variation in surface turbulence and the gas transfer velocity over

1401Q 2003 Estuarine Research Federation

Estuaries Vol. 26, No. 6, p. 1401–1415 December 2003

Variation in Surface Turbulence and the Gas Transfer Velocity

over a Tidal Cycle in a Macro-tidal Estuary

CHRISTOPHER J. ZAPPA*, PETER A. RAYMOND†, EUGENE A. TERRAY, and WADE R. MCGILLIS

Woods Hole Oceanographic Institution, Applied Ocean Physics and Engineering, Woods Hole,Massachusetts 02543

ABSTRACT: The gradient flux technique, which measures the gas transfer velocity (k), and new observational tech-niques that probe turbulence in the aqueous surface boundary layers were conducted over a tidal cycle in the PlumIsland Sound, Massachusetts. Efforts were aimed at testing new methods in an estuarine system and to determine ifturbulence created by tidal velocity can be responsible for the short-term variability in k. Measurements were madeduring a low wind day, at a site with tidal excursions of 2.7 m and a range in tidal velocity of nearly 1 m s21. Estimatesof k using the gradient flux technique were made simultaneously with the Controlled Flux Technique (CFT), infraredimagery, and high-resolution turbulence measurements, which measure the surface renewal rate, turbulent scales, andthe turbulent dissipation rate, respectively. All measurements were conducted from a small mobile catamaran that min-imizes air- and water-side flow distortions. Infrared imagery showed considerable variability in the turbulent scales thataffect air-water gas exchange. These measurements were consistent with variation in the surface renewal rate (range 0.02to 2 s21), the turbulent dissipation rate (range 1027 to 1025 W kg21), and k (range 2.2 to 12.0 cm hr21). During this lowwind day, all variables were shown to correlate with tidal speed. Taken collectively our results indicate the promise ofthese methods for determining short-term variability in gas transfer and near surface turbulence in estuaries and dem-onstrate that turbulent transport associated with tidal velocity is a potentially important factor with respect to gas ex-change in coastal systems.

IntroductionRivers and estuaries receive a steady input of nat-

ural and anthropogenic constituents from land.They are also sites of active processing, effectivelyaltering the amount, timing, and form in whichland-derived and anthropogenic constituents areexported to the open ocean. Many of these naturaland anthropogenic constituents have a gas phase,and the mechanics of gas exchange is directly rel-evant to the health and biogeochemical budgets ofthese systems. The transport of CO2 and oxygenacross the interface, or the exchange of volatilepollutants such as polychlorinated biphenyls(PCBs), polycyclic aromatic hydrocarbons (PAHs)and mercury (Hg0

(g)) are important processes af-fecting the overall resilience of these ecosystems.

Because of the difficulties inherent in direct de-termination of gas exchange, studies rely on mod-els for the gas flux. The air-water flux (F) of aslightly soluble gas can be parameterized as theproduct of its concentration difference betweenthe bulk and surface water and the gas transfer

* Corresponding author current address: Lamont-DohertyEarth Observatory of Columbia University, 61 Route 9W, P. O.Box 1000, Palisades, New York 10964; tele: 845/365-8547; fax:845/365-8157; e-mail: [email protected]

† Current Address: Yale University, School of Forestry and En-vironmental Studies, 205 Prospect Street, New Haven, Connect-icut 06511.

velocity, k, which embodies the details of the tur-bulence-mediated transfer,

F 5 kDc 5 k(Cw 2 sCa), (1)

where the solubility coefficient, s, is a function oftemperature and salinity, Dc is the difference in gasconcentrations between the bulk water (Cw) andthe surface water in equilibrium with the air (sCa),and Ca is the gas concentration in air. Since fieldmeasurements of this concentration difference formost gases are obtained readily in rivers and estu-aries, the goal from a modeling perspective hasbeen to develop parameterizations of the gas trans-fer velocity.

For slightly soluble gases, the greatest resistanceto transport resides in a thin aqueous mass bound-ary layer (MBL) at the air-water interface in whichmolecular diffusion dominates ( Jahne andHaußecker 1998). The magnitude of k is deter-mined by diffusion through this spatially and tem-porally varying MBL, whose thickness is a functionof near-surface turbulence and molecular diffusiv-ity and is on the order of 10–100 mm. Both bound-ary layer models and dimensional analysis showthat increasing turbulence levels will decrease theMBL thickness, and increase k. Empirical modelsfor k assume that turbulence regulates the ex-change and use bulk properties (e.g., wind speed)that may control air-water interfacial turbulence.

1402 C. J. Zappa et al.

While measurement options and models exist forchoosing a value for the gas transfer velocity, thedetermination of k is difficult to constrain, result-ing in a large uncertainty when estimating the ex-change of any gas in aquatic or marine systems,particularly river and estuary systems (Raymondand Cole 2001). The ability to accurately measureand predict atmospheric exchange is limited by alack of understanding of the mechanisms control-ling k.

The variability in k for the estuarine environ-ment is a result of the interaction of mechanismsforcing the generation of turbulence that affectthe MBL within a given system. In the open ocean,observations show a dependence of k on windspeed (Smethie et al. 1985; Watson et al. 1991;Wanninkhof et al. 1993), and considerable efforthas gone into determining an empirical relation-ship (Liss and Merlivat 1986; Wanninkhof 1992;Wanninkhof and McGillis 1999), since the windstress at the ocean surface plays a central role inthe generation of turbulence through the transferof momentum to waves and currents. For a wind-driven system, turbulence is generated near the air-water interface primarily through shear, buoyancy,or large- and micro-scale wave breaking. Less de-pendence is observed under low wind speed con-ditions since buoyancy may dominate the produc-tion of turbulence in the near-surface layer (Solov-iev and Schlussel 1994) and under conditions ofsurface contamination by thin organic films (Frew1997). In streams, the generation of turbulence byfriction due to flow over the bottom and side to-pography, with varying roughness, may dominate.The turbulence, in turn, is transported to the MBLat the air-water interface. k varies with hydrauliccharacteristics such as depth, H, and current ve-locity, V, and has been semi-empirically modeled(O’Connor and Dobbins 1958; Langbein and Du-rum 1967; Wilcock 1984).

Rivers and estuaries represent a case in whichboth wind forcing and boundary friction generateturbulent energy (e.g., Cerco 1989; MacIntyre etal. 1995). Laboratory measurements of transferrates in rivers for combined wind- and bottom-shear induced turbulence have suggested that thetransfer velocity transitions at a critical value forthe wind stress and that the processes within eachregime are cumulative (Chu and Jirka 1995). Thesituation is further complicated by the time depen-dence of the tidally-driven currents and changes infetch, water depth, or stratification that have spa-tial heterogeneity in most river-estuary systems.

The complex interplay of wind speed and hy-draulic conditions is illustrated in Raymond andCole (2001) where empirically derived model pa-rameterizations of k show the large potential vari-

ability in k between estuaries of differing scale aswell as within a given estuarine system. A limitednumber of direct studies exist that report gas trans-fer velocities in estuaries using methods such asnatural tracers, purposeful tracer additions, andfloating domes. These studies offer a large rangeof k for rivers and estuaries, and various windspeed parameterizations have been proposedbased upon these data (e.g., Cole and Caraco1998; Raymond and Cole 2001). At a given windspeed, measurements of k have been shown to varyby a factor of 2–12. The degree to which this var-iability is due to inherent differences in the variousmeasurement techniques, or to temporal and spa-tial variability in the exchange processes, is un-known. It is interesting to note that the floatingdome studies, which operate at smaller temporaland spatial scales, tend to report more variabilityat a given site. One point is to determine if thisvariability is the direct result of the variation in sur-face hydrodynamics due to tidal forcing at a givenwind speed.

In order to determine the relative role of tidaland wind forcing in controlling k over a wide rangeof environmental conditions, it is imperative to un-derstand the effect that near-surface turbulencehas on the MBL. The continual replacement of wa-ter in the MBL through surface renewal (Danck-werts 1951) has been suggested as a fundamentalhydrodynamic process controlling gas exchangeand has resulted in a useful conceptual model fork. Surface renewal models describe the continuousrandom renewal of the aqueous MBL with the bulkwater below due to turbulent eddies. The idealizedprocess is one in which renewal is complete andinstantaneous. As turbulent eddies renew the sur-face, bulk water parcels that are not in equilibriumwith the atmosphere come in contact with the in-terface and exchange gas with the atmospherethrough diffusion. The faster this renewal occurs,the higher the exchange rate. Surface renewalmodels predict the gas transfer velocity as

k } (D/t)1/2 5 (Dl)1/2 (2)

where D is the mass diffusivity, t is the lifetime ofa parcel of water exposed to diffusion at the sur-face, or alternatively l 5 1/t is the surface-renewalrate. Because not all renewal eddies produce com-plete fluid parcel overturning at the surface as de-scribed in random-eddy penetration models (Har-riott 1962), the MBL thickness varies over spaceand time as eddies intermittently penetrate the lay-er. From a conceptual standpoint, the implemen-tation of surface renewal does not rely on knowl-edge of the turbulence generation mechanism andmay prove to be a powerful model that is applica-ble to the estuarine environment.

Estuarine Surface Turbulence and Gas Transfer 1403

In an effort to relate the concept of surface re-newal directly to near-surface turbulence, Lamontand Scott (1970) developed a hydrodynamic mod-el based upon viscous eddies characteristic of theshortest time scale. Estimating t by the Kolmogo-rov, or dissipative, timescale, (n/«)1/2, the near-sur-face hydrodynamics are directly proportional to«1/4, and the gas transfer velocity is expressed as

k } («n)1/4Sc2n, (3)

where « is the turbulent kinetic energy dissipationrate and the Schmidt number, Sc, is defined as theratio of the kinematic viscosity of water, n, to D.The Schmidt number exponent n varies between½ (clean surface) and ⅔ (contaminated surface)(Ledwell 1984; Jahne et al. 1987). Surface contam-ination is known to modify the free surface to be-have as a rigid boundary by introducing a tangen-tial stress that works to suppress horizontal motion,and therefore near-surface turbulence and k. Asshown in Eq. 3, the transfer velocity scales with theturbulent dissipation rate, a parameter that can bemeasured in the field. This scaling demonstratesthat increasing turbulence intensity will enhance k,and this scaling has been tested with success in thelaboratory for varying surface conditions (Asherand Pankow 1986).

The ability to accurately predict k in rivers andestuaries is dependent on our ability to make ac-curate measurements of the processes occurring inthe MBL and on generating extended data setsacross a continuum of environmental and hydro-graphical conditions. Progress in this area can bemade by using observational techniques with ade-quate spatial and temporal resolution to map thevariability of transfer velocities, while simultaneous-ly carrying out measurements on the factors af-fecting the turbulence in the MBL that controlsthe transfer. We apply recently developed tech-niques to measure the gas transfer velocity for CO2,the surface-renewal rate, and the near-surface tur-bulent dissipation rate at short temporal and smallspatial scales in the Parker River estuary of Mas-sachusetts over the course of one semi-diurnal tidalcycle. The measurements were carried out fromthe mobile Surface Processes Instrument Platform(SPIP), a small research catamaran that enablesspatial sampling. Measurements were made duringa constant low wind period (;2 m s21) in order tofocus on the effects of changes in tidal velocity onk. Directly measured surface-renewal rates and tur-bulent dissipation rates may provide the ability toscale the transfer velocity in estuaries based on theprocesses that are directly controlling gas fluxacross the air-water interface.

Methods

STUDY AREA

The Plum Island Sound estuary is a coastal plainestuary in northeastern Massachusetts with averagesemi-diurnal tides of 2.9 m and a spring-neaprange of 2.6–3.6 m. Measurements were per-formed during a flooding tide through slack tideat one site in the upper Parker River, one of twomajor rivers within the Plum Island estuary thatdischarges into the Gulf of Maine. The Parker Riv-er estuary is a small 12-km macro-tidal estuary withsignificant temporal and spatial variation in ge-ometry, bathymetry, density structure, wind stress,freshwater input, and tidal forcing. The upperParker River and the Plum Island Sound estuariesexhibit large spatial gradients in depth and width,temporal gradients in freshwater discharge andwind speed, and large hourly and spring-neapchanges in tidal velocity. These gradients havebeen demonstrated to cause large spatial and tem-poral variation in the tidal dispersion coefficient(Vallino and Hopkinson 1998), and are expectedto affect the variability of gas exchange.

PLATFORM

The SPIP is a 2.1-m, side-towed, quadruple-hulled research catamaran used to measure the at-mospheric gradient of CO2 very close to the air-water interface. SPIP is shown in Fig. 1 and wasboomed from the research boat Growler as a com-prehensive unit to determine the processes that af-fect these air-water exchanges. The Growler wasmoored at the study site on the Parker River suchthat the bow of SPIP was directed into the windand the flooding tidal flow. SPIP has supportingmeasurements of atmospheric variables and of thewater-side forcing. SPIP measures gradients nearthe surface with potentially less flow distortionthan other boat-mounted instrumentation (com-parison using a numerical 2-D flow model). Thebow of SPIP has one mast with fixed and travelingatmospheric sensors to implement the gradientflux technique as well as a second mast outfittedwith an infrared system for thermal imagery of thewater surface and for performing the controlledflux technique.

The atmospheric sensors include a Licor model6262 closed path non-dispersive infrared (NDIR)sensor that measures CO2 and water vapor concen-trations simultaneously with a resolution, or rela-tive accuracy, of 60.01 matm and 60.02 g kg21, re-spectively, and with a response time of approxi-mately 0.1 s based upon the flushing rate throughthe sensor. A Vaisala HMP 235 sensor measures themean relative humidity and air temperature. A Gill2-axis Wind Observer II ultrasonic anemometer


Fig. 1. Picture of the Surface Processes Instrument Platform(SPIP) used for measurements of both the aqueous and atmo-spheric boundary layers. SPIP has four hulls each measuring 2.1m in length and two masts each 3.1 m in height. Subsurfaceinstrumentation includes an acoustic Doppler velocimeter(ADV), an acoustic Doppler current profiler (ADCP), salinity,temperature, and pCO2. Interfacial measurements include aninfrared camera and an incident 10.6 mm wavelength CO2 laserbeam. Atmospheric measurements include fixed and profilingwind speed, temperature, relative humidity, water vapor, andcarbon dioxide.

and a Met One 034A-L cup anemometer with vaneare both used to measure wind speed. The fixedatmospheric sensors are located at the top of the3.1-m gradient flux mast while a second set of iden-tical sensors is mounted to a vertical traversing sys-tem. The gradient flux technique described belowoutlines the estimation of the CO2 fluxes from themeasured gradients in conjunction with the appro-priate scalar transfer coefficients in order to deter-mine the gas transfer velocity from Eq. 1.

The primary waterside measurements includepCO2, temperature, salinity, tidal flow velocity, cur-rent shear, and tidal height. The aqueous pCO2 ismeasured using an equilibrated headspace sam-

pled with a Licor 6262 NDIR sensor with an overallsystem response time of 2 min as determined fromlaboratory tests. The water temperature and salin-ity are measured with a YSI model 660XL that wascalibrated to within 60.18C and 0.1 psu, respec-tively. A near-surface point measurement of x-, y-,and z-axis velocity components was measured usinga Sontek 3-axis acoustic Doppler velocimeter(ADV). Mean tidal flow velocity and turbulent ve-locity (e.g., energy dissipation rate) statistics wereestimated from 15-min records sampled at 25 Hz.A 1200 kHz bottom-tracking Acoustic Doppler Cur-rent Profiler (ADCP) deployed from SPIP profiledthe water column at 1-s intervals to measure cur-rent shear, tidal current, and elevation.

The second 3.1-m mast was outfitted with an in-frared (IR) system to implement both imagery ofthe aqueous thermal boundary layer and the con-trolled flux technique (CFT). A Merlin MWIR in-frared imager was mounted to the top of the IRmast and viewed the surface at a 208 incidence an-gle. This configuration resulted in a roughly 3 m(vertical) by 3.5 m (horizontal) image size. Thenoise equivalent temperature difference (or meanresolvable temperature difference) of this model isspecified at 60.028C. A Synrad model G48–2–28(W) continuous-wave 25-W CO2 laser operatingat 10.6 mm was directed at the water surface fromabove the tank using a series of 5-cm diameter IRmirrors, as depicted in Fig. 1, and was pulsed for10 ms with a gating frequency of roughly 0.25 Hz.The laser beam generated heated spots on the wa-ter surface in the field of view of the infrared im-ager roughly 2–3 cm in diameter. For the runsused to determine the decay time from the CFT,the infrared imagery was digitized at a frequencyof 20 Hz.

GRADIENT FLUX TECHNIQUE

The flux of gas through a boundary layer is di-rectly proportional to the concentration gradientthat exists within that layer. The mass flux acrossthe aqueous and airside MBLs at the air-water in-terface is in balance in steady state conditions,even though the gradient may be controlled oneither side depending on the gas solubility andtransfer rates (Liss 1973; Liss and Slater 1974;McGillis et al. 2000). It follows directly that the fluxfrom the air-water surface must be in balance withthe flux through the atmospheric surface layer un-der homogeneous conditions (Panofsky and Dut-ton 1984). The gradient flux technique uses ver-tical profiles of the mean CO2 concentration, c, inthe atmospheric surface layer (ASL) to estimatethe flux of CO2 across the air-water interface. Inthe gradient flux technique, the flux is obtainedby multiplying the vertical mean gradient of CO2


in the ASL by the turbulent eddy diffusivity, Kc,such that

]cF 5 K , (4)c]z

where z is the height above the mean water surface(Businger et al. 1971; Dyer 1974). The eddy dif-fusivity denotes the effectiveness of transportthrough the ASL, whose thickness is on the orderof 1–10 m. Empirical relationships over land (Bus-inger et al. 1971; Dyer 1974) and the ocean (Edsonand Fairall 1998) indicate that there is a similaritybetween the gradients of scalar quantities such astemperature, specific humidity, and trace scalarconstituents such as CO2. This means that the eddydiffusivities for these quantities behave similarly,and the eddy diffusivity for CO2, Kc, may be esti-mated from the diffusivity for other scalars that aremeasured within the ASL. The eddy diffusivity forCO2, Kc, is dependent on the stability of the ASL,the height within the ASL, z, and wind speed, andresults in a semi-logarithmic profile of c when in-corporated into Eq. 4. The flux of CO2 is deter-mined from the semi-logarithmic concentrationgradient according to Eq. 4. The flux estimate de-termined from Eq. 4 is used along with the mea-surements of the air-water concentration differ-ence to calculate k in Eq. 1.

The profiles are determined using one set oftraveling sensors that measure concentrations atvarious heights within the atmospheric boundarylayer. This minimizes the main drawback of thegradient flux technique that requires accuratemeasurements of the mean scalar quantities in or-der to resolve concentration gradients. A single setof instruments is used for profiling in order to aug-ment the precision of the measurement since thiswill eliminate inter-sensor biases. A second set ofsensors is held fixed in order to account for theatmospheric variability that occurs over the mea-surement time. Measurements at each height areaveraged for 7 min such that a vertical profile iscompleted within 30 to 45 min. Open-ocean mea-surements of water vapor gradients show that theatmospheric variability is a factor of 3 greater thanthe vertical gradient (McGillis et al. 2001). Sub-tracting the fixed reference from the travelingmeasurement, the atmospheric variability can beremoved. The small air-sea CO2 concentration dif-ferences on the open ocean limit the gradients inthe ASL to the ppb range, which is close to theanalytical precision of the gradient flux technique(McGillis et al. 2001).

Since the gradient flux technique relies onmean gradients in the ASL, it offers several advan-tages in determining air-water fluxes. Other meth-

ods, such as purposeful gas addition rely on mea-surement procedures that result in large temporaland spatial footprints. The gradient flux techniqueaverages over smaller spatial (on the order of 100m2) and temporal (on the order of 10 min) scales,which is necessary for sampling processes such astides. The method works best when the wind ismoderate and the stratification within the ASL isminimal. There is greater uncertainty in low windregimes where the eddy diffusivity is not well un-derstood. At very high winds, spray is generated atthe interface, carried into the ASL, and acts as asource for water vapor and a sink for sensible heat.Sources and sinks within the ASL violate the basisfor which the flux-profile relationship is construct-ed and have not been tested reliably. Since the gra-dient flux technique depends upon the atmo-spheric boundary layer, some combination of shift-ing winds and short fetch creates uncertainty inrivers and estuaries. Care was taken to ensure thatthe measurements reported here were for caseswhen the flux footprint was over water.

PASSIVE INFRARED IMAGERY AND CONTROLLED

FLUX TECHNIQUE

Analogous to the MBL, a net heat flux from thewater to the atmosphere occurs by molecular con-duction through the aqueous thermal boundarylayer (TBL) at the surface (Katsaros 1980; Robin-son et al. 1984). As a result, the temperature at thewater surface, or skin, is less than the bulk tem-perature immediately below typically by severaltenths of a degree Celsius (Schlussel et al. 1990;Wick et al. 1996; Donlon and Robinson 1997). Thisthin, gravitationally-unstable TBL is on the orderof 1023 m thick or less (McAlister and McLeish1969; Wu 1971; Hill 1972), and exists for a varietyof forcing, including shear-driven (Saunders 1967)and buoyancy-driven (Katsaros et al. 1977) turbu-lent processes. Free convection dominates duringconditions of strong cooling and low wind, and theskin temperature has been observed to be on theorder of 18C less than the bulk (Katsaros 1977). Astable TBL may even develop under intense inso-lation and low winds where the skin temperaturehas been suggested to be warmer than the bulk(Katsaros 1980; Soloviev and Schlussel 1996). Ob-servations at moderate to high wind speeds whenwavebreaking and other shear-driven processesdominate suggest that the skin temperature mayasymptote to a value that is 0.18C below the bulk(Donlon et al. 1999). This brief list, though incom-plete, demonstrates the range of processes thatgovern the behavior of the TBL and suggests thatits vertical and horizontal structure is quite com-plex due to the variability of the near-surface tur-


bulence mechanisms and due to the supportingheat flux.

Passive infrared imagery measures the micro-scale horizontal structure in skin temperature andcan be used as a visualization tool for turbulenceat water surfaces in rivers and estuaries. An infra-red imager is ideally suited to measure the skintemperature because the optical depth of the in-frared radiation detected, roughly on the order of1025 m (McAlister 1964; McAlister and McLeish1970), is much less than the thickness of the TBL.Recently developed infrared imaging techniqueshave quantified signatures of thermal variabilitythat result from renewal processes such as large-scale wave breaking ( Jessup et al. 1997), micro-breaking (Zappa 1999; Zappa et al. 2001a,b), near-surface shear, and free-convective patchiness (Zap-pa et al. 1998). Measurements show that when thecool skin layer is momentarily disrupted by abreaking wave, the skin temperature of the result-ing turbulent wake is approximately equal to thebulk water temperature. As the wake subsides, theskin layer recovers, and the skin temperature re-turns to its original, cooler value at a rate that in-creases with net heat flux. Less energetic processessuch as intermittent or free convection also pro-duce renewal of the TBL, and have longer time-scales of surface renewal than wavebreaking or oth-er shear-driven turbulent processes (Soloviev andSchlussel 1994; Wick et al. 1996; Zappa et al. 1998).In estuaries, bottom-generated turbulence that dif-fuses to the air-water interface and wind-generatedturbulence will further contribute to the disrup-tion of the TBL. Infrared measurements of thetemporal and spatial characteristics of skin tem-perature variability provide the capability to re-motely monitor free-surface turbulence under con-ditions of constant heat flux or when the heat fluxdependence is known.

The controlled flux technique (CFT) ( Jahneand Haußecker 1998) uses heat as a proxy tracerfor gas to obtain the remote measurement of thesurface renewal rate with high spatial resolutionand short response times. In the CFT, the watersurface is heated with a CO2 laser (optical depth isroughly 10.5 mm) to produce a spot with a mea-surable temperature difference that can be trackedwithin a sequence of infrared images. The MBLresides within the thermal boundary layer de-scribed above and is similarly affected by near-sur-face turbulence. Since the optical depth of the de-tected infrared radiation is on the order of themean thickness of the mass boundary layer, disrup-tions of the TBL observed in the infrared imageryserve as an estimate of the surface renewal withinthe MBL with bulk water. By tracking the decay ofthe small, circular (on the order of 10 cm2) heated

parcel of water within the TBL, CFT produces av-eraged measurements of the surface renewal rate,l, with a spatial resolution on the order of 1 m2

and over a period of minutes.The heated spot is tracked in the infrared im-

agery to determine the surface renewal rate, l,which is estimated from the thermal decay of theheated spot as predicted from a surface renewalmodel. The technique fits the normalized surfacetemperature, TN, of the patches tracked to

h2ltT 5 e (5)N 2Ïh 1 4at

where h is the penetration depth that is bound tothe optical depth of the CO2 laser waveband anda is the thermal diffusivity of water. The analyticalsolution of the one-dimensional unsteady diffusionequation shown in Eq. 5 incorporates a turbulenttransport term characterized by statistical renewalof the surface layer by subsurface eddies. In Eq. 5,the distribution of surface renewal is modeled asan exponential, which states that the most proba-ble lifetime of a water parcel at the surface is zero.Other distributions (e.g., log normal or gamma)may prove to give better prediction for the surface-renewal rate. The transfer velocity scales directlywith Ïl such that enhanced surface renewal willelevate gas transfer. The heat transfer velocity isthen calculated directly from

kH } Ïal 5 Ïa/t. (6)

Since both heat and gas are scalars, kH is believedto scale directly to the gas transfer velocity, k, by

2nSc2nk 5 k 5 k (Le) (7)H H1 2Pr

where Sc is the Schmidt number, Pr is the Prandtlnumber, Le is the Lewis number, and n varies be-tween ½ and ⅔ depending upon the cleanliness ofthe air-water interface.

Previous CFT measurements have provided re-liable estimates of k in the laboratory ( Jahne et al.1989; Haußecker et al. 1995). A limitation for thetechnique may be that not all eddies that affect theMBL and renew the surface are complete and in-stantaneous, and penetration theory (Harriott1962) may prove to be more appropriate. Thechoice of n in Eq. 7 is difficult to determine innatural systems when using this technique. CFTideally should be complemented with dual-tracertechniques (Clark et al. 1994) or another suitablemethod for determining the surface condition.

NEAR-SURFACE TURBULENCE

In steady flow with isotropic, fully-developed tur-bulence, kinetic energy cascades from large eddies


Fig. 2. Examples of infrared images of the water surface at4 different tidal phases (varying tidal speeds, V, from 18 to 75cm s21) on the Parker River on August 4, 2000. These imagesindicate the microscale structure in temperature variability atthe estuary surface that is a direct result of surface renewal gov-erned by near-surface turbulence. During the 5-h experiment,the wind speed was 1.9 6 0.5 m s21, relative humidity decreasedfrom 58% to 35%, the air temperature increased from 23.18Cto 25.68C, and the water temperature was 22.3 6 0.28C. Theimages were taken with the Merlin model MWIR and the imagesize is roughly 3 m 3 3.5 m.

to smaller eddies that finally dissipates through vis-cosity. This cascade of energy occurs within the in-ertial subrange, defined as the wavenumber rangebetween the large slow scale of turbulence produc-tion, and the small fast scale of molecular dissipa-tion. Under these conditions, the turbulent dissi-pation rate, or the rate of energy transfer in a tur-bulent fluid, can be estimated by the magnitude ofthe wavenumber spectrum in the inertial subran-ge. The inertial dissipation (ID) method is used todetermine the turbulent kinetic energy dissipationrate, «, as

S 5 a«2/3k25/3 (8)

where S is the wavenumber spectrum of the fluc-tuating vertical velocity, w, k 5 2pf/V is the wave-number, f is the frequency, and a is Kolmogorov’sempirical constant of 0.52.

Measurements of « were made in the Parker Riv-er according to this model for the inertial subran-ge of the kinetic energy spectrum in Eq. 8 usingan ADV. The ADV sampled the three componentsof water velocity at 25 Hz, 38 cm below the air-water surface. The frequency spectra were mea-sured and corrected for pulse averaging by divid-ing the measured frequency spectra by the factor[sin(pf Dt)/pf Dt]2. Assuming Taylor’s hypothesisof frozen turbulence, the frequency spectra werethen converted to wavenumber space by k 5 2pf/V and « is calculated directly from Eq. 8. A safelower bound of the inertial subrange for these datawas determined to be 20 rad m21 according to thecriterion kz . 5. A reasonable upper bound wasdetermined to be 80 rad m21 according to the cri-terion kL , 1, where L is the length scale of thesample volume (L 5 1 cm for the ADV used in thisstudy).

For steady-state, homogeneous conditions, theturbulent kinetic energy budget requires that theturbulent dissipation rate is balanced by the sumof shear and buoyant (i.e., stratification) produc-tion and the relative contributions of each to « isdetermined by the Richardson number, Ri. For in-stance, the Ri is used to characterize the state ofnear-surface mixing. For Ri less than a critical val-ue, vertical mixing is expected to occur by shearinstability. Since stratification plays a prominentrole in the dynamics of estuaries, the turbulent dis-sipation rate may be affected by the near-surfacebuoyancy production.

Surfactants are known to modify the boundarycondition at the air-water interface. Theoretical ar-guments suggest that at a clean water surface thefluid is free to undergo tangential straining mo-tions that allow for turbulent eddies to penetratethe MBL and promote k (Ledwell 1984; Jahne etal. 1987). In the presence of surfactants, the air-

water interface behaves similar to a solid boundaryand the no-slip condition inhibits turbulent mo-tion near the MBL. Laboratory studies have shownthat measurements of turbulent velocity fluctua-tions in the bulk were not representative of mixingwithin, or very near, the MBL (McKenna andMcGillis 2001). Rather, surface divergence, whichis a manifestation of surface renewal measured byCFT, showed a high correlation with the gas trans-fer velocity. Measurements of the turbulent dissi-pation rate within the interfacial boundary layersare difficult and are more tractable at depths belowthe surface (the depth of the turbulence measure-ment .5 cm, depending on the waves).

ResultsMeasurements were obtained at the Parker River

from SPIP using an infrared imager, which pro-vides a time series of two-dimensional images ofthe skin temperature as inferred from the infraredradiance. Figure 2 shows examples of infrared im-ages of the water surface at 4 different tidal phases(varying tidal speeds, V, from 18 to 75 cm s21). Thefirst example at 1,200 has a smooth appearance


Fig. 3. Comparison of two sequences of infrared images de-picting the controlled flux technique (CFT) taken at differentphases of the tidal cycle. The top sequence (V 5 32 cm s21)corresponds to the first example described in Fig. 2 showing aheated patch produced by the CO2 laser as it decays over 4 s.The bottom sequence (V 5 63 cm s21) was taken between ex-amples 2 and 3 described in Fig. 2 showing a heated patch asit decays over 2 s. The patch is observed to decay quicker forthe more turbulent regime of the tidal cycle with elevated levelsof surface renewal. The scale of the images are roughly 20 cm3 20 cm.

with small-scale spatial variability and slow-movingfeatures during a low-flow regime (V 5 32 cm s21).The second example at 1,336 is typical for peakvelocity during flood conditions and depicts activeand energetic disruption of the skin layer withwide, sweeping regions of strong upwelling ofwarmer temperature and thin veins of convergingcooler temperature. The spatial scale of these up-welling events is on the order of 0.1–1 m and thetemporal scale is on the order of 0.1 s during aflow of V 5 75 cm s21. The skin temperature dif-ferences within the image reach above 0.58C. Thethird example follows the peak velocity duringflood tide and shows features similar to the secondexample with similar spatial scales. The system isless energetic as evident by longer timescales forrenewal, on the order of 1 s, and wider veins ofconverging cooler water, probably a result of thelower flow (V 5 41 cm s21). The final example (V5 18 cm s21) is similar to the first with a smoothappearance and wispy features of small spatial scaleon the order of 1 cm and long temporal scales forrenewal on the order of 10–100 s. The spatial andtemporal variability of the skin temperature fromthe infrared imagery provides insight into the evo-lution over the tidal cycle of the near-surface tur-bulence that affects the interface and controls thegas transfer.

The surface renewal observed in the infrared im-agery of Fig. 2 varied significantly over the tidalcycle and was quantified using CFT. The controlledflux technique is demonstrated in Fig. 3, whichcompares two sequences of infrared images takenat different phases of the tidal cycle. The top se-quence (V 5 32 cm s21) corresponds to the firstexample described in Fig. 2 showing a heatedpatch produced by the CO2 laser as it decays over4 s. The bottom sequence (V 5 63 cm s21) wastaken between examples 2 and 3 described in Fig.2 showing a heated patch as it decays over 2 s. Thepatch is observed to decay quicker for the ener-getic turbulent regime of the tidal cycle when el-evated levels of surface renewal were observed.Two time series of TN are shown in Fig. 4a for thesame examples described in Fig. 3 (V 5 32 and 63cm s21). Assuming the surface cleanliness is con-stant, the transfer should increase as the tidalspeed increases. As the tidal speed increased, TN

decayed more quickly and l increased. The rate ofdecay of the heated patch in the infrared imageryvaried significantly over the tidal cycle. Figure 4bshows that the surface renewal rate increased withtidal speed and the nine independent estimates ofl ranged from 0.03 to 1.6 s21.

Lamont and Scott (1970) related surface renew-al to the turbulent kinetic dissipation rate by esti-mating the surface renewal timescale as the Kol-

mogorov timescale that resulted in Eq. 3. As « in-creases, renewal of the surface with bulk water isenhanced as is air-water gas exchange. Figure 5ademonstrates the ID method and shows two spec-tra of fluctuating vertical velocity that were takenafter the peak flood velocity (V 5 71 and 41 cms21). Note that both spectra approach an f 25/3 pow-er law in the inertial subrange and that the higherspectral level corresponds to the higher flow atthat tidal phase. The magnitude of the dissipationrate follows from Eq. 8, and Fig. 5b shows thathigher values of « occur for higher velocities in thetidal cycle. This suggests that the higher surfacerenewal observed in Fig. 2 and described by CFTin Figs. 3 and 4 is directly related to the near-sur-face turbulence. Measurements of dissipation ratein the Parker River estuary show that « rangedfrom 1027 to 1025 W kg21 (eight independent sam-ples from spectra). An order of magnitude esti-mate of « for the conditions in this estuary werecomparable according to the scaling ku where u*3*5 CD

1/2V is the friction velocity, and CD is the dragcoefficient.

The relationship of surface renewal and turbu-lent dissipation rates to gas transfer and the abilityto characterize the estuarine processes that arethought to control gas transfer require high-reso-lution measurements of k. The Parker River estu-ary is often supersaturated in CO2, and for the pre-sent study, aqueous pCO2 concentrations ranged


Fig. 4. a) Two time series of the normalized surface tem-perature, TN, of the patches tracked by the CFT are shown forthe same examples described in Fig. 3 (V 5 32 and 63 cm s21).b) Surface renewal rate, l, determined by CFT versus tidalspeed. Assuming the surface cleanliness is constant, as the tidalspeed increased, TN decayed more quickly, and l increased.

Fig. 5. a) Comparison of two frequency spectra, S, of fluc-tuating vertical velocity measured from a downward-lookingacoustic Doppler velocimeter (ADV) are shown for V 5 71 and41 cm s21. Both spectra show a f 25/3 power law dependence inaccordance with the inertial dissipation subrange modeled inEq. 8. b) Turbulent dissipation rate, «, versus tidal speed. High-er levels of the inertial subrange correspond to higher values of«, and greater dissipation rates occur for high current speedsobserved during the flooding tide.

from just under 3,000 to over 6,000 matm makingit ideal for the gradient flux technique for CO2 inestuaries. Figure 6a shows the measurements of thefixed and traveling atmospheric pCO2. The meth-od continually measures the background atmo-spheric CO2 concentrations at the fixed referenceheight, in order to correct for the localized varia-tion in atmospheric CO2. A single traveling instru-ment was implemented for profiling in order toeliminate inter-instrument biases that make preci-


Fig. 6. a) Example of the CO2 measurements within the ASLand b) a summary of the CO2 gradients measured on the ParkerRiver estuary. Calibrated CO2 was measured at the 3 m heightusing one set of instruments, and a second set of instrumentsprofiled the atmospheric surface layer. The profiling instru-ments spent 7 min at each height. Simultaneous calibrated mea-surements made at the top of the mast were subtracted fromthe profiled measurements. The precision of the gradient is in-creased by removing the variability of atmospheric CO2 duringthe course of a gradient measurement. Using a single instru-ment to profile avoids inter-instrument biases.

sion profiles difficult. Figure 6b shows the foursemi-logarithmic CO2 gradients in the ASL mea-sured during this study. Note that the atmosphericvariability observed at the fixed sensor is account-ed for in the profile when determining the gradi-ent, and Kc was determined for the stable ASL. The

flux was calculated from the measured atmospher-ic gradients according to Eq. 4, and the gas trans-fer velocity determined from Eq. 1 ranged from 2.2to 12.0 cm hr21.

DiscussionThe significant variability observed in the gas

transfer velocity measured on the Parker River overa tidal cycle and under low-wind conditions is re-lated directly to the surface renewal rate and theturbulent dissipation rate. Figure 7 shows k deter-mined from the gradient flux technique as well asl determined from CFT and « determined fromthe ID method over the tidal cycle compared tothe tidal speed. The transfer velocity is shown tofollow the tidal speed because the wind speed waslow and constant (1.9 6 0.5 m s21) during the mea-surement period. Estuarine transfer velocities atlow wind speeds similarly track both the turbu-lence («) and surface renewal (l) generated dur-ing the tidal cycle. The measurements of k are con-sistent with previous results summarized in (Ray-mond and Cole 2001), though with finer spatialand temporal resolution. Tidal variability leads tosignificant variation in the near-surface turbulencethat directly affects the surface renewal. Similarvariations are observed for the gas transfer. Theresults show that the surface renewal characterizedby CFT is consistent with the observations of thespatial and temporal variability of surface renewalobserved in the IR imagery of Fig. 2. This surfacerenewal is tightly coupled to the near-surface dis-sipation rate, and shown to directly affect the CO2

gas transfer across the air-water interface.Surface renewal is the transport of water into the

aqueous MBL with the bulk water from below. Thisrenewal is a function of turbulence that exists at ornear the water surface. Because gas exchange isalso governed by turbulence at the surface, CFTrepresents an important method for understand-ing the relationship between turbulence, the pro-cesses that generate turbulence, and gas exchange.CFT produced measurements of l with a spatialresolution on the order of 1.0 m and temporalmean on the order of 100 s. This technique showsthe extensive spatial variability of the surface re-newal rate in a dynamically evolving estuarine sys-tem on short timescales. Since the controlled fluxtechnique is measured within the aqueous MBL,exactly where the gas transfer velocity is controlledfor slightly soluble gases such as CO2, CFT de-scribes the effect that near-surface turbulence hasat the air-water interface by the surface renewalprocess. CFT not only provided a record of thesurface renewal rate under all conditions, but alsoproved to be a powerful complement to the gra-dient flux technique, which produces results that


Fig. 7. Results show the transfer velocity measured by the gradient flux technique, surface renewal rate measured by the controlledflux technique (CFT), and the turbulent dissipation rate. Measurements were made during a low wind day (;2 m s21) on the ParkerRiver Estuary over one-half of a tidal cycle.

are difficult to interpret under no or low wind con-ditions when tidally generated turbulence domi-nates.

Previous estimates of l during laboratory exper-iments of microscale wave breaking ranged from1.5 to 7.3 s21 for wind speeds of 4.2 to 9.3 m s21

(Zappa 1999; Zappa et al. 2001b) as well as similarlaboratory wind-forced surface renewal rates thatranged from 0.8 to 4.8 s21 for wind speeds of 2.5to 11.0 m s21 (Haußecker et al. 1995), while openocean estimates have been reported to range from1.0 to 1.8 s21 for wind speeds of 3.5 to 6.0 m s21

(Haußecker et al. 1995). The estimates of surfacerenewal for the Parker River estuary at peak veloc-ity during flood tide are comparable to the lowestwind speeds in the laboratory studies and theopen-ocean measurements. The measurements ofsurface renewal at less energetic phases of the tidalcycle show a few orders of magnitude lower thanthe strongly wind-forced laboratory measurements.This suggests that at low wind speeds in the ParkerRiver estuarine system surface renewal is driven bybottom-generated turbulence that is transported tothe surface through the kinetic energy flux.

In the present study, near-surface turbulent dis-sipation rates ranged from 1027 to 1025 W kg21 asshown in Fig. 5b. For comparison, estimates ofnear-surface « using a microstructure profiler inthe Hudson River near Manhattan ranged from1027 to 1026 W kg21 during neap tides and from

1027 to 1025 W kg21 during spring tides (Peters andBokhorst 2000). During that experiment, the peakHudson River tidal flow was double that of theParker River and exhibited half the tidal excursion.Since the mean depth of the Hudson River wasroughly 15 m compared to only 2.5 m at the ParkerRiver, comparable levels of « are expected. TheParker River estuary typically is a weakly stratifiedsystem compared to the Hudson suggesting thatthe stratification does not play a significant role inthe Parker River. In comparison to these estuarinesystems, estimates of turbulent dissipation underbreaking waves on Lake Ontario ranged from 1025

to 1022 W kg21 (Agrawal et al. 1992; Terray et al.1996) and energetic mixed layers show « valuesfrom 1026 to 1024 W kg21 (MacIntyre et al. 1995).This comparison suggests that the Parker River es-tuary exhibits near-surface dissipation levels similarto larger estuarine systems under comparably lowwind speeds, but significantly less than that foundunder strongly wind-forced conditions. Our resultsdemonstrate that turbulence that generates sur-face renewal is tidally forced under low wind con-ditions in the Parker River.

The measurements made during this study allowfor an investigation of the various models that es-timate the gas transfer velocity assuming differinggoverning processes. Commonly-used models forgas transfer in estuaries have been described thatare based on wind speed (e.g., Raymond and Cole


Fig. 8. Transfer velocities measured by the gradient fluxtechnique, surface renewal theory, and the dissipation ratemethod versus kOD, the transfer velocity determined using theO’Connor and Dobbins (1958) model. The model is calculatedas kOD 5 3.6 3 105(D V/H)0.5(600/Sc )0.67 where D andO O O2 2 2

Sc are the diffusivity and the Schmidt number of oxygen, re-O2

spectively.

TABLE 1. Average and range in transfer velocities corrected to a Schmidt number of 600 (k600) for the measurements conductedduring this field study on the Parker River under low wind conditions (1.9 6 0.5 m s21) over a single tidal cycle.

Type of Measurement/ModelRange in k600

(cm hr21)Average k600(cm hr21) Sample size

Gradient Flux Technique (This study)Controlled Flux Technique (This study)Dissipation Rate Technique (This study)Water Depth and Flow Speed Model (River), O’Connor and Dobbins (1958)Wind Speed Model (Estuary/River), Raymond and Cole (2001)

2.2–12.01.2–9.02.8–8.11.4–10.33.1–4.6

6.65.66.36.43.8

498

214

2001), and water depth and flow speed (e.g.,O’Connor and Dobbins 1958). Comparison of land « with previous studies of energetic wind-forced systems and the results shown in Fig. 7 sug-gests that gas exchange on the Parker River underlow winds may be tidally driven. Figure 8 shows thegas transfer velocity referenced to Sc 5 600 (CO2

at 208C) determined from the gradient flux tech-nique, surface renewal theory, and the turbulentdissipation rate versus kOD, the gas transfer velocitydetermined from the O’Connor and Dobbins(1958) model for bottom-friction driven processes.Surface renewal theory predicts k from Eq. 6 usingl and is referenced to Sc 5 600 using the relation-ship in Eq. 7. Lamont and Scott (1970) predict kin Eq. 3 using « from the ID method. The choiceof exponent n in Eqs. 3 and 7 depends on the

cleanliness of the water surface and was set to n 5⅔ for a surfactant-influenced interface. All threemethods correlate with the O’Connor and Dob-bins (1958) model. The surface renewal (SR) andthe dissipation rate (DR) estimates of k have cor-relation coefficients, R2, of 0.75 and 0.74 respec-tively. The gradient flux technique measurementsof k have an R2 of 0.49 and visibly show more var-iability in Fig. 8 than the SR or the DR estimates.This is a consequence of the limited sampling aswell as of the uncertainty in Kc in this low windregime where the gradient flux technique mayshow more variability than actually exists (McGilliset al. 2001). Our data give quantitative support tothe functional dependence of k based on both sur-face renewal theory in Eq. 2 and dissipation ratein Eq. 3. These are the first results to show thatthe gas transfer velocity varies significantly over atidal cycle and that this variability is directly relatedto the turbulence and surface renewal at the air-water interface.

The choice of n 5 ⅔ for this study shows thebest comparison of measurements to the model.This assessment is reasonable considering the po-tential sources for contamination of the water sur-face by surfactants from the neighboring marshesand the nearby marina. A dilemma with the DRmethod, the SR method using CFT, or any methodthat does not measure the specific gas of interest,is the importance placed on the choice of n torelate the measured passive scalar to the Schmidtnumber of the gas of interest. A choice of n 5 ½would result in transfer velocities twice as high de-termined by the SR method and 3 times as highfor the DR method. Therefore, independent de-termination of n is needed during future studiesthat attempt to develop a universal parameteriza-tion for k in estuaries. For the present study, theobserved trends in Fig. 8 are not affected by thechoice n and show that the gas transfer velocity isgoverned by tidally generated turbulence underlow wind conditions in the Parker River.

Table 1 summarizes the estimates of k for thisstudy referenced to Sc 5 600. The results in Table1 and Fig. 8 show that the three methods for k usedin this study are in good agreement with the widely


used river model of O’Connor and Dobbins (1958)in the trend, range and average value of k. Sincethe wind speed was low and constant during thisstudy (;2 m s21), an estimate of k using the Ray-mond and Cole (2001) empirical relationship doesnot capture the variability observed over the tidalcycle and underestimates the measured k. Themeasurements of k from these three methods showvariability relative to the O’Connor and Dobbins(1958) model. It is likely that the estimate of kfrom O’Connor and Dobbins (1958) does notcompletely capture the variability in gas transfervelocity due to the interplay between tidally- andwind-driven exchange. Though the transfer duringthis study appears to be tidally dominated, somefraction of the exchange may be explainedthrough wind-driven exchange that is not capturedby the model. The turbulence that produces sur-face renewal and promotes gas transfer is not solelygenerated at the bottom boundary. A componentof the turbulence is generated through shear atthe air-water interface, contributes to the overalltransfer, and leads to variability in the model com-parison. Therefore, the proper function for k inrivers and estuaries must consider tidal forcing aswell as other processes, including wind.

Estimates of k from the SR and the DR methodscompare well, suggesting that these estimates of kmay prove to be useful in developing statisticalmodels for gas exchange in estuaries that encom-pass the processes driving the transfer. The com-parison with estimates of l and « to other systems,for example, shows that wind-forced systems havethe potential to contribute significantly to, if notdominate, the forcing for gas exchange in estuar-ies. In particular, the direction of the wind speedcould be significant when the near-surface sheargenerated during highly wind-forced events ismodulated by the direction of the tidal currents.Shear will also be modulated by the sinuosity, ormeandering, in rivers and estuaries where sharpbends cause eddies to form that may add turbu-lence to the MBL. Surfactants (Frew 1997), strati-fication, waves (Bock et al. 1999; Zappa et al.2001b), and rain (Ho et al. 2000) are additionalproperties of the system other than tidal velocity,tidal height, wind speed, and sinuosity that effectnear-surface turbulence and cause variability in k.The effects of surfactants and stratification are pro-nounced in rivers and estuaries and are of partic-ular interest to explore. While the DR method cap-tures the variability of k comparable to the SRmethod, the SR method may prove to be morepowerful since it directly measures surface renewalby CFT whereas the DR method is applied at depthand may not capture the effects of surfactants ongas transfer that occur at the air-water interface.

The turbulent dissipation rate measured at shallowdepths also may be modified at the surface due tonear-surface shear or stratification and lead to var-iability in k.

In this study, gas transfer measurements were de-veloped and implemented over a tidal cycle to be-gin to understand the processes that produce thevariability in k observed in rivers and estuaries.This work shows that gas transfer velocity over thecourse of a semi-diurnal tidal cycle at low windspeeds is driven by tidally-generated near-surfaceturbulence and surface renewal. Future studies willprovide the ability to better determine all process-es governing surface turbulence and k, to exploreprocesses at higher wind speeds, and to incorpo-rate the processes that are crucial in developing ariver-estuary gas transfer model.

ConclusionsMeasurements of k for CO2 using the gradient

flux technique were made from the mobile plat-form SPIP during a low wind period (;2 m s21) inorder to focus on the effect of changes in tidalvelocity on near-surface turbulence at the surfacemicrolayer. These measurements of k were com-pared directly with measurements of turbulence(controlled flux technique and the dissipation ratemethod) and with models for k based on turbulentstatistics and environmental factors controlling tur-bulence such as wind speed, tidal velocity and wa-ter depth. Infrared imagery showed considerablevariability in the turbulent spatial and temporalscales that affect the interfacial boundary-layertransport processes, and this variability is consis-tent with the measurements of the surface renewalrate, l, that ranged from 0.02 to 2 s21 and turbu-lent dissipation rate, «, that ranged from 1027 to1025 W kg21. Measurements of k ranged from 2.2to 12.0 cm hr21 over a tidal cycle during low windconditions and are shown to scale with tidal veloc-ity as well as with the estimates of l and «. Tidalvariability leads to significant variation in the near-surface turbulence («) that directly impacts surfacerenewal (l) of the aqueous boundary layer, andtherefore controls similar variations observed forthe measured gas exchange. The observed corre-lation between the measurements of k by the gra-dient flux technique, CFT, and the DR methodand the O’Connor and Dobbins (1958) model fork demonstrates that the variability in the gas trans-fer velocity under low wind conditions is governedby tidally-generated turbulence. The surface re-newal rate and the turbulent dissipation rate havebeen used to model k in estuaries based upon theprocesses that are directly controlling gas fluxacross the air-water interface. This work providesfundamental information on determining the link-


ages between physical processes affecting the tur-bulence in the aqueous surface boundary layerthat govern k and the spatial and temporal scalesof gas flux in river and estuary systems. The resultsof this work are a step toward a more accurate pre-diction of k for any gas in river, estuary and poten-tially coastal systems with varying wind, tidal, strat-ification, and morphological regimes.

ACKNOWLEDGMENTS

We wish to thank J. Kremer and an anonymous reviewer fortheir thoughtful and insightful critique of the original manu-script. The authors thank the Riverfront Marina of Rowley, Mas-sachusetts, for their assistance and support during the fieldworkon the Parker River. Riverfront Marina provided covered stagingspace, technical assistance, and access to facilities and resourcesfor the successful completion of this study. The authors thankA. Jessup and W. Asher of the Applied Physics Laboratory at theUniversity of Washington for the use of their CO2 laser. Theauthors thank C. Hopkinson, J. Vallino, and the Plum IslandLTER for their generous support and commitment to this re-search. The authors also gratefully acknowledge support fromthe Rinehart Coastal Research Center at the Woods HoleOceanographic Institution. This is a Woods Hole Oceanograph-ic Institution contribution 10720.

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Received for consideration, May 21, 2002Revised, December 2, 2002

Accepted for publication, January 29, 2003

variation in surface turbulence and the gas transfer velocity over

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