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Episodic and Long-Term Sediment Transport Capacityin The Hudson River Estuary

David K. Ralston & W. Rockwell Geyer

Received: 1 September 2008 /Revised: 21 June 2009 /Accepted: 14 July 2009 /Published online: 6 August 2009# Coastal and Estuarine Research Federation 2009

Abstract A tidally averaged model of estuarine dynamicsis used to estimate sediment transport in the Hudson Riverestuary over the period 1918 to 2005. In long-term andseasonal means, along-channel gradients in sediment fluxdepend on the estuarine salinity gradient and along-channeldepth profile. Lateral depth variation across the estuaryaffects the near-bottom baroclinic circulation and conse-quently the direction of net sediment flux, with generallyup-estuary transport in the channel and down-estuarytransport on the shoals. Sediment transport capacity in thelower estuary depends largely on river discharge, but ismodified by the timing of discharge events with respect tothe spring–neap cycle and subtidal fluctuations in sea level.Sediment transport capacity also depends on the duration ofhigh-discharge events relative to the estuarine responsetime, a factor that varies seasonally with discharge andestuarine length. Sediment fluxes are calculated with theassumption that over long periods, the system approachesmorphological equilibrium and sediment accumulationequals sea level rise. The inferred across- and along-channel distributions of sediment erodibility correspondwith observations of bed properties. Equilibrium is assumedat long time scales, but at annual to decadal time scales theestuary can develop an excess or deficit of sediment relativeto equilibrium. On average, sediment accumulates in theestuary during low- and high-discharge periods and isexported during moderate discharge. During high-discharge

periods, maximum export coincides with maximum sedi-ment supply from the watershed, but the nearly cubicdischarge dependence of fluvial sediment supply over-whelms the roughly linear increase in estuarine transportcapacity. Consequently, sediment accumulates in the estu-ary during the highest flow conditions. Uncertainty remainsin the model, particularly with sediment properties andboundary conditions, but the results clearly indicatevariability in the sediment mass balance over long timescales due to discharge events.

Keywords Estuarine sediment transport . Episodic dischargeevents . Morphological equilibrium . Hudson River estuary

Introduction

Estuaries efficiently trap sediment and accumulate deposit-ed material (Schubel and Hirschberg 1978). Rivers deliversediment into the upper estuary and gravitational circulationtransports marine sediment from the seabed and shorelineerosion into the lower estuary (Postma 1967; Meade 1969).Suspended sediment concentrations and the rate at whichsediment accumulates in an estuary depend on the rate ofsediment supply and on the hydrodynamic conditions, withfeedbacks between hydrodynamics and sediment transportproducing equilibrium morphologies. For example, if thewater column deepens due to erosion or dredging, flow areaincreases, velocities decrease, and deposition increases untilbed accretes to an equilibrium depth. Many estuaries arenear morphodynamic equilibrium, where long-term sedi-ment accumulation rates correspond to the rate of sea levelrise (Meade 1969; Olsen et al. 1993). Disturbances such asdredging, infilling, or changes in watershed sedimentsupply can shift an estuary away from equilibrium andinduce sedimentation or scour (Panuzio 1965; Bokuniewicz

D. K. Ralston :W. R. GeyerWoods Hole Oceanographic Institution,Woods Hole, MA 02543, USA

D. K. Ralston (*)Applied Ocean Physics and Engineering, MS #11,Woods Hole Oceanographic Institution,Woods Hole, MA 02543, USAe-mail: [email protected]

Estuaries and Coasts (2009) 32:1130–1151DOI 10.1007/s12237-009-9206-4

and Ellsworth 1986; Olsen et al. 1993; McHugh et al. 2004;Klingbeil and Sommerfield 2005).

The Hudson River estuary offers a well-documentedexample of estuarine sediment transport processes (Panuzio1965; Woodruff et al. 2001; Geyer et al. 2001). The Hudsonis a partially mixed estuary with the salinity intrusionranging between 30 and 120 km upstream from the Battery,depending on river discharge and tidal forcing (Abood1974; Ralston et al. 2008). The Mohawk and UpperHudson Rivers converge 250 km upstream from the Batteryand together supply between 0.2 and 1.0 million metric tons(MT) of sediment annually (Panuzio 1965; Olsen 1979;Ellsworth 1986; Woodruff 1999; Wall et al. 2008). Thelong-term accumulation rate in the estuary is consistentwith the rate of sea level rise of 1–3 mm/year (Olsen et al.1978; Hirschberg et al. 1996; Carbotte et al. 2004; McHughet al. 2004; Klingbeil and Sommerfield 2005; Slagle et al.2006), although short-term accumulation rates can besignificantly greater (Sommerfield 2006).

Two distinct regions with persistently high suspendedsediment concentrations have been identified as estuarineturbidity maxima (ETM). The lower ETM is located 12–20 km up-estuary from the Battery near the GeorgeWashington Bridge (Geyer et al. 2001; Traykovski et al.2004), while the upper ETM is 55–60 km up-estuary inUpper Haverstraw Bay (Bokuniewicz and Arnold 1984).The ETMs feature high suspended sediment concentrationsand localized accumulation rates that exceed the long-termmean. In the lower ETM, near-bottom concentrations canexceed 1,000 mg/L (Geyer et al. 2001; Traykovski et al.2004) and short-term accumulation rates can be 10–30 cm/year (Olsen et al. 1978; Feng et al. 1998; Geyer et al. 2001;Woodruff et al. 2001). At tidal time scales net accumulationcan be greater, with 1–4 cm of accumulation in a tidalperiod (Woodruff et al. 2001; Traykovski et al. 2004).

The 100-fold discrepancy between long- and short-term accumulation rates in the lower ETM presents anapparent contradiction. Most observations indicate thatthe local short-term sediment trapping is much greaterthan the volume required to maintain equilibrium withrising sea level. One hypothesis is that relatively in-frequent large-magnitude storm events erode and exportsediment to balance the sediment accretion during low tomoderate river discharge. Stratigraphic evidence in thelower ETM indicates that decadal to centennial scaleevents scour material that is trapped at monthly to yearlytime scales (Klingbeil and Sommerfield 2005). Geochro-nology of a resistant subsurface layer in the lower ETMdated a recent major erosion event to several years before1954 (Klingbeil and Sommerfield 2005). Extreme eventsmay also have the opposite effect of providing a large netinput of sediment to estuaries if supply exceeds export. InChesapeake Bay, just two major storms supplied half of the

total sediment input between 1900 and 1975 (Schubel andHirschberg 1978).

The time scales of suspended sediment variabilityinclude tidal cycle resuspension, meteorological events ofa few days, the fortnightly spring–neap cycle, seasonal riverdischarge, inter-annual droughts or wet periods, anddecadal or longer recurrence intervals for extreme events.In the Hudson higher discharge occurs during the springfreshet (∼2,000 m3 s−1) and lower discharge during the latesummer (∼200 m3 s−1). Recent observations also indicate ahigh-discharge period November through January that isless evident in the long-term record (Wall et al. 2008).Fluvial sediment load (Qs) from upstream varies seasonally,typically depending on the discharge (Qr) raised to a powerbetween 1.5 and 2.5 (Nash 1994). In the Hudson, the powerlaw (Qs∼Qr

n) varies with discharge. At low to moderatedischarge (Qr<500 m3 s−1), n∼1.5, while at higherdischarge n∼2.9 (Woodruff 1999). Extreme meteorologicalevents disproportionately affect the long-term sedimentbudget because of the non-linear dependence of sedimentload on discharge. Sediment load measurements from anysingle year cannot represent processes with natural vari-ability over much longer time scales (Woodruff 1999).

Observations in the lower ETM of the Hudson havedocumented both intra- and inter-annual variability in sedimenttransport. During spring freshets with moderate to highdischarge, sediment flux is down-estuary and sediment depositsin New York Harbor (Woodruff et al. 2001). In the summermonths after the freshet, sediment flux is up-estuary towardthe ETM (Hirschberg et al. 1996; Feng et al. 1999; Woodruffet al. 2001). However, during relatively low-dischargefreshets, sediment flux may be persistently up-estuary becausebaroclinic trapping remains strong (Geyer et al. 2001). Forexample, the 1998 spring freshet moved sediment into theHarbor, but during the weaker freshet in 1999 sediment fluxin the lower ETM remained up-estuary (Geyer et al. 2001;Woodruff et al. 2001). During the moderate freshet of 2001,sediment flux in the lower ETM was down-estuary atmaximum discharge and then turned up-estuary during lowerdischarge summer months (Traykovski et al. 2004).

The goal of this work is to quantify the effects ofextreme discharge events on sediment transport and long-term sediment budgets in the Hudson, and more generallyin partially mixed estuaries. We are interested in thediscrepancy between the short- and long-term rates ofsediment accumulation, and in understanding how themismatch depends on the intermittency of discharge events.Changes in river discharge are expected to affect both thesediment transport capacity of the estuary and the supply offluvial sediment, with consequences for the net accumula-tion or export of sediment. By simulating conditions usinghistorical forcing, we can quantify the factors that affecttransport such as event timing with respect to the tidal

Estuaries and Coasts (2009) 32:1130–1151 1131

forcing and event duration, as well as time scales ofsediment retention in the system.

Model Description

To calculate sediment transport capacity over time scalesranging from days to decades, we use a tidally and cross-sectionally averaged model of the salinity and along-estuaryvelocity (MacCready 2007; Ralston et al. 2008). The modellocally applies the quasi-steady Hansen and Rattray (1965)solution for residual shear and stratification to determinethe subtidal baroclinic salt flux. The temporal evolution ofthe estuarine salinity distribution depends on the balancebetween the residual salt flux up-estuary and advectiondown-estuary due to the river discharge. The mean velocityis the river discharge modulated by subtidal water levelfluctuations at the downstream boundary. At meteorologicaltime scales (3–5 days), volume flux due to sea levelfluctuations can increase the mean velocity by a factor of 2or reverse the mean flow toward up-estuary (Bowen andGeyer 2003; Ralston et al. 2008). The model was calibratedand tested against salinity and velocity observations atmultiple locations along the Hudson during 2004. Modelinputs and the sediment transport calculations are describedhere, but the development, calibration, and application ofthe model are described elsewhere (Ralston et al. 2008).

Model Inputs

Model simulations ran from 1918 to 2005, producingsubtidal salinity and velocity fields along the estuary. Inputsinclude bathymetry (depth H(x) and cross-sectional area A(x)), tidal velocity amplitude Ut(x,t), mean velocity U0(x,t),and salinity at the open boundary Sbc(t). Channel depth andcross-sectional area were derived from data from theHudson River Estuary Program of the New York StateDepartment of Environmental Conservation, the NationalOceanic and Atmospheric Administration (NOAA), and theUS Geological Survey (USGS; Stedfast 1980). The modeldomain was from 0 to 180 km from the Battery withdiscretization of 1 km. To account for depth variationbetween channel and shoals, cross-sections are subdividedrelative to the median cross-sectional depth and averagedlaterally to get channel (H1) and shoal (H2) depths along theestuary. In a rectangular channel, H1=H2, but in a cross-section with broad, shallow shoals, H2<<H1.

Discharge data were collected from USGS stream flowgages (Fig. 1). From 1946 to present, discharge wasdetermined from measurements at Green Island Dam(#01358000), about 250 km north of the Battery. For prioryears, we combined discharge measurements in thetributaries that converge upstream of Green Island: the

Mohawk River at Cohoes (#01357500, from 1917) andthe Upper Hudson River at Waterford (#01335754, from1887). When measurements from all three stations wereavailable, the sum of the tributary discharges agreed withthe measurement at Green Island. The gage discharge wasmultiplied by a factor of 1.6 to account for tributariesdownstream of Green Island based on comparisons betweengage data and observations of mean flow in the lowerestuary (Lerczak et al. 2006).

Mean velocity depends primarily on the river discharge,with U0=Qr/A. However, subtidal water level fluctuations atthe downstream boundary change the volume of the estuaryand thus U0. Water level data (ηbc) during the observationperiod were taken from a NOAA tide gage at the Battery(#8518750; Fig. 1). Hourly water level data at the Batterywas available as far back as 1958, so prior to that and duringperiods when the Battery station was out of service the tidegages at Sandy Hook (#8531680) and Atlantic City, NJ(#8534720) were used to determine the subtidal sea levelvariability. The Battery, Sandy Hook, and Atlantic City waterlevel records were highly correlated at subtidal frequenciesbecause of their proximity relative to the large-scale forcingthat generates coastal set-up or set-down.

Tidal velocities determine vertical mixing rates and thusaffect estuarine circulation and stratification. We use tidalcurrent harmonic predictions to calculate Ut (Fig. 1). Weincorporate spatial variability in Ut based on predicted currentspeed ratios at 24 stations along the Hudson referenced toThe Narrows, New York Harbor, and interpolate betweenstations onto the model grid by conserving tidal volume flux.Current speeds are calculated using the T_TIDE softwarepackage (Pawlowicz et al. 2002) and harmonic constituentsfrom the XTide software1. Node factors and equilibriumarguments prior to 1970 are taken from the Institute of OceanSciences Tidal Package (Schureman 1959; Foreman 1978).

Without long-term observations of near-bottom salinity atthe Battery or in New York Harbor, we base Sbc oncorrelations with Qr and Ut. Salinity in the Harbor decreaseswith increased river discharge. A quasi-empirical relationshipwas developed in which we assumed that salinity gradientscales as Qr

−1/3 (Abood 1974; Monismith et al. 2002;Ralston et al. 2008). The origin of the estuary with oceanicnear-bottom salinity (S0) is an unknown distance from theBattery. The salinity at the Battery varies as Sbc ¼S0 1� c1Q

1=3r

� �, where c1 is a constant fit based on obser-

vations (Fig. 2a). The available bottom salinity data includetidally averaged observations in 2004 and instantaneousmeasurements at stations in the Harbor.

Generally Sbc decreased with river discharge, but thescatter about the best-fit relationship to Qr was significant.The misfit depended in part on spring–neap variability in

1 http://www.flaterco.com/xtide/

1132 Estuaries and Coasts (2009) 32:1130–1151

http://www.flaterco.com/xtide/

Fig. 1 Time series of forcingduring model period (1918–2005): river discharge (Qr), tidalvelocity amplitude (Ut), andsubtidal water level (at the Bat-tery, ηbc). Periods of salinityobservations (from USGS,WHOI, and NYCDEP) formodel validation are indicatedabove the top panel

Fig. 2 Bottom salinity bound-ary condition at the Battery asfunction of Qr (lagged 7 days)and Ut. a Observed bottomsalinity at the Battery (subtidaltime series in 2004, dark gray)and in New York Harbor (in-stantaneous measurements from1968 to 2005, light gray) vs.Qr. Solid line isSbc ¼ S0 1� c1Q

1=3r

� �,

where S0=31 and c1=0.020.Dashed lines showSbc ¼ S0 1� c1Q

1=3r

� �� c2 U

0t

with c2=7.9 andUt

’=±0.3 m s−1, the rangeof tidal velocity variability.b Plot of salinity boundarycondition misfit basedon Qr alone(Sbc � S0 1� c1Q

1=3r

� �)

and tidal velocity variability(U

0t ¼ Ut � Ut). Slope

of line is c2 in Eq. 1


tidal mixing. During spring tides, mixing decreasedstratification and near-bottom salinity for a given depthaveraged salinity. During neaps, stronger stratificationcorresponded with higher near-bottom salinities. Weaccounted for variability in Sbc due to tidal mixing byfitting the difference (ΔSbc) between observed salinitiesduring 2004 and the prediction based on Qr alone to U

0t ,

where U0t ¼ Ut � Ut and Ut is the long-term average Ut

(Fig. 2b). The salinity boundary condition was

Sbc ¼ S0 1� c1Q1=3r

� �� c2 U

0t ; ð1Þ

where c2 is determined from the linear fit between ΔSbc andΔUt. The parameters fit from the observations were S0=31 psu, c1=0.020, and c2=7.9. Sbc calculated from Qr andUt produced simulations that better matched salinityobservations in the estuary than using a constant S0.

Calibration and Validation

The model is calibrated by adjustment of two parametersthat scale the vertical mixing of momentum and salinity.These mixing coefficients were optimized by comparisonwith salinity and velocity at multiple locations along theHudson during the spring and summer of 2004 (Ralston et

al. 2008). The simulations presented here use the coef-ficients found for the 2004 period, but we validated themodel by comparison with additional salinity observations(Fig. 3). The model skills (as defined in Ralston et al. 2008and Warner et al. 2005) for the longer simulation periodwere similar to the detailed observations in 2004, andcompared well with the skills reported for a three-dimensional hydrodynamic model of the Hudson (Warneret al. 2005). The model skill over the extended period forbottom salinity was 0.96 and for surface salinity was 0.97(R2 of 0.89 and 0.91, respectively).

To compare against observations over an even longerperiod we use surface and bottom measurements from theNew York City Department of Environmental Protection(NYCDEP) monitoring of the lower Hudson. The NYC-DEP has regularly visited seven stations from the Battery to25 km up-estuary, primarily during summer months. Themodel corresponds with the observations, albeit with scatterlikely due tidal cycle variability (Fig. 4). The model agreesmore consistently with surface observations, but tends toover-predict bottom salinity. The bottom salinity discrep-ancy could be due to errors in the open boundary condition,or could be due to field sampling outside of the channelthalweg that would bias observed salinities low. Compar-isons between instantaneous and tidally averaged quantities

Fig. 3 Time series of surface(dashed) and bottom (solid) tid-ally averaged salinity observa-tions (black), withcorresponding model results(gray). Locations range from 6to 83 km and are indicated onthe map. The source of obser-vations (WHOI or USGS) arealso indicated


are not ideal, but the historical observations generallysupport extension of the model to decadal time scales.

Near-Bottom Velocities

We use the prescribed (Ut) and calculated (U0, andestuarine velocity Ue) velocities to calculate the tidalmaxima of near-bottom velocities during ebb and flood asfunctions of space and time. The estuarine velocity is thesubtidal baroclinic circulation, and based on a frictionalbalance is calculated as Ue ¼ gb @s=@xð ÞH3

�48Kmð Þ,

where ∂s/∂x is the along-estuary salinity gradient, Km isan effective eddy viscosity, and β is the coefficient of salineexpansivity (7.7×10−4psu−1; Hansen and Rattray 1965).The estuarine circulation is up-estuary near the bed anddown-estuary near the surface, and Ue is part of the modelsolution because it depends on ∂s/∂x.

The vertical structures of the velocity components are usedto define near-bottom velocities: Ut and U0 have parabolicdistributions, while Ue has a cubic form with flow upstreamnear the bed and downstream near the surface (Hansen andRattray 1965; MacCready 2004). The near-bottom velocity isthe sum of the three velocity components, and the relativecontribution of each differs between flood and ebb. Duringfloods, Ue enhances near-bottom flow and U0 retards it,while during ebbs the roles reverse. The model calculatesconditions in the channel thalweg, so we account for lateralvariation in depth to determine near-bottom velocities on theshoals. On the shoals, the estuarine circulation is muchweaker than in the thalweg, and potentially can be directeddown-estuary. The contribution of Ue to the near-bottomvelocity on the shoals is determined by projecting thethalweg cubic estuarine velocity profile laterally to thenear-bottom elevation of the shoals. Details on the velocitycalculation can be found in the Appendix.

To evaluate the near-bottom velocity parameterization,we compare the model results with ADCP measurements atnine locations in the lower Hudson estuary over 4 years(Fig. 5). The observations range from near the Battery to44 km up-estuary, and include both channel and shoalstations. The data have been processed into maximum near-bottom flood and ebb velocities, and model velocities havebeen calculated according to Eqs. A1 and A2. The modelvelocities and the observations correspond well, especiallyconsidering the wide range of conditions sampled. Themodel skill for near-bottom flood velocities was 0.91 (R2 of0.71) and for ebb velocities was 0.95 (R2 of 0.81). Note thatthese velocity observations were used to develop functionsfor parameters that depend on cross-sectional geometry toquantify the lateral distribution of velocity (see Appendix).Ideally, independent data from a different period or from adifferent estuary would be used to validate this model.

Sediment Transport and Transport Capacity

Sediment erosion rate depends on the excess bottom shearstress above a minimum threshold stress (Partheniades1965). Based on this functional form and a correlationbetween excess shear stress and suspended sedimentconcentrations observed previously in the lower Hudsonestuary (Traykovski et al. 2004), we calculate the tidalmaximum sediment concentration (Ct) using a quadraticdrag formulation for the excess bottom shear stress as

Ct ¼ C0U2�U2

cð ÞU 2

cU � Uc

Ct ¼ 0 U < Uc

; ð2Þ

where Uc is a critical velocity for resuspension and C0 is areference concentration. Sediment flux depends on bothsediment concentrations and velocities, and the net flux

Fig. 4 Instantaneous surfaceand bottom salinity observa-tions from NYCDEP (1968–2005) and corresponding tidallyaveraged model results. Colorsindicate distance of samplingstation from Battery (0 to25 km), as shown in the map


after a tidal cycle is the difference between up-estuary fluxduring the flood and down-estuary flux during the ebb.Sediment fluxes are sensitive to the erosion parameters Uc

and C0 that can vary spatially and temporally and aredifficult to quantify in the field.

To address the uncertainty in the erosion parameters wetake two approaches to estimate sediment transport. Firstwe note that for reasonable values of Uc (∼0.5 m s−1),sediment flux is approximately proportional to U3. The netsediment transport capacity after a tidal cycle is

U 3net ¼ U3

flood � U3ebb; ð3Þ

and U 3net is indicative of how sediment moves given an

available supply of erodible material. When U3net < 0,

tidally averaged sediment transport is down-estuary orexporting, and U3

net > 0 represents net sediment flux up-estuary. Near-bottom velocities determine U 3

net, incorporat-ing both sediment resuspension proportional to bottomshear stress and net advection resulting from tidal asym-metry in the sense of the estuarine and river velocities. Weset Uc proportional to the minimum local tidal velocityamplitude, and for Uflood or Uebb < Uc, the sediment flux

during that phase of the tide is zero. The spatial andtemporal patterns of U3

net are not sensitive to Uc over arange of values (including Uc=0), but Uc does affect themagnitude of U 3

net.The U3

net approach does not directly quantify sedimentflux, as it is independent of the erodibility C0 and inputfrom upstream or downstream boundaries. In subsequentsections, we derive the spatial variability in sedimenterodibility based on simplifying assumptions to directlycalculate sediment fluxes. Initially (Sections SedimentTransport Capacity and Extreme Events) we focus on thesediment transport capacity (U 3

net) that depends on fewerassumptions about sediment properties. U 3

net reflects localresuspension and net sediment transport capacity. Thesediment flux calculations (Sections Erodibility and Mor-phological Equilibrium, Comparison with Sediment Obser-vations, and Long-term Sediment Flux) incorporate thetransport capacity, but also incorporate the fluvial sedimentsupply and heterogeneity in sediment properties. The 1Dmodel does not track sediment fluxes at high-spatial andtemporal resolution, so the sediment flux calculations arerepresentative of broader scales rather than a specificlocation.

Fig. 5 Comparison betweenmodeled and observed near-bottom velocities. Panels on theright show data from differentobservation periods (1999through 2004), and station loca-tion is indicated by color shownon map. Open markers on themap are stations on shoals; filledmarkers are stations in thethalweg


Results

Sediment Transport Capacity

The along-estuary distributions of channel and shoal depthsdirectly affect the estuarine sediment transport capacity(Fig. 6a). Averaging over the simulation period producesthe long-term mean of sediment transport capacity in thechannel and on the shoals (Fig. 6b). Positive U 3

net corre-sponds with sediment transport up-estuary, and in much ofthe lower Hudson, mean near-bottom sediment transport inthe channel is up-estuary. In shallower regions, meansediment transport is predominantly down-estuary. Thelateral difference in mean U3

net is largely due to estuarinecirculation. In the channel, Ue enhances near-bottom veloc-ities during floods and retards flow during ebbs, creating netflux in the flood direction. On the shoals, the contribution ofUe is much weaker (or reversed), so U0 produces ebb-dominant fluxes.

Both channel and shoals have significant along-estuaryvariability in mean transport capacity. In the channel, thegreatest up-estuary transport occurs near the lower ETM(∼14 to 24 km); farther upstream U 3

net magnitude decreases.

Near the Battery (<8 km) where the cross-section hasrelatively uniform depth, mean transport over the entirewidth is up-estuary. Farther north in the Tappan Zee andHaverstraw Bay (∼40 to 60 km) the estuary has broadshoals and a relatively narrow, shallow channel. Nettransport on the shoals is down-estuary, and net transportin the channel is nearly zero. The along-estuary gradients inU 3

net depend on Ue, but also include effects of along-estuarychange in cross-sectional shape.

The long-term mean of U 3net masks variability at

meteorological, seasonal, and inter-annual time scales.During low-discharge periods, U 3

net can be relatively steady,such as during a severe drought when transport was up-estuary in the channel and down-estuary on the shoals(Fig. 6c). The U 3

net distribution reflects variability in Ut andUe (response due to changes in mixing) over the 7-dayperiod, as Qr and U0 were relatively steady. When Qr andU0 (including the sea level set-up or set-down) changerapidly, U 3

net can change rapidly. During a 7-day periodaround a high-discharge event, U3

net in the channeltransitioned from up-estuary transport prior to the storm todown-estuary transport with the increase in U0 (Fig. 6d).Sediment transport on the shoals also fluctuated during that

Fig. 6 Sediment transportcapacity U 3

net ¼ U3flood � U3

ebbas a function of distance alongthe estuary, with positivevalues for sediment transportup-estuary. a Hudsonbathymetry with the depthof the thalweg (black) andof the channel and shoals (gray).b Mean U3

net over model period(1918–2005) for channel (dark)and shoals (light). c U 3

net forchannel and shoals during a7-day period of lowQr (August 19 to 25,1964, Qr,mean=150 m3 s−1,Qr,max=170 m3 s−1). d U3

netfor channel and shoalsduring 7 days with highQr (December 29, 1948 toJanuary 4, 1949,Qr,mean=4,300 m3 s−1,Qr,max=6,400 m3 s−1)


period, including a period of up-estuary transport when sealevel set-up reversed the direction of U0.

The seasonal variability in U3net depends largely on the

annual cycle of river discharge (Fig. 7). During the springfreshet (day∼70 to 140), the salinity intrusion and region ofup-estuary transport in the channel are confined to thelower estuary. The maximum sediment transport capacityon the shoals occurs during the freshet, when rivervelocities augment down-estuary transport. During lowerdischarge summer months, up-estuary transport in thechannel expands northward into Haverstraw Bay. Duringthe late fall and winter, the channel of the upper estuaryshifts back toward down-estuary transport as Qr increases.

Extreme Events

The seasonally averaged sediment transport capacity maynot correspond with long-term transport if infrequent butlarge discharge events dominate the total flux. In the lowerestuary ETM (16 km) and to the north of the ETM (34 km),U 3

net exhibits temporal variability due to meteorologicalevents (Fig. 8). U 3

net at each station is approximatelynormally distributed around the long-term means, withchannel transport strongly up-estuary in the ETM anddecreasing in magnitude to the north. Transport on theshoals is largely down-estuary at both stations. However,extreme values of U 3

net corresponding with the tails of thehistograms can be opposite the long-term mean. Thenormal distribution of U 3

net depends on the spring–neapvariability in tidal amplitude, but extreme values of U3

net

depend on the combination of Qr, Ut, and ηBC.To highlight the variability at meteorological time scales,

we focus on a period from 1998 to 2002 with sediment

transport observations in the lower Hudson (Geyer et al.2001; Woodruff et al. 2001; Traykovski et al. 2004; Fig. 9).In January 1998, a high-discharge event (Qr∼6,100 m3 s−1)generated strong down-estuary transport, both in thechannel and on the shoals. In 1999, the freshet dischargewas much weaker and net transport remained persistentlyup-estuary in the channel. The model results correspondwith observations that down-estuary sediment flux duringthe 1998 freshet deposited material in the Harbor and themobile sediment moved back up-estuary during lowerdischarge periods of 1998 and 1999 (Geyer et al. 2001;Woodruff et al. 2001). Another major discharge eventoccurred in April 2001 (Qr∼4,300 m3 s−1), consistent withobservations of down-estuary sediment flux in the lowerETM (Traykovski et al. 2004). After the freshet, flux in thechannel shifted back up-estuary, also consistent withobservations. Note that both 1998 and 2001 had relativelylarge flow events. The 1998 freshet ranked as the sixthlargest event during the model period (1918–2005) and the2001 freshet ranked 23rd.

In general, significant down-estuary sediment transport inthe lower ETM results from high river discharge (Fig. 10).Focusing on the lower ETM (16 km), U3

net correlates with Qr,particularly at large Qr. In the channel, export occurs only atvery high Qr, as transport capacity remains up-estuary for Qr

less than about 3,000 m3 s−1. Summing across the estuary,the correlation between U3

net and Qr remains strong, but thetransition from sediment import to export occurs at lowerdischarge (Qr∼1,500 m3 s−1).

A few large discharge events dominated the down-estuary sediment flux. The highest river discharges from1918 to 2005 were ranked as independent events if theyoccurred at least 7 days apart. During each independent

Fig. 7 Spatial and temporalmaps of sediment transportcapacity for the channel andshoals, plotting U 3

net averagedover the period 1918–2005 as afunction of distance along theestuary and day of the year.Upper panel shows seasonaldischarge in the Hudson includ-ing mean, 5th and 95th percen-tile discharges (Green IslandUSGS station #01358000 from1946 to 2005, multiplied by 1.6to account for watershed inputsdownstream of gage)


event, we identified the maximum sediment export basedon U 3

net, noting that in some cases the maximum exportlagged the maximum Qr by 1 or 2 days due to theadjustment of the salinity field. The 25 largest flow eventsand the U 3

net during each event are highlighted, along withthe relative magnitude of the tidal velocity during eachevent (Fig. 10). Transport capacity during the largest events

followed the general trend of greater export with larger Qr,but with scatter due to the timing and duration of eachevent. If a discharge event occurred during spring tides,stronger tidal velocities enhanced vertical mixing andweakened the up-estuary transport by Ue. Spring tidalvelocities during discharge events also enhanced the ebb-flood disparity in transport through terms such as U0Ut

2

Fig. 8 Time series of sedimenttransport capacity U3

net withpositive values for sedimenttransport up-estuary. Two loca-tions are shown, in the lowerETM (16 km) and farther up-estuary (36 km), with resultsfrom the channel and shoals.Period shaded gray is shown ingreater detail in Fig. 9

Fig. 9 Time series of sedimenttransport capacity U3

net withpositive values for sedimenttransport up-estuary. Two loca-tions are shown, in the lowerETM (16 km) and farther up-estuary (36 km), with resultsfrom the channel and shoals.Period corresponds with obser-vations discussed in Woodruff etal. (2001), Geyer et al. (2001),and Traykovski et al. (2004).Top panel shows discharge dur-ing the same period


from Eqs. 3 and A1. When a discharge event occurredduring neap tides, mixing was weaker, estuarine circulationstronger, and transport in the lower estuary less likely to bedown-estuary. Consequently, high-discharge events duringspring tides had greater down-estuary transport capacitythan similar magnitude flows during neap tides. Forexample, events in 1948, 1984, and 1986 (ranked #12, 13,and 14, respectively) all had discharges of about 4,700 m3 s−1.The calculated U 3

net during the three events varied widelydespite the similar Qr because of their timing with respect tothe spring–neap cycle. The 1948 event during a spring tidehad much stronger down-estuary transport than the 1986event during a neap tide.

In addition to Qr, U0 depends on subtidal fluctuations insea level due to coastal waves or storm surge. At low tomoderate Qr, variability in water level can alter thedirection of sediment transport in the lower ETM(Fig. 11). Falling sea level transports volume out of theestuary and enhances sediment export, while rising sealevel opposes river discharge and can generate net up-estuary transport. While the sea level forcing of meanvelocity is important at lower Qr, the largest sediment

export events remained linked to high Qr. For high riverdischarge (Qr>2,500 m3 s−1 in Fig. 11), sea level fluctua-tions had a moderate effect on net transport, but the primaryfactors determining U3

net remained the magnitude of Qr andtiming with respect to Ut.

Erodibility and Morphological Equilibrium

U 3net is indicative of sediment transport capacity, but

quantifying long-term sediment flux in the estuary requiresassumptions about sediment properties, fluvial inputs, andthe vertical distributions of U(z) and C(z). We start byassuming that the suspended sediment concentrationdecreases exponentially above the bed:

CðzÞ ¼ Cte� ws

Kmz ð4Þ

where ws is the settling velocity, Km is the eddy viscosity,and Ct is from Eq. 2. Settling velocities in estuaries varyspatially and temporally depending on sediment composi-tion and flocculation, but here we use a representative valueof ws=0.5 mm s−1 based on previous observations and

Fig. 10 Sediment transport ca-pacity (U3

net) in the lower ETM(16 km) vs. river discharge.Instantaneous values (every0.5 day) are shown for thechannel and the total cross-section. The 25 largest dischargeevents are identified with themaximum U 3

net during eachevent. Additionally, the relativetidal velocity during the eachevent is indicated by the size ofthe marker. The dates of some ofthe largest events are indicatedfor reference. Large dischargeevents that occur during springtides result in greater down-estuary transport than eventsduring neap tides when estuarinecirculation is stronger


modeling in the Hudson (Geyer et al. 1998; Traykovski etal. 2004). Eddy viscosities were taken from the modelresults, and typical values of 5 to 25 cm2 s−1 producedvertical e-folding scales (Km/ws) from 1 to 5 m. We alsotested a Rouse profile formulation for C(z), but found that ityielded unreasonably high near-surface sediment concen-trations compared with observations. The velocity profilewas assumed to be parabolic, and the sediment flux wascalculated as the depth integral of U(z)C(z). Sediment fluxremains proportional to U3 as assumed previously, but themagnitude of the flux depends on ws, C0, and Uc.

To determine Ct, we start with an initial assumption thaterodibility C0 is spatially uniform along the estuary andbetween channel and shoals. This simplification does notcorrespond with the heterogeneity observed in naturalsystems, but we use it as a null hypothesis to test whetherlateral gradients in sediment properties are necessary forequilibrium transport. After demonstrating that spatiallyuniform erodibility does not satisfy the long-term sedimentbudget, we use the constraint of equilibrium transport tocalculate the lateral heterogeneity in erodibility.

We initially assume that Uc scales with the minimumlocal tidal velocity amplitude (Uc∼0.9Ut min), and that C0=

0.4 kg m−3 everywhere. These values for Uc and C0

correspond with suspended sediment observations from theHudson lower ETM (Traykovski et al. 2004). Based oncomparisons with observations of suspended sediment atPoughkeepsie (Wall et al. 2008), sediment erodibility ismodified by a seasonal factor that varies with meanmonthly temperature (Kirkby and Cox 1995). This ap-proach supposes that winter storms erode sediment fromunvegetated hillslopes and that the excess sediment input tothe estuary deposits as a relatively unconsolidated, erodiblebed. During summer months, sediment supply decreasesand without resupply of new material, the bed becomesmore consolidated, fine particles are winnowed away, andbed sediment is more resistant to resuspension. To reflectthis we multiply C0 by a seasonal scaling factorsf ¼ 1� T � T

� �=ΔT , where T is the monthly mean

temperature (at Albany), T is the annual average, and ΔTis the annual range. Comparisons of this formulation withobservations are shown in Section Comparison withSediment Observations.

The sediment loading from the watershed was empiri-cally based on daily discharge and sediment load (Qs, tonsday−1) observations from the Mohawk River (at Cohoes)

Fig. 11 Sediment transportcapacity (U 3

net) in the lowerETM (16 km) vs. subtidalwater level at the Battery(∂ηbc/∂t). Instantaneous values(every 0.5 day) of U 3

net for thecross-section total are shown,distinguishing between periodswith relatively high discharge(Qr>2,500 m3 s−1) andlow to moderate discharge(Qr<2,500 m3 s−1). Volumeflux due to falling subtidal waterlevel can produce mean currentsthat can transport sediment outof the estuary, but the largestdown-estuary transport occursduring high discharge eventsrather than due to fluctuations atthe open boundary


and the Upper Hudson River (at Waterford). The sedimentloads (Qs) were fit to the form

Qs ¼ Qs0Qr=Qr0

� �a; ð5Þ

where Qr0 represents a transition between low and high-discharge conditions (Woodruff 1999). The sedimentloading parameters for each river are given in Table 1.The total sediment loading is the sum of the Mohawk andUpper Hudson rating curve fluxes plus an additional 30%for sediment input by tributaries downstream of GreenIsland (Wall et al. 2008). Over the model period (1918–2005), the mean fluvial sediment load was 0.37 MT year−1

at Green Island Dam and 0.48 MT year−1 includingdownstream tributaries. The sediment loadings calculatedfrom the rating curves were consistent to within 10% ofobservations: 0.72 MT during 1959–1960 (Panuzio 1965),1.0 MT during 1976–1977 (Olsen 1979), and an annualaverage of 0.74 MT between 2002 and 2006 (Wall et al.2008). The long-term average from the rating curve issignificantly less than measurements during relatively high-discharge years of 1959–1960 and 1976–1977. Measure-ments at Poughkeepsie from 2002 to 2006 ranged annuallybetween 0.68 and 0.83 MT, with an estimated 20% to 40%of the sediment input from tributaries downstream of GreenIsland (Wall et al. 2008).

Over long time scales, we assume that estuarinemorphology approaches equilibrium such that the accumu-lation rates correspond with sea level rise (Meade 1969;McHugh et al. 2004; Klingbeil and Sommerfield 2005;Nitsche et al. 2007). Summed over the estuary, theaccumulation required to keep pace with sea level rise of2 mm year−1 accounts for about 0.2 MT year−1, roughlyhalf of the long-term average input. To maintain morpho-logical equilibrium, the estuary then must export the fluvialsupply in excess of equilibrium accumulation. This equi-librium assumption constrains the long-term average sedi-ment fluxes in the system so that we can solve for theimplied distribution of erosion properties.

At each grid cell along the estuary, we calculate theerodibility (C0) in the channel and on the shoal that yieldsthe net sediment flux consistent with equilibrium morphol-ogy over the simulation period. Under our initial assump-

tion that erodibility is laterally uniform, up-estuary flux inthe channel of the lower estuary is greater than the down-estuary flux on the shoals (Fig. 12a). Consequently, thelong-term sediment export would be insufficient to removethe fluvial input and sediment would accumulate in thelower estuary. For the system to maintain morphologicalequilibrium, bed sediment in the channel of the lowerestuary must be more resistant to erosion than on theshoals. We solve for the necessary distribution of erodibility(C0) such that at every position along the estuary the long-term mean sediment transport equals the difference betweenthe fluvial sediment input and the bed accumulationcorresponding to sea level rise. To constrain the calculation,we hold the erosion threshold Uc constant and solve at eachlocation for the C0 that meets the net flux constraint.Alternatively, C0 and Uc could co-vary. If both C0 and Uc

were part of the solution the resulting bed sedimentparameters would be quantitatively different but wouldproduce qualitatively similar trends in erodibility along-and across-estuary.

To maintain long-term morphological equilibrium, bedsediment in the channel of the lower estuary must be moreresistant to erosion than the adjacent shoals, or C0

decreased in the channel and increased on the shoals(Fig. 12b). Farther north (40 to 50 km), the estuary widensand shallows, and a lateral gradient in sediment propertiesis not necessary because up-estuary transport in the channelis much weaker. Instead, both channel and shoal sedimentmust be more resistant to erosion than initially hypothe-sized to match the long-term sediment flux. Moving fartherup-estuary (>50 km) the estuary becomes wider andshallower, and lateral variation in erodibility is required tomaintain equilibrium long-term transport.

Comparison with Sediment Observations

To evaluate the sediment transport calculations, we comparethe model results with suspended and bed sediment observa-tions. Suspended sediment concentrations in the modeldepend on calculated near-bottom velocities, the sedimentconcentration formulation (Eq. 2), and the erodibility C0

calculated from the long-term equilibrium assumption. Eachof these steps introduces potential errors or erroneousassumptions can skew the results.

For comparison we use near-bottom sediment measure-ments in the lower estuary from observations in 1999(Geyer et al. 2001) and 2000 to 2001 (Traykovski et al.2004), including sites both in the channel and on the shoals(Fig. 13). We also evaluate the seasonal scaling factor forC0 using a longer time series of suspended sediment atPoughkeepsie (124 km) (Wall et al. 2008). At Poughkeep-sie, C0 is a best fit to the observations rather than anindependent result of the model simulation because the

Table 1 Parameters for fluvial sediment loading (Eq. 5; Woodruff1999)

Mohawk River Upper Hudson River

Qr0 [m3 s−1] 500 400

Qr<Qr0 Qr>Qr0 Qr<Qr0 Qr>Qr0

α 1.35 2.87 1.43 2.87

Qs0 [tons day−1] 990 1,600 300 370


sediment calculations did not extend into the freshwaterriver. At locations in the estuary, C0 is independentlycalculated from the equilibrium transport constraint(Fig. 12b) and the resulting sediment concentrations arecompared with observations.

The model sediment concentrations are within a factor of2 of the observed values, and at some stations thecorrespondence is much better. Spring–neap tidal variabilityin sediment concentration was observed at most sites, andthe timing and the amplitude of the variability are repro-duced in the model. The seasonal modulation of erodibilityprovides a better fit to the observations at Poughkeepsie(skill=0.85, R2=0.56) than a constant C0 (skill=0.50, R

2=0.08). Skill scores for suspended sediment in the estuaryranged between 0.84 (R2=0.67) at 14 km and 0.35 (R2=0.08) in the channel at 35 km.

The skills are significantly lower than for salinity orvelocity, reflecting the uncertainty in the parameterizationof the bottom boundary condition. We must emphasize thatthis modeling approach is not suited for detailed compar-isons at high spatial or temporal resolution. The model istidally averaged and the discretization is coarse both along-and across-estuary. Bed sediment properties are likelyheterogeneous and unsteady at scales that are not capturedin the model, but that affect observed conditions. Ratherthan highly resolved simulations of suspended sediment,the strength of this approach is to integrate over estuarinespatial scales and decadal time scales to capture lowerfrequency variability in sediment flux and accumulation.

A more integrative evaluation of the results is tocompare the bed sediment properties derived from themodel with bed sediment observations. A benthic mappingproject2 over the tidal extent of the Hudson River combinedmulti-beam bathymetry, side-scan sonar, sub-bottom profil-ing, and sediment cores to classify bottom sediment typesand erosional or depositional regions (Nitsche et al. 2007).Erosional areas were defined as regions with high side-scanbackscatter indicative of winnowing, scour, or armoring,higher sediment density, and larger grain sizes (Nitsche etal. 2004). Depositional regions had low side-scan back-scatter, lower density sediment layers, and finer grain sizes.To directly compare the model results with the observedbed properties, we projected the map of sediment classi-fications (categories defined in Table 2 of Nitsche et al.2007) on to the channel and shoal sections used here.

The fractional areas of the channel and shoal regions thatwere labeled depositional are plotted against distance fromthe Battery (Fig. 12c). Depositional regions correspondwith bed sediment that was less consolidated and finergrained, and presumably more easily resuspended. Erosion-

al regions had bottom sediment that was more consolidated,coarser grained, and likely required greater energy toresuspend. In the lower estuary (<35 km), the channelwas predominantly erosional and the shoals were deposi-tional, consistent with lower C0 in the channel where scourand armoring lend resistance to erosion and higher C0 onthe shoals where less consolidated sediments were moreprone to resuspension. At the deep constriction near theGeorge Washington Bridge (18 km) the shoals were locallymore erosional, in agreement with the model decrease inC0. Up-estuary in the Tappan Zee (35 to 50 km), channeland shoals both were relatively erosional, consistent withdecreased C0 in this region. Up-estuary of 50 km inHaverstraw Bay, the model suggests the shoals are moredepositional while the observations say the opposite. Herethe estuary is significantly wider than in the lower estuary(<40 km), and wind waves may be important for resus-pension and lateral redistribution of sediment, and mayaffect bottom properties on the shoals. Such wind effectsare not incorporated in this model. Overall, the comparisonbetween model and observed bed properties supports thehypothesis that lateral gradients in bed sediment propertiesare required to balance sediment flux, particularly in thelower estuary.

Long-term Sediment Flux

Based on the sediment rating curves and inferred distribu-tion of C0, we calculated sediment fluxes as a function oftime and distance along the estuary. Fluvial sediment inputdepended strongly on river discharge and was highlyunsteady. Over annual to decadal intervals, the estuaryhad an excess or deficit of sediment relative to long-termequilibrium (Fig. 14). Annually, the freshet deliveredsediment and subsequent moderate discharge periodsprovided net export from the system. This was consistentwith radionuclide observations that indicated sedimentresidence times on the shoals of the lower ETM of 0.5–1 year (Feng et al. 1998). However, a sequence ofparticularly dry or wet years could produce more substan-tial accumulation or removal of sediment. For example, the1960s were a period of severe drought, and millions of tonsof sediment accumulated in the estuary. Average dischargeincreased in the 1970s, and estuarine transport removedsediment from the system.

The mass excess or deficit is indicative of the pool of thepotentially mobile bed sediment. We converted the cumu-lative mass at each point along the estuary to an equivalentchange in bottom depth by assuming laterally uniformdeposition or erosion (Fig. 14). The maximum depth ofaccumulation or erosion was about 0.5 m, with accumula-tion greatest in the ETMs following the largest storm eventsand the drought of the 1960s. In reality, accumulation and2 http://cugir.mannlib.cornell.edu/bucketinfo.jsp?id=7885


http://cugir.mannlib.cornell.edu/bucketinfo.jsp?id=7885

erosion may be localized on the shoals rather than laterallyuniform across the estuary (Woodruff et al. 2001).Similarly, observations in the Delaware Estuary haveshown that inter-annual storage of sediment in depositionalregions can exceed the annual sediment input from the river(Cook et al. 2007).

Estuarine sediment transport capacity increases approx-imately linearly with discharge (Fig. 10), but fluvialsediment supply increases nearly cubically (Eq. 5). Thenet sediment flux depends on both factors (Fig. 15). Duringlow discharge periods (Qr<∼400 m3 s−1), estuarine circu-lation traps sediment in the estuary, with the greatestaccumulation in the ETM regions. At moderate discharge(Qr∼400 to 2,000 m3 s−1), sediment flux is on averageseaward as the estuarine transport capacity increasessediment export, especially on the shoals. During veryhigh-discharge events (Qr>∼2,000 m3 s−1), sediment inputfrom the river is much greater than the estuarine transportcapacity and excess sediment is stored in the system until itcan be exported at more moderate Qr. Note the discharge

dependence is only one factor, and that the substantialspread in net flux for a given Qr demonstrates theimportance of tidal amplitude and sea level fluctuations.

The sediment flux dependence on Qr may appear to be atodds with the previous calculations of sediment transportcapacity. According to U 3

net, the greatest down-estuarytransport occurs during the highest discharge events. Inthe sediment flux calculations, the estuary actually gainssediment during the highest discharge events, and netexport only occurs at moderate Qr. The discrepancy reflectsthe difference between the transport and the net conver-gence or divergence of sediment. The flux calculationsinclude the fluvial sediment supply that is far moresensitive to Qr than the estuarine sediment transportcapacity. While estuarine transport is strongly down-estuary during high-discharge events, the increased trans-port is not sufficient to keep up with the increased supply ofsediment from the watershed. The excess sediment must bestored in the estuary temporarily until it is exported duringperiods of moderate Qr.

Fig. 12 a Net sediment fluxbased on initial assumption ofspatially uniform C0. b Refer-ence concentration (C0) distri-bution that satisfies long-termmorphological equilibrium (netinput rate equal to net transport).c Fraction of bed sediment inchannel and shoal regionsclassified as depositional(Nitsche et al. 2007)


Discussion

Tidal Forcing

Extreme discharge events dominate sediment export in thechannel of the lower estuary, but the relative impact of agiven discharge depends on the coincident tidal velocitiesand the sea level forcing. Consequently, estimates of theprobability of a given magnitude of transport must considernot only statistics of the basin hydrology, but alsovariability in tidal forcing and subtidal sea level (whichmay be correlated with Qr). Tidal velocities in particularhave a major effect on the potential U 3

net. Significant down-estuary transport in the channel of the lower ETM requiressimultaneously high discharge and strong tides. Leavingaside monthly to annual modulation of spring tidalamplitude, a discharge event has about a 20% probabilityof occurring within 1 day of maximum spring tides, and ifthe high discharge extends over 3 days then the oddsincrease to about 40%.

Large tidal velocities increase resuspension by erodingmore deeply into bed sediment. Tidal amplitude also altersvertical mixing and estuarine circulation, affecting whether

suspended material moves downstream or remains in theestuary. Seismic reflection profiles and sediment geochro-nology indicated that a major erosion event occurred in thelower Hudson estuary several years prior to 1954 (Klingbeiland Sommerfield 2005). In the model results, two high-discharge events that coincided with spring tides occurredless than a year apart in March 1948 and January 1949 (Qr

ranked 12 and 4, respectively). With little time for sedimentaccretion between events, the second event may haveeroded more deeply than if it had been isolated, producingan erosion-resistant layer still evident in the sub-bottom ofthe lower ETM.

Estuarine Response Time

In addition to the tidal forcing, sediment transport dependson the duration of discharge events relative to the estuarineresponse time. Estuaries adjust to changes in forcing overperiods depending on the length of the estuary (Lx) and thefreshwater velocity (Qr/A) (Kranenburg 1986; MacCready2007). Observations in the Hudson (Lerczak et al. 2008)and results from a 3D hydrodynamic model (Hetland andGeyer 2004) indicate that estuarine response times scale as

Fig. 13 Suspended sedimentobservations and model results.Data from 1999 are from near-bed optical backscatter sensorsand data from 2000–2001 arefrom acoustic backscatter pro-files. Dashed lines indicateobservations on the shoals andsolid lines are in the channel.Top panel is from USGS obser-vations at Poughkeepsie(124 km) based on acousticalbackscatter profiles


Tresponse � LxA=Qr. If a discharge event is shorter than the

estuarine response time, then the salinity intrusion remainslonger than its equilibrium and down-estuary sedimenttransport is reduced.

Spring freshets in the Hudson typically occur inMarch or April due to rain and snow melt with broadpeaks of a week or longer. However, intense winter rainevents can generate high discharges over just a fewdays. For example, winter storms in 1949, 1996, and1998 had similar discharges (∼6,000 m3 s−1), and alloccurred during spring tides (Fig. 10). Equilibrium scalingwould predict similar salinity distributions and sedimenttransport for the three events, but the transport during the1996 event was less than the other two cases despitestronger tides. The durations of the 1949 and 1998 eventswere approximately equal to the estuarine response time,but the event in 1996 was much shorter and lasted only 1/4 the estuarine response time. For snow melt freshets withbroad discharge peaks, the high-discharge period greatlyexceeds the estuarine response time. For winter rain andlate summer hurricanes (e.g., hurricanes in 1927, 1938,and 1955), the runoff period is often too brief for theestuary to adjust and sediment export is less than wouldoccur in a freshet with similar Qr.

Estuarine Turbidity Maxima

The results show both along-channel and across-channelgradients in sediment resuspension and transport. Estu-arine circulation in the channel produces a localmaximum in up-estuary transport in the channel of thelower ETM (Figs. 7 and 15). The convergence of along-estuary sediment flux could provide a supply of sedimentfor tidal resuspension to maintain the high concentrationsof suspended sediment observed there (Geyer et al. 2001;Traykovski et al. 2004). During low-discharge periods inthe summer, the region of up-estuary transport in thechannel expands northward to upper Haverstraw Bay (55–60 km) where an upper estuary ETM has also beenobserved (Bokuniewicz and Arnold 1984; Figs. 7 and 15).The formation of the upper ETM may be seasonal with thenorthward extension of the salinity field during low flowconditions. The location of an ETM depends not only on aconvergence of sediment flux, but also on a supply of bedmaterial for resuspension (Sanford et al. 2001). Conse-quently, the formation of the upper ETM may lag theexpansion of the salinity field by several spring–neapcycles as the mean currents redistribute the supply oferodible material.

Fig. 14 Cumulative sedimentmass. a Discharge. b Cumula-tive sediment mass in the estu-ary relative to long-termequilibrium with sea level rise.c Spatial distribution of accu-mulation or erosion relative tolong-term equilibrium


Model Uncertainty

Model assumptions and uncertainties can substantiallyinfluence these results, and additional model validation isneeded. Foremost, the results are sensitive to the erosionparameters, yet we lack sufficient spatial or temporal obser-vations of bed erodibility to define the erosion parameters apriori. The long-term equilibrium constraint permits an es-timate of the lateral variability in erodibility that appears tobe consistent with observations, but the approach simplifiesa system with heterogeneous bed composition ranging fromunconsolidated mud to sand, gravel, or shell fragments(Woodruff et al. 2001; Klingbeil and Sommerfield 2005;Nitsche et al. 2007).

To limit the degrees of freedom, we held Uc constant andsearched for C0 that satisfied the equilibrium transportconstraint, but the solution is not unique. We started with aninitial C0 based on observations at a point (Traykovski et al.2004), and then searched for C0 that both allowedequilibrium transport and minimized the difference betweenthe final and the initial C0. Other approaches are plausible,

such as beginning with along-estuary variability in C0 orallowing Uc and C0 to co-vary. Similarly, we incorporated aseasonal scaling factor to represent the increased erodibilityof sediment from winter storm events. An alternativeformulation might be to quantify and track a mobile poolof sediment trapped after discharge events, includingcoupling to the time dependence of erodibility. In general,the bed erosion parameters remain underconstrained andthese results may not be unique or locally optimal.However, the larger scale and longer period patterns ofsediment transport that are our focus are less sensitive tothese uncertainties than are the local near-bottom suspendedsediment concentration.

In addition to erodibility, the sediment fluxes depend onthe suspended load at the estuarine boundaries. The ratingcurves for fluvial sediment load provide a better estimatethan single year of observations, but the observations usedto derive the curves span an order of magnitude for a givenQr (Woodruff 1999). The long-term supply of marinesediment from New York Harbor is poorly documented,and it is likely to vary seasonally with discharge (Hirschberg

Fig. 15 Sediment flux in thelower estuary (16 km), includingfluvial supply (black), estuarinetransport (gray), and the sum forthe net transport (gray squares,bin averaged). Lines show bestfits to the fluvial (cubic polyno-mial) and estuarine (linear)components, and the sum of thetwo for the net transport


et al. 1996; Feng et al. 1999; Woodruff et al. 2001). Storageof sediment in the Harbor and subsequent flux back into thelower estuary may increase the overall residence time in thesystem.

By distinguishing between channel and shoals, themodel incorporates lateral depth variability that affects thealong-estuary sediment fluxes. However, the model doesnot account for lateral circulation that redistributes momen-tum and stratification at tidal timescales and may contributeto sediment trapping in the lower ETM (Geyer et al. 1998;Traykovski et al. 2004). Lateral estuarine dynamics remainpoorly understood, so incorporating lateral flows into thetidally averaged model with low spatial resolution remainsa challenge. Similarly, the sediment flux calculations aresensitive to the vertical structure of the suspended sediment.We have formulated the sediment profile as a function ofsettling velocity that can vary over orders of magnitude inspace and time, but alternative formulations are alsoplausible. Additional observations and robust formulationsfor suspended sediment profiles would improve thepredictive ability of the model.

Simulations would be enhanced by linking the sedimenttransport explicitly with estuarine morphology. Modifica-tions due to dredging or bank erosion can provide asignificant sink or source of sediment independent of sealevel rise or fluvial input (Klingbeil and Sommerfield2005). Historical changes in bathymetry may modifyestuarine and river velocities, and thus the regions ofexpected trapping and deposition. Effects of major shifts inbathymetry such as a cessation of dredging and subsequentinfilling could potentially be addressed with this model, butto completely represent the feedbacks among morphology,sediment transport, and hydrodynamics would requireresolution at tidal timescales.

Despite the limitations, the model results are supportedby correspondence with observations of sediment flux(Geyer et al. 1998; Traykovski et al. 2004) and bottomproperties (Nitsche et al. 2007). The simple modelframework permits simulations over extended periods toquantify long-term patterns and capture episodic events.Once identified by the simple model, the episodic transportevents should be examined in greater detail using 3Dhydrodynamic and sediment transport models. Note thatboth the simple model and a 3D hydrodynamic simulationremain limited by the lack of data to parameterize bedproperties, boundary sediment fluxes, and salinity at theopen boundary (Warner et al. 2005).

Summary

Infrequent, extreme discharge events are critical to the long-term sediment budget in estuaries. Elevated river discharge

enhances down-estuary sediment transport through themean velocity, but the transport capacity depends on thetiming and duration of discharge events. Discharge eventsduring spring tides have greater down-estuary transportbecause of reduced estuarine circulation and sedimenttrapping. Spring freshets when the period of elevateddischarge exceeds the estuarine response time have propor-tionally greater down-estuary transport than isolated storms.

Extreme discharge events also supply large amounts ofsediment to the estuary, and the sediment load has a nearlycubic dependence on discharge. Sediment transport capacityin the estuary is nearly linear with discharge, so thediscrepancy between sediment supply and export leads toperiods of sediment excess or deficit in the estuary. Onaverage, the estuary accumulates sediment during low- andhigh-discharge periods and exports sediment during moderatedischarge periods. The intermittency of droughts and wetperiods determines sediment residence time in the estuary.

Lateral gradients in water depth produce lateral gradientsin estuarine sediment transport capacity, with greater up-estuary transport in the deeper channel due to enhancedbaroclinic circulation. On the shoals sediment transport ispredominantly down-estuary, but lateral gradients in sedi-ment erodibility are required for the net transport to balancethe sediment input from the river. Model calculations basedon an assumption of long-term equilibrium transportindicate that bed erodibility on the shoals must besignificantly greater than in the channel. The model resultsare consistent with observations of sediment flux and bedproperties.

Acknowledgments This research was supported by the HudsonRiver Foundation through grant #005/05A.

Appendix

Near-bottom velocities are less than the surface magnitudesfrom tidal harmonics, so we use coefficients to calculatenear-bottom, tidal maximum velocities:

Uflood ¼ f1 Ut � U0ð Þ þ f2Ue

Uebb ¼ f1 Ut þ U0ð Þ � f2Ue

ðA1Þ

where f1 modifies the parabolic velocity magnitudes and f2modifies the cubic velocity. We fit the coefficients based onvelocity data from the Hudson, comparing model resultswith observations. The velocity profiles depend on frac-tional depth z=H ¼ 0;�1f gð Þ, so we define “near-bottom”as a distance above the bed equal to 20% of the water depthz=H ¼ �0:8ð Þ.To calculate f1, we add Eq. A1 such that 1

2 UfloodþðUebbÞ ¼ f1Ut. Plotting the sum of observed flood and ebb


Fig. 16 a Schematic descriptionof ebb (f1(Ut+U0)−f2Ue) andflood (f1(Ut−U0)−f2Ue) velocityprofiles based on polynomialshape functions. b Near-bottomvelocities at four stations during2004, plotting 1/2(Uebb+Uflood)|O against Ut|M, where“O” indicates observations and“M” indicates model results; theslope is the factor modifyingparabolic velocity profile, f1.c Near-bottom velocities at fourstations during 2004, plotting1/2[2f1U0|M−(Uebb−Uflood)|O]against Ut|M; slope is factormodifying cubic velocityprofile, f2. f2 is different foreach station depending oncross-section shape, as shownin Fig. 17

Fig. 17 Estuarine velocityfactor (f2) as a function ofcross-section shape. Ab isnear-bottom area (flow areabelow H/2) and As is near-surface area (above H/2). Thevalues of f2 are from linearregressions at locations alongthe Hudson as shown in Fig. 16.Solid squares are observationsin the thalweg, while opendiamonds are from stations onshoals. Dots connected by linesare predicted f2 on the shoalsbased on Ab/As and the depthrelative to the thalweg. Top threepanels show cross-sectionsspanning a range of Ab/As.Reference line is the best fitused to define f2 basedon Ab/As (Eq. A2) to calculatenear-bottom velocities in themodel (Eq. A1). Verticaldashed lines indicate rangeof Ab/As in the Hudson


near-bottom velocities against Ut we find the slope f1. In theobservations f1 was about 0.7, to within about 10%(Fig. 16). To account for lateral shear in the tidal velocity,we assume the cross-channel structure of tidal velocity isproportional to the square root of the local depth:UtðyÞ ¼ Uth i h1=2 hh i

h3=2h i , where h is the local depth and bracketsrepresent cross-section averages (Smith 1983).

We estimate f2 by subtracting Eq. A1 so that 12 Uflood�ðð

UebbÞ þ 2f1U0Þ ¼ f2Ue. Again, the slope of 12 Uflood�ðð

UebbÞ þ 2f1U0Þ versus Ue (using observed Uflood and Uebb

and modeled U0 and Ue) is fit to find f2. We find that f2varies spatially depending both on cross-sectional shapeand the local water depth relative to the thalweg. Cross-sections that have a narrow, deep channel and broad,shallow shoals have higher f2 values in the thalweg thancross-sections with relatively uniform depth. We quantifythis by plotting f2 as a function of the ratio of near-bottomcross-sectional area (flow area below H/2, where H is thethalweg depth) to near-surface cross-sectional area (flowarea above H/2; Fig. 17). The ratio Ab/As has a maximum of1 for a rectangular channel, but in the Hudson the ratioranges between 0.82 (for a laterally uniform region near theBattery) and 0.17 (for a narrow, deep channel with broadshoals, as in the Tappan Zee). The f2 for calculating near-bottom velocities is based on a linear fit of the observed f2(found from regression fits as in Fig. 16c) to the ratio Ab/As:

f2 ¼ �0:89 Ab=Asþ 0:97; ðA2Þ

yielding a range of f2 from 0.24 to 0.82. Conceptually, theup-estuary volume flux due to estuarine circulation (∼UeAb)should balance the down-estuary volume flux (UeAs). Themagnitude of Ue depends on the thalweg depth, so in cross-sections with narrow, deep channels (small Ab/As), mea-sured velocities near the bed will be greater than in laterallyuniform channels with equivalent Ue. To project theestuarine velocity profile onto the shoals, we use thevelocity in the thalweg (including the direction of flow)that corresponds with the near-bottom depth on the shoals.We compared f2 on the shoals predicted from the lateralprojection of Eq. A2 against f2 from regression fits ofobservations (as in Fig. 16c) and found good agreement inthe six available cases (Fig. 17).

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