 MC 65 1.06×109 27.38 59 1.94×108 14.94 60 5.61×107 8.853 AS 28 4.51×108 11.64 32 8.27×107 6.36 37 3.54×107 5.604 AS 32 3.95×108 10.22 40 6.34×107 4.88 40 2.59×107 4.085 AS 16 7.75×107 2.00 No flushing No flushing6 MC 34 1.13×109 29.25 37 2.66×108 20.46 42 9.47×107 14.957* MC 32 1.60×109 41.28 32 4.15×108 31.94 33 1.50×108 23.688 MC 34 8.02×108 20.73 37 1.66×108 12.76 37 5.66×107 8.949 MC 42 3.01×108 7.79 39 1.44×108 11.05 37 5.69×107 8.9910 MC 30 7.38×108 19.06 69 1.69×108 12.98 27 3.73×107 5.9011* MC 32 1.54×109 39.68 32 4.91×108 37.80 34 1.83×108 28.8512* MC 32 1.33×109 34.32 32 3.71×108 28.58 33 1.64×108 25.9513 MC 60 4.33×108 11.19 58 1.56×108 11.98 25 6.75×107 10.6714* MC 35 1.48×109 38.28 36 5.84×108 44.90 39 2.39×108 37.6815 MC 30 7.71×108 19.92 30 2.42×108 18.63 60 1.57×108 24.7816 MC 32 8.76×108 22.64 32 2.52×108 19.39 38 1.26×108 19.9317 MC 42 1.26×109 32.67 33 2.80×108 21.51 34 8.65×107 13.6718 MC 48 6.16×108 15.91 54 1.29×108 9.95 52 5.41×107 8.5519 MC 29 4.85×108 12.54 25 1.37×108 10.57 29 8.74×107 13.8020 AS 33 3.00×108 7.76 41 6.71×107 5.16 No data21 MC 35 7.18×108 18.54 33 1.72×108 13.24 24 1.80×107 2.8422 MC 26 8.29×108 21.42 27 2.80×108 21.56 26 1.22×108 19.3523 MC 31 6.18×108 15.97 29 1.66×108 12.78 26 4.18×107 6.6024 MC 27 6.67×108 17.22 27 1.79×108 13.76 28 7.27×107 11.4825 MC 34 1.03×109 26.74 36 3.16×108 24.33 43 1.60×108 25.2726 MC 31 8.04×108 20.76 33 2.31×108 17.78 34 1.08×108 17.0627 MC 41 7.28×108 18.81 60 1.43×108 10.97 63 5.22×107 8.2428* MC 32 1.62×109 41.86 31 5.10×108 39.21 33 2.11×108 33.3929 MC 41 8.64×108 22.33 38 2.23×108 17.17 73 9.78×107 15.45

Notes: The duration of flushing is consecutive time period with seaward subtidal fluxes or negative flux values. Total volume transport is total flushed volume for each event.Percentage of volume is the ratio between total volume transport and the bay volume.

254 Z. Feng, C. Li / Journal of Marine Systems 82 (2010) 252–264


system, winds shift directions and rotate clockwise, and force thewater levels to decrease. As a result, when cold fronts pass throughthese bays, winds are often abruptly reversed and intensified. Theincreasing wind stresses accelerate bay flushing. Finally, the waterlevels rebound again 10–25h after frontal passage. In our study, wehave found that most major flushing events are associated with coldfronts, except two events in mid-October and the other two in earlyDecember. Prior to the two events in October, an obvious and distinctwind surge was induced by strong, sustained and long-fetch onshorewinds (with a minimum speed of ∼10 m/s) that blew for 2–3 daysfrom southern or southeastern quadrants (Fig. 3). The water level waspiled up by up to 0.8 m at both Lawma Amerada Pass (LAP) andCypremort Point (CP). The first flushing event may be a result of theweakened winds and the relaxation of high bay water level. Thesecond flushing event was driven by the north or northeast windsaround Oct 20th (Fig. 3). The other two events in December followed amajor cold-front-induced flushing event, and were mainly induced bystrong offshore winds. Between two water level drops, the subtidalwater level rebounded for two days when the winds weakened andreversed to southeasterly. Also note that during Event-5, there waslittle transport through the bays, probably because of the atypicalwind time series during this event (Fig. 3 and Table 1): the pre-frontalsoutherly winds were very weak, being less than 2 m/s for about 15h,followed by an abrupt change in wind direction to northeasterly. Afterwinds further rotated to easterly, the water levels subsequentlyincreased.

Wind roses, compiled from CSI-3 measurements for the entiretime series (Fig. 4a) and cold-front-induced flushing periods (Fig. 4b),exhibit remarkable contrast. In the eight-month periods, east–southeast and southeast winds are the most prevalent, occurring

about 12.9% and 12.5% of the time, respectively. Although northwestand north–northwest winds are infrequent, strong winds of speedmore than 11 m/s seem relatively common, which mostly occurredimmediately after frontal passages. During flushing periods, however,four most frequent winds are north (15.5%), north–northeast (14.7%),northwest (13.0%) and north–northwest (8.3%) winds, suggestingwinds from those directions aremajor driving forcings for the subtidalbay flushing.

To better understand cold front forcing, five largest flushing eventswere isolated for more in-depth analysis (highlighted numbers inTable 1 and vertical solid lines in Fig. 2). One interesting finding wasthat all these events were associated with migrating cyclones withunique frontal orientations normal to the Louisiana coastline (Fig. 5).This finding suggests that wind direction is one of the controllingfactors in determining the flushing because it is largely related to thefrontal orientation, consistent with Walker and Hammack (2000).This conclusion is also illustrated by the corresponding wind rose(Fig. 4c). Northwest winds are the predominant, accounting for 40.5%.The other total 36.8% of the winds are from north–northwest (14.1%),north (12.9%) and west–northwest (9.8%). In addition, winds fasterthan 11 m/s account for 35.6%, revealing that major bay flushingevents also correspond to strong winds.

The combination of two mechanisms may explain the largeexchange rates produced by strong northwest winds: (1) transportdue to offshore-wind-induced set down; (2) Ekman pumping producedby alongshore winds. Fig. 6 shows cross-shore and alongshorecomponents of subtidal winds at CSI-3. Note that during these events,cross-shore wind component abruptly reversed from inflow favorableonshore winds to outflow favorable offshore winds. Also note thatstrong and sustainedwest–northwestwindswere correlatedwith these

Fig. 2. The subtidal water exchange fluxes of the Atchafalaya/Vermilion Bays (upper panel), the Terrebonne/Timbalier Bays (middle panel), and the Barataria Bay (lower panel) fromSeptember 2006 to April 2007. The positive and negative values mean flux in and out, respectively. Vertical lines indicate cold fronts passing through the bays, and the solid thicklines are cold fronts associated with the selected five largest flushing events (Event-7, -11, -12, -14, and -28). Time is in UTC (Universal Time Coordinated).



events, suggesting that the Ekman effect appeared to be important.Compared with five largest flushing events, the wind statistics for theother twenty-four events does not have very distinct directionalproperties (Fig. 4d).

The AVB were selected as an example to examine the relationshipbetween wind, subtidal water level and volume flux, associated withthe five extreme events (Fig. 7). The responses of low-frequencywater level to four typical cold fronts showed very similar patterns,except Event-14. Due to the Ekman pumping effect, the water levelstarted to drop 6–9h prior to the frontal passage when wind directionrotated clockwise. The outflow reached themaximum 8–11h after thefrontal passage with persistent and strong northwest winds (N11 m/s), and then decreased with the weakening of wind stress and furtherclockwise rotation of wind direction. The northwest winds corre-sponded to the maximum outward flux for all four events, whichappeared to be the most effective in flushing water out of the AVB.This finding agreed with previous satellite imagery and numericalmodel studies that northwest winds maximized bay flushing and theAtchafalaya River plumes (Walker and Hammack, 2000; Cobb et al.,2008).

The winds and subtidal water level variations during Event-14were different from the other events. As the low pressure systemlocated in the northern Kentucky intensified, this distinct cold frontwas formed at around 0300Z December 26, spreading from Kentuckyto the eastern Louisiana, following the other front extending north–south along the east coast (Fig. 5d). Only 3 h after the formation, thiscold front moved eastward and left Louisiana. Although the frontinfluenced the study area, it did not actually pass through the middleand western Louisiana, including the AVB. As a result, the windvariation was different from a typical frontal passage. Moreover,winds were fairly strong in this period but wind directions varied

quickly. Subtidal water level decreased with an abrupt switch of winddirection from northeast to northwest, mainly due to the Ekmantransport. As the winds strengthened, the outflow gradually increasedto the peak value of 19,530 m3/s about 7h before the frontalformation. The wind direction reversed to southeasterly one dayafter the frontal formation, but the water level started to rebound 15hprior to the wind reverse, which may be related to the weakeningwinds and barotropic pressure gradient from inner shelf to the bay.Previous study suggested that the shallow water of Atchafalaya Bayand adjacent shelf was more sensitive to cross-shore wind thanalongshore wind (Chuang and Wiseman, 1983), but our studyindicated that within the AVB, strong alongshore wind may alsodrive considerable water level variation through Ekman process.

All flushing events associated with cold front passages weresummarized in Table 1. The duration of flushing and total volumetransport varied greatly with events. Basically, the volumes flushed byarctic surgeswere smaller for all three bays, accounting for about 10% orless of the bay volume. For migrating cyclones, the associated flushingspanned wide ranges in both duration and volume. The time scales formost events were between 25 and 45h, including the five largest ones.Although some flushing events (i.e., Event-2, -13 and -27) could last formore than 60h, the total volume transport was not high due to smallerexchange rates. The volume percentages ranged 2.00–41.86%, 4.88–44.90%, and 2.84–33.39% for the AVB, TTB, and BB, respectively. Strongcold front events may flush more than 40% of the bay waters onto theshelf within a less than 40-hour period. These findings have importantimplications for the physical–biological interactions and biogeochem-ical processes over the Louisiana–Texas shelf because the baywaters areusually rich in nutrients and organic matters that are important to theecological activities on the adjacent shelf. Previous satellite imagerystudy also revealed that westward Atchafalaya flow during cold front

Fig. 3.Wind vectors, subtidal volume fluxes of the AVB, TTB and BB from October 10 to 21, 2006. The wind surge occurred between October 14 and 16. The winds are plotted in thestandard oceanographic vector orientation that points to the blowing direction.



passages stimulated high chlorophyll-a concentrations and primaryproductivity on the shelf area southwest of the Atchafalaya Bay (Walkerand Rabalais, 2006).

4. Theoretical model

4.1. Model development

Garvine (1985) constructed a simple one-dimensional barotropicmodel to explain the estuarine subtidal fluctuation forced by local andremote winds in the Chesapeake Bay and Delaware Estuary. Here, amodified Garvine's model, allowing a rotating cold front wind, isapplied to the AVB (Fig. 8).

A major difference of the present model from that of Garvine(1985) is that the wind function is rotary clockwise to betterrepresent a cold front event. In contrast, a rectilinear and harmonicwind was used in Garvine's model (1985). We impose a constantmagnitude, spatially uniformed and clockwise rotating wind field

with angular velocity ω and initial phase Θ (Fig. 8). The cross-shore(or local) and alongshore (or remote) winds are represented by:

τx = τeiðωt + ΘÞ ð1aÞ

τy = iτeiðωt + ΘÞ ð1bÞ

in which τ is the magnitude of wind stress and i is the imaginary unit.They are only slightly different from that in Garvine's model: Thealongshore and cross-shore winds are 90° out of phase for the windfield of this paper, while they are in phase in Garvine's model.

Since the model is 1-D, a boundary condition of the subtidal waterlevel η at the mouth is applied to represent the remote wind effect:

η 0; tð Þ = αE ð2Þ

Fig. 4. Wind roses compiled from CSI-3 wind data for (a) the total eight months, (b) cold-front-induced flushing periods, (c) five largest flushing events and (d) twenty-four otherevents. Percentage frequencies were shown for each 22.5° wind delineation. Courtesy of Lakes Environmental Software for wind rose plots software, WRPLOT View.



and

E = iτf

� �eiðωt + ΘÞ

where E is the cross-shelf component of the Ekman flux, f is theCoriolis parameter, and α is a remote wind coefficient which relates

the cross-shelf Ekman flux with subtidal sea level at the estuarinemouth (Garvine, 1985).

The governing equations are:

∂u∂t = −g

∂η∂x +

τx−τðxÞb

ρhð3Þ

Fig. 5. Surface weather maps corresponding to the five largest flushing events. Cold fronts are dark lines with triangles on the warm side of the front. (from HydrometeorologicalPrediction Center's surface analysis archive).



∂u∂x = −1

h∂η∂t ð4Þ

where u is the vertically averaged or barotropic subtidal currentvelocity in the x-direction, η is the subtidal water level, ρ is waterdensity, h is depth, g is gravitational acceleration, and τb(x) is thebottom frictional stress.

The bottom friction is linearized by:

τðxÞb = ρCDuTu ð5Þ

where CD is a bottom drag coefficient and uT is the root mean squaresubtidal current velocity.

A series of dimensionless parameters are introduced to simplifythe governing equations:

X≡ðω = cÞx ð6Þ

T≡ωt ð7Þ

H≡η= σ ð8Þ

U≡hu= ðσcÞ ð9Þ

W≡τ = ðρωcσÞ ð10Þ

λ≡CDuT = ðhωÞ ð11Þ

where c=(gh)1/2 (i.e., the phase speed of shallow water gravitywave), σ is the standard deviation of the subtidal water level, and λ isdimensionless bottom friction parameter.

Now, the dimensionless governing equations can be expressed bythe parameters from Eqs. (6)–(11):

∂U∂T +

∂Η∂X + λU = WeiðT + ΘÞ ð12Þ

∂U∂X +

∂Η∂T = 0 ð13Þ

The dimensionless boundary conditions become:

Η 0; Tð Þ = iAð0ÞeiðT + ΘÞ ð14Þ

and

U L; Tð Þ = 0 ð15Þ

where A(0)≡ατ/(σf), the scaled water level amplitude at theestuarine mouth. L≡(ω/c) l, or the scaled length of the estuary.

4.2. Model solution

The equations are solved by introducing the wave-form sea leveland velocity terms:

Η = iA Xð ÞeiðT + ΘÞ U = BðXÞeiðT + ΘÞ

A second-order ordinary differential equation is derived from thedimensionless governing Eqs. (12) and (13):

B0 0 + 1−iλð ÞB = −iW ð16Þ

The solution of the above equation subject to the boundaryconditions (14) and (15) is:

B Xð Þ = −1K2coshðKLÞ A 0ð ÞK sinh K L−Xð Þ½ �−iW½cosh KLð Þ− cosh KXð Þ�f g

ð17Þwhere K is a complex wave number of order unity given by:

K≡ð−1 + iλÞ1=2 = ½ðr−1Þ=2�1=2 + i½ðr + 1Þ=2�1=2

in which r≡(1+λ2)1/2, a real number.Therefore, the analytical solutions of subtidal current and water

level expressed by the dimensionless parameters are:

U X; Tð Þ = −1K2coshðKLÞ A 0ð ÞK sinh K L−Xð Þ½ �−iW ½cosh KLð Þ− cosh KXð Þ�f g eiðT + ΘÞ

ð18Þ

Fig. 6. Subtidal cross-shore (upper panel), and alongshore components (lower panel) of windsmeasured at CSI-3. Vertical lines indicate cold fronts passing through CSI-3. The axis ofonshore wind is 24° clockwise rotated from the north direction.



Fig.

7.W

indve

ctors(u

pper

pane

ls),mea

suredan

dsu

btidal

water

leve

l(middlepa

nels),an

dsu

btidal

volumeflux

(low

erpa

nels)of

theAVB,

associated

withthefive

largestflus

hing

even

ts.



Η X; Tð Þ = iKcoshðKLÞ A 0ð ÞK cosh K L−Xð Þ½ �−iW sinhðKXÞf g eiðT + ΘÞ

ð19Þ

Or, we may rewrite a complete expression of water level solution:

η x; tð Þ = Rei

KcoshKωlc

� � ατKf

coshKωðl−xÞ

c− iτ

ρωcsinhðKω

cxÞ

� �eiðωt + θÞ

8>><>>:

9>>=>>;

ð20Þ

4.3. Model coefficients

The averagedepthof theAVB is 2.0 m, based on theDEMbathymetrydata from NOAA's NOS Estuarine Bathymetry database. Thus, the phase

speedof thegravitywave (c) is 4.43 m s−1.Weassume that the constantperiod of wind event is 80h, or an equivalent angular frequency of2.2×10−5 s−1. The wind stress is 0.161 kg·m−1·s−2, calculated fromthequadratic lawusing thedensity of air of 1.3 kg·m−3, a constantwindspeed of 10 m·s−1 and a drag coefficient of 1.24×10−3, determined bythe following relationship (Gill, 1982):

Cd = 1:1 × 10�3 for j u j ≤6m= s0:61 + 0:063 ju jð Þ × 10�3 for 6m= sb ju j b22m= s

(ð21Þ

The density of seawater is 1027 kg·m−3. The Coriolis parameter f is7.18×10−5 s−1, using latitude of 29.5°N. We use a bottom dragcoefficient of 5.0×10−3 (Li, 2003) and root mean square subtidalcurrent of 0.1 m·s−1 to estimate the dimensionless bottom frictionparameter λ of 11.4. The station LAP is 15 km upstream of the baymouth, so x in the equation equals 15,000 m. Since east–southeastwind (i.e., positive wind stress in y-direction in current analyticmodel) is downwelling favorablewith an increase of water level in theestuary, the remote wind coefficient αmust also be positive. It shouldbe noted that α is geographically dependent, since it is determined byboth the estuary itself (e.g., depth, length, andwidth) and the complexoffshore shelfmorphology. Garvine (1985) estimated a value ofα to be5×10−4 m2·s·kg−1 based onobservations (Wong andGarvine, 1984).However, the number is not applicable to the AVB, since here the baydepth (∼2 m) is much smaller than those of the Chesapeake Bay andDelaware Estuary (∼10 m), and the basin geometries are also different.In addition, shelf morphology of the northern Gulf of Mexico is quitedistinct from that of the U.S. Atlantic coast. For the very shallowLouisiana estuaries, the frictional damping effect on the remote-wind-induced fluctuations becomes dominant, so the expected value of αshould be much less than Garvine's estimation.

From the analytical solution of subtidal water level (20), one cansee that it contains two independent parts. The first term in thebracket represents the water level variations induced by remote

Fig. 8. The plain view of modified Garvine's model. The AVB are simplified as arectangular estuary with a length (l) of 20 km and a width (b) of 50 km. Thelongitudinal axis (i.e., x-axis) is perpendicular to the coastline, and 24° clockwiserotated from the north direction. The initial wind direction is assumed southeasterly, orthe equivalent initial phase Θ in the equation is –0.383π.

Fig. 9. (a)Wind field observed at CSI-3. The vertical solid line indicates a cold front passed through the AVB; (b) idealized clockwise rotating windwith 80-hour period; (c) measuredand subtidal water level at LAP; (d) analytical-model-predicted water levels at LAP. The thin solid line and dotted line demonstrate water level variations induced by cross-shorewinds and alongshore winds, respectively and thick solid line is the total water level.



winds, which is directly proportional to α through water level term A(0) at the open boundary. The second term in the bracket representsthe water level fluctuations driven by local winds, which is not relatedto the coefficient α. Now, an experiment is conducted to estimate α bycomparing the model results using different values of α with theobserved water level records. From eight-month water level recordsat LAP, we find that the average amplitude of subtidal water levelvariations during typical cold front events is about 0.2 to 0.25 m. If weuse the same α as in Garvine's paper (i.e., 5×10−4 m2·s·kg−1), theresultant subtidal sea level amplitude is nearly fivefold of theobservations. A value of 8×10−5 m2·s·kg−1 for α is found to best fitthe observations if a mean amplitude of 0.225 m is used.

4.4. Model validation and comparison with observations

The left panels of Fig. 9 illustrate typically observed wind field andwater level variation during a cold front event; while the right panelsshow the idealized wind field and model-predicted water levelvariation, which are generally consistent with the observed results.From the analytical model, we find that water level fluctuationsinduced by cross-shore and alongshore winds have the same order ofmagnitude, although the amplitude of water level from cross-shorewind forcing (0.12 m) is slightly smaller than that from alongshorewind forcing (0.17 m). Furthermore, the model-predicted curvereaches the maximum 3h before the onshore wind component

Fig. 10. Amplitudes of water level variations from cross-shore and alongshore winds and amplitude of total variation for the AVB.

Fig. 11. (a) Idealized wind field, (b) contour of total water level variations, (c) contour of water level variations from cross-shore winds and (d) contour of water level variations fromalongshore winds for the AVB.



reachesmaximum, earlier than subtidal water level record at LAP. Thismay suggest that a phase lag exists between subtidal water levelvariations and remote wind effect. The phase lag may be identifiedfrom the phase relationship between subtidal wind stress and waterlevel record. Also, the observed amplitude of water level falling isgreater than that of rising, which is mainly caused by the asymmetryof wind field or the strengthening of wind stress in the post-frontalperiod. For real winds, the magnitudes of pre-frontal winds areusually less than 10 m/s, but the post-frontal ones exceed 10 m/s andlast longer.

4.5. The relative importance of cross-shore and alongshore winds

From the previous section, one can see that water level fluctua-tions in the AVB induced by cross-shore and alongshore wind stresseshave the same order of magnitude. However, the conclusion is madefrom only one specific location at LAP. Using the analytical solution,we can study the relative importance of cross-shore and alongshorewinds to the entire estuary. Here, we use the same conditions andcoefficients as in the previous section.

In the AVB, alongshore wind seems to be more important thancross-shorewind in producing subtidal water level variation along theentire estuary, since its corresponding water level amplitudes arealways larger (Fig. 10). Furthermore, distance is the most importantfactor that determines the amplitudes of cross-shore-wind-inducedwater level variability, with the zero amplitude at the mouth and thelargest at the head of the estuary. The zero amplitude at themouth is aresult of the boundary condition, excluding the waves generatedoutside of the estuary that may propagate into the estuary. Theamplitudes of water level variation induced by alongshore wind (orthe remote wind effect through Ekman process) are almost constantalong the estuary, only slightly decreasing with distance. This isbecause the bay is much shorter than a quarter of the wave length andthe remote-wind-induced motion is basically a standing wave (Li,2001). Water level variations near the bay mouth are producedprimarily by alongshore wind, but cross-shore wind effect becomessignificant near the bay head. The smallest amplitude of total waterlevel variation is found around 5 km to themouth, and the largest is atthe head.

Both highest and lowest total water levels are found at the headwhere cross-shore wind effect is the most obvious (Fig. 11). The highwater levels are coherent with southeast/south/southwest winds,while the lows are with winds from opposite directions. Thisconclusion is consistent with wind and water level observations inFig. 7. The highest and lowest water levels produced by cross-shorewind occur at the head, associated with southwest and northeastwinds, respectively. The alongshore-wind-induced water level varieswith time and is almost independent of the location, and the highestand lowest values correspond to southeast and northwest winds,respectively.

5. Discussion

The river discharge is not included in the previous estimation, butit may be a major water source for the AVB because approximately30% of the total Mississippi River water is discharged through theAtchafalaya River (Walker and Hammack, 2000). For the studyperiods, the daily mean discharge measured at Lower AtchafalayaRiver at Morgan City, LA (USGS 07381600) was 3300 m3/s, equivalentto a flushing time of 13.6 days. The maximum discharge (about7000 m3/s) occurred in the late January and early February of 2007.River discharge contributed additional amount of freshwater of 0.25,0.34, 0.36, 0.33 and 0.48 billion m3 corresponding to the same timeperiods of the five extreme events. The total volume transport fromthe combined effects of both wind and river discharge can account forabout half of the bay volume. The large amount of freshwatermay also

exert baroclinic forcing on the estuarine circulation and transport,which is ignored in this study based on the following considerations:(1) this study only tries to provide a first-order approximation so thata barotropic model is adequate, and (2) the Louisiana estuaries arebroad and shallow with very short channels; when cold fronts occurand strong winds stir up the bottom, the process of flushing becomesessentially barotropic.

The impacts of other factors (e.g., rainfall, evaporation, and runoff)are usually minor. However, the opening of theman-made Davis PondFreshwater Diversion, which is located in the upper Barataria Basin(Fig. 1), may introduce a substantial amount of freshwater from theMississippi River to the Barataria Basin during major floods. OnNovember 30 and December 1, 2006, the daily mean dischargemeasured at Davis Pond Freshwater Diversion near Boutte, LA (USGS295501090190400) was 133 and 113 m3/s, respectively. The totaldiverted volume corresponding to Event-12 was 14 million m3, or 2%of the volume of BB. The maximum daily mean discharge through thediversion could reach nearly 300 m3/s during the great Mississippiflood such as that in the spring of 2008 (White et al., 2009). Therefore,occasionally the diverted Mississippi water may influence theBarataria Basin but the effect of diversion is usually negligible.

6. Summary

The major findings of this study on cold-front-induced flushing ofthe Louisiana bays are: (1) cold fronts play important roles in flushingwater out of the Louisiana bays; (2) coastal bays have different waterexchange rates depending on their water body area and geomor-phology; (3) all five largest flushing events correspond to migratingextra-tropical cyclones with their frontal orientations perpendicularto the coastline; (4) both alongshore and cross-shore winds caneffectively induce the bay-shelf water exchange, and the northwestwinds appear to be the most influential; (5) strong cold front eventscan flush more than 40% of bay waters out onto the continental shelfwithin 30–40h; (6) the analytical model, modified from Garvine(1985), yields water level changes of the same order of magnitude forthe two wind components; (7) the amplitude of cross-shore-wind-induced water level variation increases from zero at the bay mouth tothe maximum at the bay head, while alongshore winds have almostequal effects along the estuarine longitudinal axis; (8) the model-predicted high subtidal water levels are coherent with southeast/south/southwest winds and the lows coincide with winds fromopposite directions, agreeing well with observations.

Acknowledgments

This work is part of a thesis of Z. Feng (http://etd.lsu.edu/docs/available/etd-06102009-153456/). This project is supported under anaward NA06NPS4780197 by NOAA NGoMex and NA06OAR432026406111039 to the Northern Gulf Institute by NOAA's Office of Oceanand Atmospheric Research, U.S. Department of Commerce and Shell(http://www.ngi.lsu.edu/), and through a contract, NNS05AA95C, byLouisiana Board of Regents. The authors would like to thank Dr.Gregory W. Stone, director of WAVCIS at LSU, for the access of theirdata. Additional thanks to B. Babin and H. Hebert at LUMCON forsharing water level data and Q. Tang and Y. Chen for their technicalsupport in ArcGIS. Two anonymous reviewers are highly appreciatedfor the valuable comments.

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