Particle Trapping in Stratified Estuaries -- Definition of a Parameter Space

Transcription

1 Particle Trapping in Stratified Estuaries -- Definition of a Parameter Space by David A. Jay Philip M. Orton Douglas J. Wilson Annika M. V. Fain John McGinity Department of Environmental Science and Engineering Oregon Graduate Institute NW Walker Rd. Beaverton, OR USA Submitted to Continental Shelf Research

2 Abstract Estuarine turbidity maxima (ETM) retain suspended particulate matter (SPM) through advection. Yet, there is no conceptual framework to explain this process across the broad range of estuaries with ETM. This contribution provides such a framework through a scaling analysis of the local and integral SPM balances that defines a parameter space descriptive of ETM particle trapping. There are five parameters in the problem for the large particles or aggregates that are typically trapped: supply number S R (defining a non-dimensional river flow), trapping potential T p (defining the shear fluxes that carry SPM landward), trapping efficiency E (quantifying the efficiency with which particles are accumulated), advection number A (quantifying for large particles the strength of horizontal advection in the local SPM balance), and Rouse number P (specifying the settling velocity of the trapped SPM relative to ambient bedstress). In order to test the theory developed here, observations must be available that cover a considerable dynamic range (in terms of the parameters defined) and time scales from at least tidal to seasonal. This study uses new observations from two advection-dominated systems (the Columbia and Fraser Rivers) plus literature values from several other estuaries to illustrate the applicability of the above scaling. The primary question investigated is the variation of trapping efficiency E with river flow (expressed in terms of supply number S R ). The most effective particle retention (maximal E) occurs in the Columbia at intermediate values of S R. The extreme high flows observed in the Fraser River estuary show how ETM trapping becomes ineffective as the estuary length contracts to one tidal excursion. The low-flow response of E may, however, be system dependent. Although E decreases at low river flow (low S R ) levels in the Columbia, estuaries with longer SPM residence times may not export SPM rapidly enough for E to drop significantly 2

3 during low-flow periods. Finally, the very high flows in the Fraser also provide an analog to conditions in the Columbia before flow regulation and diversion. Scope and Challenge Concentration of suspended particulate matter in estuarine turbidity maxima (ETM) is a ubiquitous phenomenon. ETM also play a vital role in secondary production in many estuarine ecosystems (Simenstad, et al., 1995). Despite pioneering numerical studies by Festa and Hansen (1978) and Dyer and Evans (1989) there is no comprehensive theory defining how estuarine turbidity maximum (ETM) processes vary with river flow or tidal forcing. There is not even a conventional set of parameters (a parameter space) to describe particle trapping and retention by horizontal advection. Most analyses of SPM dynamics have, moreover, focused on laterally uniform environments where advection is irrelevant or non-existent. While this approach has allowed a focus on the vital issues of erosion, particle settling and deposition, the existence of an ETM implies horizontal SPM advection -- there must be landward SPM transport against a mean gradient (Jay and Musiak, 1994). Thus, understanding how estuaries retain SPM requires: a) an appropriate theoretical framework, and b) observations over a substantial part of the parameter space defined by the theory. The primary focus of this paper is conceptual. A scaling analysis of the local and integral SPM conservation equations is employed to define a five-parameter space that serves as a theoretical framework in which observations may be interpreted. Testing this parameter space requires use of data sets that are broad in terms of the ETM trapping processes encompassed. SPM concentration and transport vary, moreover, on a range of time scales from intra-tidal to interan- 3

4 nual. Understanding the role of turbidity maxima in one estuarine ecosystem would require observation of the entire annual cycle of ETM processes, probably several times. Instead, this study uses recent observations in two advection-dominated systems (the Columbia and Fraser River estuaries) and literature data from less strongly forced systems as a means to understand the particle trapping parameter space defined. The Columbia and Fraser systems both exhibit a highly stratified, salt wedge state during high-flow periods (despite strong tidal currents), yet there are significant differences in their ETM and ecosystems that are clarified using the parameter space defined here. Comparison of these two systems also has a historical aspect the Fraser is an analog to the Columbia, before the latter was tamed by flow regulation and diversion. Observations during a major freshet in the Fraser provide, therefore, insight into the historic sediment transport regime of the Columbia. One example of the utility of the conceptual framework is presented here. It involves the potentially contradictory influence of river flow strong buoyancy input may intensify stratification and upstream bottom flow, but also shortens the estuary, reducing the volume in which particles may be trapped. Results for the Columbia suggest that intermediate values of river flow provide maximal trapping, at least in systems with a residence time short relative to the seasonal time scale of river flow and SPM input. In systems with longer SPM residence times, decreased flow and sediment supply manifest themselves through an increase in trapping efficiency as flow decreases. The Weser, Elbe, and Hudson River estuaries Bay provide examples of systems with weak advection and long residence times. Resolving the challenges described above requires: a) a description of the Columbia and Fraser estuaries, b) a definition of instrumental and data analysis methods employed, c) a scaling 4

5 analysis of the SPM conservation (the heart of the paper), and d) a test of the utility of the parameters defined. Setting The longest available data set is for the Columbia River estuary. The Columbia River is the largest on the Pacific Coast of North America, with a mean flow of ~7,300 m 3 s -1. This considerable river flow enters an estuary that has both topographically constrained reaches and large tidal flats. The tide is mixed diurnal and semidiurnal; the greater diurnal tidal range is ~2-4 m The result is very strong barotropic and internal circulation at tidal and subtidal frequencies. The salinity and SPM transport regimes of the Columbia River Estuary (Figure 1a) are characterized by (Jay and Smith, 1990a,b,c; Jay and Musiak, 1994): a) strong horizontal density gradients, b) a range of estuarine conditions from partially mixed to highly stratified, c) two primary ETM, one each in the North and South channels, and d) compact ETM that are strongly affected by advection. Aggregates dominate the fastest settling velocity (W s ) class in the Columbia. The Columbia River Estuary Land-Margin Ecosystem Research (CRE-LMER) Program provides extensive vessel observations regarding ETM phenomena in an environment suitable for understanding ETM processes over the period (Simenstad et al., 1995; cretmweb/cretm. html). These data have been augmented by moored SonTek acoustic Doppler profiler (ADP) records provided by the CORIE program (Baptista et al., 1998; The Fraser River estuary (Figure 1b) provides even starker conditions than the Columbia, because its ratio of river flow to tidal prism is larger, and its topography simpler. The Fraser 5

6 broadens the available range of observations and serves as an analog to historic conditions in the Columbia. In the Fraser: a) salt-wedge salinity intrusion is persistent (Geyer and Farmer, 1989), b) bedstresses are high, c) a compact ETM is strongly affected by advection (Kostachuk et al., 1989), and d) aggregate concentrations are low (at least during the sampling period considered here). Like the Columbia, the Fraser has a mixed tide with greater diurnal range up to ~4 m, but the ratio of diurnal to semidiurnal forcing is larger in the Fraser. Geometric simplicity is a vital characteristic for simplifying dynamics. Both the Columbia and Fraser are highly channelized, with channel widths that are only O(50%) of their internal Rossby radius R f. Thus, lateral processes are less important than in other systems with a channel width closer to R f (e.g., the Hudson River, Geyer et al., 1997). Because it has only a single narrow channel constrained by a jetty, the Fraser approximates a two-dimensional (2-D) ideal more closely than the Columbia. The Columbia River estuary moored data were collected during 1997, a La Niña year with the strongest spring freshet since 1974 and the largest total flow of any year of the 20 th Century. Four CORIE moored ADPs provide velocity and backscatter data from May to December 1997, encompassing both the freshet and low-flow seasons. There were three 15-day LMER cruises to provide calibration data. Although large by contemporary standards, peak flows during the 1997 spring freshet were much smaller than they would have been without flow regulation and irrigation diversion (~16,000 m 3 s -1 instead of >25,000 m 3 s -1 ). LMER carried out vessel observations in the Fraser River in 1999 during one of the largest freshets in the last 50 years (peak flows >11,000 m 3 s -1 ). The mean annual flow of the Fraser River (2720 m 3 s -1 ) is only 36% of that for the Columbia (7,300 m 3 s -1 ). Thus, the 1999 observed 6

7 flows in the Fraser were, relative to the long-term mean, almost twice those in the Columbia, and this fact is reflected in the observations presented below. Extreme flow conditions such as those observed in the Fraser in 1999 have not occurred in the Columbia since Such flows did occur with some regularity, however, before construction of 28 major dams for flood control, irrigation and power generation (Simenstad, et al., 1992). In contrast, there is only one major dam in the Fraser River drainage; it diverts about 3% of the flow (Church and McLean, 1992). River flow time series for both systems and hindcast sediment input for the Columbia are shown in Figure 2a,b. Instrumentation and Methods Conventional measurements of SPM concentration and particle size spectra are labor intensive and not readily automated. Determination of SPM properties from acoustic backscatter (ABS) provides an attractive alternative, if sufficient calibration data are available. A singlesensor inverse analysis approach is used here to separate settling velocity (W s ) classes in the SPM profiles obtained from the moored ADPs in the Columbia River estuary. A moored ADP provides a time series of gated ABS profiles. Optimum use of this information requires that the ABS profiles from a single acoustic beam be converted (after correction for beam spreading, absorption and non-linear transducer effects) to profiles of SPM concentration for a small number of SPM classes, using appropriate calibration and verification data. An inverse method is used to accomplish this task, taking advantage of dynamical information present in observed SPM vertical profiles. Backscatter data is first converted to concentration data using a bulk calibration from pumped water samples. Then, a small number of theoretical pro- 7

8 files ( basis functions ) are defined for each sampling time, each corresponding to a size or W s - classes assumed to be present. The contribution of each basis function to each observed profile is determined by an inverse analysis (a non-negative least-squares or NNLS). Results depend, therefore, on the assumed SPM dynamic balance used to form the basis functions. Previous analyses (e.g., Lynch and Agrawal, 1991; Lee and Haines, 1995, Orton and Kineke, 2001) have used a balance in the vertical between turbulent SPM flux and particle settling. A modified Rouse balance approach is used here that improves upon most previous single-sensor analyses in two respects (Fain, 2000; Fain et al., 2001). First, the presence of aggregates of unknown density means that scattering behavior and W s are not known functions of particle size. This analysis has been formulated, therefore, around W s, not size classes. Second, the NNLS inverse technique used is sensitive to mismatch between the assumed and actual W s -spectra. Thus, observed W s - spectra, obtained from extensive LMER Owen tube sampling (Reed and Donovan, 1995), have been employed to guide the inverse analysis. Three 1997 cruises in the Columbia provide calibration data. Calibration and verification of the single-frequency inverse analysis have been described in Fain (2000) and Fain et al. (2001). Owen tube results suggested four W s -classes (C 1 = mms -1, C 2 = 0.3 mms -1, C 3 = 2 mms -1, and C 4 = 14 mms -1 ) as descriptive of the SPM present in the system. Gravimetric samples defined a bulk ABS vs. OBS calibration for LMER cruise periods. OBS profiles collected near each of the four ADP moorings were used to provide a bulk ABS vs. OBS calibration, which was then converted to an ABS vs. bulk SPM calibration using OBS profiles collected as close as possible to the ADP moorings. Verification of the inverse analysis results was carried out through comparison between calculated (inverse analysis) W s - spectra for each ADP and the observed (Owen tube) W s -spectra at the nearest vessel station. 8

9 This single-sensor inverse approach is relatively simple and can readily be applied to moored instrument records. It has, however, two weaknesses: a) it neglects horizontal advection of SPM in structuring the vertical SPM distribution, and b) a bulk SPM calibration is employed, whereas ABS strength may depend significantly on particle size under conditions where a broad range of particles are present. The advection problem is dealt with after the fact by identifying times when advection may distort SPM profiles. We have used the single-sensor inverse approach in the Columbia, where the particle field sampled by the moored ADPs (which starts 2 m off the bed) contains primarily aggregates not sand. Comparison of inverse analysis and Owen settling tube results suggest that the aggregates do not scatter an acoustic signal as strongly as sand grains with similar W s values, so that the single-sensor inverse analysis works quite well in the Columbia (Fain, 2000). The limited Fraser River data presented below were obtained according to methods described in Orton et al. (2001). As with Columbia SPM data, backscatter data are first converted to concentration data using a bulk calibration. Then, a multiple-sensor inverse method is used, with two stages. The first stage consists of separate inverse analyses of optical backscatter (OBS) and ABS, by the method outlined in the previous paragraphs. The second stage uses conservation of mass to define response coefficients for each W s -class and instrument. These provide, in effect, a size dependent calibration of the backscatter signals, removing the sensitivity of the inverse approach to particle size. Definition of a Parameter Space for Estuarine SPM dynamics A scaling analysis of the local and integral (time and space averaged) SPM conservation equations provides insight into the parameters governing particle trapping and the role of advec- 9

10 tion in an ETM; it is the basis of the data analyses discussed below. First, we define the parameters governing particle trapping, and then show how they emerge from the scaling analysis. The parameters are: The Rouse number P = W s /ku ; P is familiar as the ratio of particle settling (W s ) to vertical diffusion, represented by the product of von Karman s constant k = 0.41 with the shear velocity U. The Advection number A = P H m /H; A represents the effect of horizontal shear advection in lifting the maximum SPM concentration up from the bed; H is mean depth, and H m = is the elevation of the height off the bed of maximum SPM concentration during advective episodes. A is a non-dimensional form of H m /U, first used by Lynch et al. (1991) as an indicator of advection. The Flux number F V = E T P H m /H, where the Trapping Potential T P = U/kU (the ratio of the near-bed shear scale ( U) to vertical mixing) represents the ability of the flow to trap particulates via shear advection, independent of the properties of the SPM present. We will focus on T P not F V, because T P is less redundant with A and E. The Supply number S R = A U R /(ϖh); S R is A times the ratio of river flow (U R ) to the product of mean depth H times the frequency of subtidal processes in the system ϖ; ϖ is defined here by the neap-spring time scale. The trapping efficiency, E = C E /C R ; E is defined as the ratio of maximum estuarine ETM concentration (C E ) of large particles to a fluvial source concentration (C R ) of cohesive particles supplied to the ETM. E is an integral measure of the ability of the system to retain SPM. 10

11 The analysis that follows considers the SPM balance in a channel that is vertically stratified but laterally uniform, a good approximation in advection dominated systems like the Fraser and the Columbia. Under the assumption of lateral uniformity and neglecting horizontal turbulent mixing, the local dimensional SPM conservation equation may be written: C j t C j + u x C j + w = W z sj C j z + K z s C j z + k j ( C ) γ f (1) k where: primed variables are dimensional, C j is concentration of the j th settling class; t is time; z is height above bed; u and v are horizontal velocities; w is vertical velocity; K s is vertical sediment diffusivity; W sj is settling velocity of the j th settling class; γ is a source/sink rate constant for aggregation; and x is the horizontal coordinate. If the vertical velocity w << W s, the nondimensional SPM concentration C j (x,z,t) for W s -class j is governed by the conservation equation: C 2 j m t C j + ΠU x C j = P z C + K z z + Γ f k ( C ) (2) where: non-dimensional variables are without primes, K(z) is a non-dimensional vertical SPM j k diffusivity, U(x,z,t) is horizontal velocity, Π = U T /(ku )H/L x scales advection, m 2 = ωh 2 /K 0 scales time variation, P =W s H/K 0 is a ratio of settling to vertical mixing, Γ = γh/(ku ) scales source/ sink behavior, U T is estuarine tidal velocity, L x is an SPM horizontal scale length, ω = s -1 is tidal frequency, and K 0 = ku H scales vertical diffusivity. Boundary conditions for (2) are: a) no vertical flux at the free surface, and b) the net vertical flux at the bed is time-averaged erosion minus deposition. Eq (2) suggests that the 2-D (x and z) SPM balance is governed by the Rouse number P and three other non-dimensional numbers, m 2, Π and Γ. Time variation scales as m 2 which may 11

12 alternatively be considered a non-dimensional depth (Ianniello, 1977); m 2 is typically small (~0.1) in the present context and will not been considered further. The most familiar parameter in (2) is Rouse number P. P for the large aggregates that predominate in the Columbia estuary ETM typically varies between ~1 and 15. Horizontal SPM advection, described by Π =U T (H/L x )/(ku ), depends inversely on length scale L x, but L x is not a priori known. An upper limit on L x for fines is the tidal excursion length L T, under the assumption that the particles suspended from a source region are too small to settle back to the bed. Then Π = U T /(ku ) H/L T ~ T P H/L T (for the typical case where U ~ U T ). In this case, Π is a function of the flow only. A lower limit on L x is the horizontal distance over which a particle, once suspended, settles without mixing a distance H m ; then Π =A =P H m /H, a measure appropriate for large particles. Thus, the actual L x is between an outer advection limit controlled by T P and an inner settling limit set by A. Fine material is not concentrated in the ETM, and T P H/L T is quite small (~0.05). Because it describes the behavior of large particles, A is more relevant than T P in the present context, though T P will appear again in a different context. Because scaling only sets limits, the actual value of L x must be an output of a theoretical analysis not an input. It is worth mentioning the analogy between L x for an ETM and the length scale for salinity intrusion L s. L s is set such that the total amount of salt is conserved (Hansen and Rattray, 1965; and Jay and Smith, 1990c). One of the most important factors to determine about the ETM is the effectiveness with which it traps particles; i.e., the dependence of trapping potential E on external parameters. The definition of E stems from integral mass conservation. Its definition requires that (1) be inte- 12

13 grated over the volume of the ETM and averaged over tidal time scales. The resulting 2-D (in x and z) spatially integrated, subtidal equation in non-dimensional form is (Jay and Musiak, 1994): E t x2 x1 BH FV c2h B [ ] { C } dx = S c Q { C } j x 1 n x2 x2 { U }{ C } + { U C } + Γ B f ( C ) dx + ε { e }dx Vj Vj R 1 m= 1 R Vjm j Vjm x1 x2 + x2 x1 k j k x1 j (3) where: brackets < > indicate a vertical average, curly brackets { } indicates a tidal average, a subscript V indicates a vertical deviation from a vertical average, B is width, Q R is river flow volume, ε scales net (non-tidal) erosion/deposition e, Γ is a non-dimensional number for aggregation, the flux summation is over m = 1,n tidal frequencies (including overtides), x 1 and x 2 are seaward and landward boundaries of the ETM (respectively), velocity shear has been scaled by U, c 1 = kc ½ D, c 2 = c 1 W s /(ϖh), C D is the drag coefficient, and C ½ D U T = U. Eq. (3) makes use of a key simplification described by (Middleton and Loder, 1989) that expresses the scalar transport by waves (tides in this case) in terms of a Stokes drift transport of the mean scalar field. Lateral flux variations have been suppressed here for simplicity, but could be included if necessary, as per Jay et al. (1997). Eq. (3) says that the subtidal variations in the total inventory of SPM (on the left-hand side) are controlled by fluxes in and out of the ETM at its ends (x 1 and x 2 ), and net changes due to aggregation and erosion/deposition within the ETM. Assume for the moment that the inventory is constant, so the left-hand side of (3) vanishes. It is also convenient to set the boundaries of the ETM (x 1 and x 2 ) such that <{C}> x1 = <{C}> x2. Then the river flow provides the buoyancy that creates shear and inhibits vertical mixing, and supplies material to be trapped. It is not, however, directly involved in particle trapping because it removes as much material (at x 1 ) as it sup- 13

14 plies (at x 2 ). The actual trapping of particles in an ETM is brought about by convergent shear fluxes within the ETM (between x 1 and x 2 ), that is, by spatial correlations between SPM stratification and velocity shear at all tidal and sub-tidal frequencies (Jay and Musiak, 1994). Since SPM is concentrated near the bed, flow processes that cause landward flow near the bed will be effective in trapping SPM. Relevant processes include gravitational circulation, the salt wedge advance, and internal tidal asymmetry (Jay and Musiak, 1996; Burchard and Baumert, 1998). The analysis of the previous paragraph does not explain what processes determine the location of the middle of an ETM. Another choice of x 1 and x 2 clarifies this point, still under the assumption that the inventory is constant in time. Let both x 1 and x 2 be initially located on the seaward side of the ETM in an area where SPM concentrations and transports are small. Leaving the seaward boundary (x 1 ) fixed, consider a series of cases where the landward boundary (x 2 ) is positioned successively more landward, closer to the middle of the ETM (i.e., toward the point where {<C>} is maximal). <{C}> x2 increases, by definition, along this trajectory. The seaward transport by river flow at the landward boundary (Q R <{C}> x2) also increases, because Q R is spatially uniform. Clearly, the landward transport by the shear fluxes must also increase at x 2 to balance this seaward flux, if the inventory is to remain constant for all these choices of ETM boundaries. As x 2 is positioned at and then landward of the midpoint of the ETM, <{C}> x2 reaches a maximum and begin to decrease again. Clearly, the shear fluxes must have also have a maximum landward transport in mid-etm. The mid-etm position is then controlled by spatial gradients in the horizontal shear fluxes that produce landward SPM transport. An obvious location for a maximum in the landward horizontal transport of SPM is near the head of salinity intrusion. This is because internal tidal asymmetry and gravitational circulation are both present in the saline water mass, but drop abruptly to zero in the tidal freshwater part of the system. In fact, 14

15 internal tidal asymmetry may have a maximum near the head of salinity intrusion, because tidal variations in stratification are maximal there the water column alternates tidally between quite stratified (when salt is present) and neutrally stratified (when salt is absent). Lateral flux mechanisms may set the ETM position in some systems, but analyzing such fluxes would require a three-dimensional (3-D) conceptual framework more complex than (3). The 2-D framework explored here provides insights valid in many systems and has a workable number of nondimensional numbers. There are five non-dimensional parameters in (3): Trapping Efficiency E, Supply number S R = A U R /(ϖh), Flux number F V = T P E H m /H, ε and Γ. Our analysis will focus, for simplicity, on three of these: E, S R and F V (in the form of T P ), along with the two numbers derived from local SPM conservation, A and P. Neglect of cycles of deposition and erosion (represented by ε) in this study is based the character of the bed in the ETM in both systems. At spring tides, almost all fines are removed, leaving a bed that is ~99% sand. Thus, there is no deposition or erosion of fine material within the ETM from one spring tide to the next, though deposition on neaps followed by erosion on springs does occur. Finally, inclusion of aggregation effects (Γ ) would be speculative for the systems considered here. Although aggregation is biologically significant in the Columbia (Crump et al., 1998), its dynamical importance for the SPM balance is unclear. Cycles of aggregation and disaggregation are dynamically important for systems with high concentrations of organic material (Partheneides, 1993; van Leussen, 1996), but observations in systems more similar to the Columbia and Fraser do not suggest dominant aggregation effects (Schubel et al., 1978, Kranck et al., 1993). Due to very low levels of biological activity, Γ was likely not important in the Fraser in

16 In summary, the balance of settling vs. vertical mixing is described by P. Advection is described by two parameters, T P and A, that represent the behavior of the flow and large particles, respectively. Fluvial supply of SPM to the ETM is described by S R, and particle trapping by shear fluxes by F V (or T P ). The overall efficiency of a system in trapping and retaining SPM is described by E. Practical use of these parameters for data analysis requires decisions as to how to compute them from the time series of velocity and SPM concentration. This information is given in Appendix A. The analyses that follow assume that the parameters determine the character of the solution; i.e., that the terms scaled by the non-dimensional parameters are O(1). Results Parameter-Space Explorations The May to December of 1997 mooring data set for the Columbia River estuary include both the spring freshet and the lowest flows of the year. This period provides, therefore, a good view of the seasonal trajectory of ETM dynamics, with river flow Q R varying from ~4,000 to 16,000 m 3 s -1 (Fig. 2a). The minimum flow of ~4,000 m 3 s -1 was, however, well above usual levels (2-3,000 m 3 s -1 ) for the fall season. The absence of flows <4,000 m 3 s -1 reflects the exceptionally large snow pack of the previous winter and flow regulation. The moored records also do not cover the highest flows of the year, in early January This is unfortunate, because SPM input in January (and stored in peripheral areas) may have influenced SPM dynamics in the system during the period for which we have records. The results presented here focus on the records for Tansy and Am012. These stations were chosen because they: a) contrast the properties of the two major topographic components of the Columbia River estuary (the North and South Channels), and b) are the two stations most 16

17 often in the ETM. Both the Tansy and Am012 stations have a gap in the backscatter record in late summer-fall due to biofouling; the velocity record was not affected. Unfortunately, the gap in the Am012 record removes much of the dynamic range (in terms of S R ) for some variables. Results from stations AM169 and Red26 are used to illustrate specific points. Intratidal Patterns Subtidal patterns of SPM concentration and transport are the long-term result of intratidal variations, as in (3). Thus, it is important to understand how along-channel velocity and SPM concentration vary over tidal cycles. Tidal currents at all stations in the Columbia are dominantly semidiurnal, with a semidiurnal: diurnal (D 2 :D 1 ) ratio of ~4 at all depths. Substantial terdiurnal (D 3 ) and quarterdiurnal (D 4 ) currents with strong phase variations with depth are indicative of internal asymmetry. Figure 3 show near-bed amplitude scaleograms of SPM variability for Tansy, Am012 and Red26 for SPM concentration at all stations is more non-stationary than the velocity field. Neap-spring SPM variations are also strong at all stations, reflecting the loss of sediment on each strong spring tide. Am012, consistently in the North Channel ETM, shows dominantly D 4 SPM variability, representing resuspension on each flood and ebb. At the other extreme, Red26, a station that is never in the center of the South Channel ETM, shows predominantly D 2 SPM variability, though with substantial D 1, D 3 and D 4 as well. The strong D 2 SPM variability represents two processes: a) tidal advection of SPM from the ETM or the estuary entrance, and b) preferential flood or ebb resuspension related to tidal variability in the density field (internal asymmetry). Tansy presents an intermediate case D 4 SPM variability predominates early in the season when Tansy is in mid-etm. As the ETM migrates landward after ~d 200, the degree of D 2 variability increases. All stations show D 1 SPM variability during some periods; this is related to the removal of SPM to the sea during a once-daily washout of salt from 17

18 the ETM reach. This interaction of the D 1 and D 2 tides creates a D 1 internal asymmetry bedstresses are usually different on the greater flood than on the greater ebb. All stations show more D 2 variability near the free surface than at the bed, likely indicative of advection of SPM from peripheral bays or the entrance area. Patterns of SPM transport are related to the SPM variability shown in Figure 3; transport by the D 4 tide is substantial at AM012, but is usually small at Tansy (Jay and Musiak, 1994; Fain et al., 2001). Eq. (3) shows how the SPM fluctuations in Figure 3 relate to global SPM conservation and the five non-dimensional numbers defined above. The form of (3) suggests that both mean flow SPM transport and wave fluxes (i.e., spatial correlations between tidal variations in velocity and SPM concentration at the various tidal frequencies) play an important role in ETM particle trapping. Flux calculations for the 1997 data set suggest that: a) net fluxes (tidal plus subtidal) are strongly seaward in both channels during the freshet, especially on spring tides, b) net fluxes later in the summer are seaward in the South Channel and landward in the North Channel, c) removal of SPM is principally by the net outflow, as suggested by (3), d) tidal fluxes (aside from that associated from the D 1 tide) are often landward in both channels, especially after the freshet season, and e) the mixed nature of West Coast tides and the removal of salt from the ETM reach only once per day renders the flux patterns more complex in West Coast estuaries than is the case in areas with dominantly D 2 tides (e.g., Dyer, 1978). Finally, it is likely that small-scale topographic features cause substantial variations in flux mechanisms, both within a cross-section and between nearby cross-sections. Tidal Monthly and Seasonal Patterns The seasonal cycle of SPM concentration is shown in the form of low-passed near bed concentration for each W s class (Fig. 4). Typical for ETM stations, faster settling material made 18

19 up primarily of aggregates (W s classes C 3 + C 4 ) predominates near the bed at both stations, though C 4 also contains some sand on spring tides (Fain, 2000). C 4 concentrations are uniformly larger than those for C 3 at Tansy, but there is more C 3 than C 4 at Am012 during part of the freshet. Near-surface concentrations are dominated by medium silt (C 2 ), and C 4 is almost absent near the surface, because of its rapid settling. Material that is washload in estuarine channels (C 1 ) is relatively uniform throughout the system, whereas C 2 shows more spatial variability. Another important feature is the seasonal pattern of trapping efficiency E (Fig. 5). As expected from the elevated concentrations there, E is considerably higher in the North Channel (station Am012) than in the South Channel (Tansy and Am169). Am169 is also shown in Figure 5 because it is the only station that was not affected by biofouling in the late summer-fall. Vessel sampling results suggest that SPM concentrations at Am169 are somewhat higher than those at Tansy, primarily because Tansy is on the edge of the South Channel, not in the deepest part of the cross-section. The other stations are all in relatively deep parts of their channel crosssections. Figure 5 shows that E was low at all stations during the freshet and increased at Am012 and Tansy to a maximum in November, at the onset of seasonal storms. There was an earlier maximum in E at Am169 (ca. d 260), a station that is probably less influenced by peripheral bays than Am012 and Tansy. The Material Trapped in an ETM One of the most basic questions about an ETM is the identity of the material trapped, given ambient bedstresses. Jay et al. (2000) argued that the material trapped in an ETM must have an intermediate value of Rouse number P. If the material settles to rapidly (large P), it will travel, if at all, only as bedload (the bedload limit limit). Material that settles too slowly (the 19

20 washload limit of small P) cannot be trapped at all, because its distribution is almost vertically uniform the shear fluxes in (3) vanish (C V 0 for washload). Furthermore, systems that are too deep (e.g., fjords) will not exhibit an ETM and will accumulate cohesive materials more or less permanently on the bed. Systems too shallow to sustain significant stratification (e.g., some embayments) cannot develop the vertical shear to trap SPM by the mechanisms considered here. However, they may still accumulate SPM by lateral mechanisms. This analysis focuses on P for W s -class C 4 (P 4 ), because this W s -class consists primarily of large aggregates that make up the bulk of the material in the ETM. Fain et al. (2001) found that the tidal-cycle minimum P 4 (i.e., P 4 at the time of maximum bedstress) typically varied over only a narrow range, 0.9 P 2. An exception was for the weakest neap tides, when P was observed to be as large as 3. This is consistent with fact that when P > ~2, bedload sediment transport predominates. Material travelling as bedload cannot be observed with acoustic data beginning 2-3 m off the bed. Nor are the sands that travel as bedload relevant to the ETM ecosystem. We argue that the aggregates formed in the system adjust to the hydrodynamic so that they can be both retained and cycled into the water column. It appears that the aggregate size distribution represents a dynamic equilibrium defined by continual aggregation and disaggregation (Kranck et al., 1993). Under the high bedstress conditions typical of the Columbia, the limiting aggregate size is related to the Komolgorov scale (Berhane et al., 1997), which decreases slowly with the energy level of the system. Particle density is, however, also variable and, given the small relative density of aggregates, more likely to control aggregate behavior than the limiting aggregate size. Thus, particle properties can adjust to the flow; but a biogeochemical impact on particle density is also implied. If, moreover, the aggregate distribution did not adjust to favor particles 20

21 that could be retained, loss of smaller particles would imply a continual leakage of material, perhaps preventing formation of an ETM at all. Fain et al. (2001) did not tabulate separately the flood and ebb values of P, leaving ambiguous the issue of whether the maximum stress values favored flood or ebb transport. The record at Tansy (Fig. 6a) is striking for the disparity between P f (P on flood) and P e (P on ebb) during the freshet season and summer (up to ~d 230), with the greatest stress (P small) always occurring on ebb. Accordingly, Fain et al. noted persistent near bed SPM export at Tansy during the spring freshet (~d 180). Two features are evident after d 180: a) a gradual increase of P (a response to the sum of tidal and fluvial forcing), and b) a change in the ratio of P f and P e, particularly on spring tides. As the season progresses, bedstresses on flood become more comparable to those on ebb. This is accompanied by a trend toward net landward SPM transport, at both the surface and the bed. Minimum P f and P e values on spring tides at Am012 are quite similar (~ ) to those at Tansy (Fig. 6b). P f, however, never exceeds about 1.8 on the neaps, whereas P e is sometimes >12. This suggests that the North Channel is a more favorable environment than Tansy for retention of SPM. Consistent with this idea, Fain et al. (2001) found that: Mean SPM concentrations were higher at Am012 than at Tansy by about a factor of two (as in Fig. 4), despite the fact that the supply of SPM to the North Channel is indirect, via the South Channel rather than directly from the river. A residence time index R T suggested sediment retention times for the North Channel up to 60 d, whereas R T was <20-30 d for the South Channel. 21

22 Although SPM export occurred at Am012 on spring tides during the freshet (as at Tansy), the transport patterns at the two stations diverged after the freshet. There was a strong landward transport near the bed at AM012 after d 200, much stronger than at Tansy. The asymmetry in bedstress shown in Figure 6b in part explains the lack of export at Am012, which in turn explains the greater R T and SPM concentration values at that station, relative to Tansy. Global SPM Conservation E, S R, T P, and A The substantial residence time for sediment in an ETM suggests that analyses of E as a function of the other parameters of the integral SPM conservation equation should be carried out on a seasonal basis; i.e., by averaging over tidal monthly variability. Advection number A, trapping efficiency E, supply number S R and trapping potential T P were, therefore, low-passed to remove tidal monthly variability. It was also found useful to form flood-ebb ratios for A and T P. There is at Tansy a clear increase of flood-ebb A ratio with supply number S R (Fig. 7). This monotonic increase in A with S R does not translate, however, into an increase in trapping efficiency E with A (Fig. 8); i.e., E exhibits a maximum at an intermediate value of A. The reason is simple a high value of A indicates that the maximum SPM concentration is well above the bed. SPM concentrations are, however, generally low under the highly stratified neap tide conditions leading to maximal. Trapping potential T P is a better guide to trapping efficiency E increases monotonically with the flood-ebb T P ratio (Fig. 9). This emphasizes the role of flood shear the strongest near-bed flood velocities occur at intermediate river flows. If the river flow is too weak, flood shear is weak because of lack of stratification. If the river flow is too strong, the salt wedge stagnates, as was observed in the Fraser. In either case SPM trapping is poor. 22

23 The tidal-monthly averaged E vs. S R trajectory for Tansy and Am012 is shown in Figure 10 for May to December 1997, along with points for selected tidal cycles for other temperate estuaries. Table 1 provides values for selected tidal cycles for the Columbia, that may be compared directly to those for other stations. The desirability of tidal monthly averaging is emphasized by the considerable variability of S R in the Columbia in Table 1, though other systems may be less variable in this regard. Even after tidal monthly variability has been smoothed, the dependence of E on Supply number S R is non-monotonic in the Columbia (Fig. 10), with the most effective particle trapping occurring at intermediate values of S R (and Q R ). The fact that the most effective particle trapping occurs at moderate values of S R and Q R also emphasizes the ambiguous role of buoyancy forcing. On the one hand, increased river flow sharpens the along-channel salinity gradient that drives both gravitational circulation and internal tidal asymmetry. These internal circulation modes are the primary source of the shear fluxes in (3). On the other hand, increasing Q R shortens the estuary by forcing the salinity intrusion seaward, decreasing the ability of the system to trap particles in at ETM. A point for freshet conditions on the Fraser has been added to Figure 10 to clarify the highflow asymptote of E. It is based on vessel observations (Orton et al., 2001). The high-flow E vs. S R behavior shown by the Fraser is likely fairly universal and has three aspects: Salinity is totally removed from the estuary on each greater ebb, exposing the bed to very high stresses. This prevents the intertidal accumulation of SPM on the bed of an ETM. A very short estuary (only a few km long) allows little settling of fluvial material into the lower, saline layer where landward transport and aggregation into rapidly settling particles is possible. The result is an SPM distribution that is upside down relative to typical estuarine 23

24 conditions -- the highest concentrations are between the free surface and the top of the pycnocline. The surface currents never reverse to a flood condition, so that there is no respite from the near-surface export. This drastically reduces the residence time of particles in the estuary, again preventing settling into the lower layer. The available data for the Columbia River estuary do not represent the low flow asymptote of E vs S R behavior very well, because flows in 1997 were high, even for the Columbia. Low river flow levels should, however, further decrease E in the Columbia by reducing the along-channel salinity gradient and the strength of upstream bottom flow driven by gravitational circulation and internal asymmetry. There is, however, a qualification to this interpretation of the E vs S R relationship. Fain et al. (2001) argued that the observed high values of E at intermediate flow levels were in part related to storage of fines in peripheral bays during the freshet, with subsequent export to the ETM on spring tides after the freshet. Still, the influence of peripheral bays does not appear to be the dominant factor in determining E. The data in Figure 10 show a general increase in E with decreasing S R, perhaps because many less strongly forced estuaries do not export SPM rapidly enough for E to drop significantly during low-flow periods. Still, there are order of magnitude differences between the Hudson (on one hand) and the Weser and Elbe (on the other). These diverse results suggest that the low-flow asymptotic behavior for E may be system-dependent and influenced by factors other than S R. For example, the Hudson estuary receives additional sediment from the seaward end of the estuary, New York Harbor (Feng et al, 1999). Lateral trapping mechanisms also help form shoals along the west side of the estuary (Geyer et al, 1995) that may, like the peripheral bays of the Columbia River estuary, serve as a sediment source during low flow periods. Finally, neap- 24

25 spring variations are also responsible for some of the variation of E in Figure 10, for all estuaries except the Columbia. Long-term data sets will be needed to fully understand the trapping properties of these and other temperate estuaries during low-flow periods. Tropical estuaries may with ETM, moreover, respond in a somewhat different manner. Discussion Observations from several estuaries with different degrees of buoyancy input suggest that ETM dynamics respond to tidal and fluvial forcing in ways that, while not simple, are still explicable. To explain the ETM response to external forcing, five non-dimensional parameters were defined by a scaling analysis of the relevant SPM conservation equations. This approach deserves further testing in the systems considered here, and elsewhere. It is an open question, however, whether the three additional parameters that emerged from the scaling analysis, but were not used here, may be important in some systems. Neglect of m 2 (which scales the tidal rate of change of SPM concentration) is likely a safe choice, given the time scales of interest. Aggregation (represented by Γ) is more problematic. Its influence on the global SPM balance needs to be addressed in systems with less advection and more aggregation than the Fraser and Columbia. Seasonal and longer-term deposition/erosion (represented by ε) may also be important in some systems. Another potential complication not resolved here is the importance to the ETM of two types of lateral processes: a) exchange with shallow peripheral areas (seen in the Columbia), and b) shear fluxes related to lateral variations in velocity and SPM concentration (important in the Hudson and certain other estuaries). The integral balance of (3) is analogous to a box model. 25

26 Fluxes through the bottom boundary (erosion and deposition) are already included. Fluxes through lateral boundaries could be included, if they could be quantified. Similarly, Jay et al. (1997) has shown how fluxes driven by lateral shear could be represented in an equation analogous to (3). This would add additional numbers to both (2) and (3), however, considerably complicating the analysis. The data sets available for the Fraser and Columbia will, however, allow us to evaluate the importance of lateral fluxes and flux variations in future analyses. Finally, it was noted above that comparison of ETM processes in the Columbia and Fraser River estuaries has a historical dimension. Before dredging, flow regulation and flow diversion, the Columbia had bed depths and discharges similar to those now seen in the Fraser. The food web of the Columbia River ETM ecosystem is presently based on microbial processing of detrital input from the river and zooplankton grazing of these particles and microbes (Simenstad et al., 1995; Crump et al., 1998). Yet, zooplankton populations were extremely low in the Fraser during the 1999 freshet (C. A. Simenstad, personal communication). If contemporary Fraser River conditions are indicative of historic Columbia River estuary processes, freshet season secondary productivity in the Columbia was even lower than it is at present. LMER results for the period suggest that low secondary productivity during strong freshets is related to the low residence time of particles and organisms in the ETM. Low freshet-season productivity may, however, be compensated by higher productivity later in the season, apparently based on organic matter stored in the ETM and peripheral bays. There are two additional factors pointing to the historic importance of SPM retention in peripheral areas: The reservoir system has increased the input of fluvial particulate organic detritus because the warm summer temperatures and long residence times of the reservoirs encourage conversion of nutrients to organic matter (Small et al., 1990). 26

27 Macrodetritus supplied by peripheral marshes (about 70% of which have been removed from the marine ecosystem; Sherwood et al., 1990) was more important than at present. Both of these factors suggest that exchange with lateral embayments was historically very important to the food web. Summary and Conclusions This contribution uses new observations from the Fraser and Columbia River estuary, literature data for several other systems, and a scaling analysis to explore the SPM dynamics in estuarine turbidity maxima (ETM). Scaling of the local (2) and time-averaged global (3) SPM conservation equations led to the definition of five primary processes that govern the SPM balance in an estuarine turbidity maximum. Each of these five processes is represented by a nondimensional parameter; these are: a supply number S R, a trapping potential T p (alternatively expressed as a flux number F V ), a trapping efficiency E, an advection number A, and Rouse number P. Three additional processes were neglected as being of secondary importance to the SPM balance in the Columbia and Fraser River estuaries. These processes are: time variability of SPM concentration on tidal time scales, the balance of deposition and erosion from the bed on subtidal time scales, and aggregation vs. disaggregation. The latter two may be of greater importance in systems with less advection than the Fraser and Columbia. Also neglected in the present analysis are lateral variations in along-channel fluxes, and lateral input from peripheral areas. Both processes may be of considerable importance in some estuaries. Moored ADP velocity and backscatter data from two stations in the Columbia River estuary ETM were used to investigate tidal monthly and seasonal variations in SPM dynamics. It was 27

28 found that peak flood values of P (P f ) were maintained within a relatively narrow range for the large aggregates that dominate the ETM, suggesting that the aggregate population adjusts to ambient hydrodynamic forcing in such a way that material can be retained in the estuary. The flood advection number A f increased with P f, confirming the results (Fain et al., 2001) that advection plays a strong role in the SPM balance during highly stratified neap tides, especially under salt wedge conditions. The most highly stratified conditions (those with maximal A) do not, however, lead to the most efficient trapping of SPM, as measured by the trapping efficiency E. E is maximal at intermediate levels of A. In contrast, E did increase monotonically with trapping potential T P, which scales the shear fluxes that transport SPM landward into the ETM. Moreover, the most effective particle retention (maximal E) occurred at intermediate river flow levels in the Columbia (moderate S R ). Observations in the Fraser during a major freshet show that trapping efficiency is minimal for very high flow levels (high S R ), because the estuary is too short to retain SPM. The low river-flow asymptote (low S R ) is more ambiguous. Although E is small for low flow in the Columbia, estuaries with longer SPM residence times may not export SPM from the estuary or ETM rapidly enough for E to drop significantly during low-flow periods. Based on the examples of the Weser, Elbe and Hudson River estuaries, it appears that the low-flow trapping efficiency behavior of estuary may depend on factors other than S R. Acknowledgements This work was supported by the National Science Foundation through: a) the Columbia River estuary Land-Margin Ecosystem Research Program, b) a Small Grant for Exploratory Research (OCE ) and c) a physical oceanography project entitled: Suspended particulate dynamics in advection-dominated environments. Development of inverse analysis methods was 28

29 supported by the Office of Naval Research through grant N and AASERT grant N ; the latter supported the graduate work of Annika Fain. A Murdock Foundation Fellowship supported the participation of John McGinity. We thank Dr. Denise Reed of Louisiana State University for providing Owen tube results and other calibration data for the inverse analysis and Dr. António Baptista of Oregon Graduate Institute for providing the CORIE moored data. Wayne R. (Rocky) Geyer and Dan MacDonald of Woods Hole Oceanographic Institute participated in the Fraser River data collection and have provided helpful discussions of the results. Captain Ray McQuin and First Mate Nikki Hix of the R/V Barnes were extremely helpful during sampling in the Fraser and Columbia. References Baptista A. M., D. A. Jay and others (1998) Towards a multi-purpose forecast system for the Columbia River Estuary. Proceedings of the Marine Technical Society 1998 Conference, Baltimore, Maryland, November Berhane I., T. G. Milligan, K. Kranck K., R. W. Sternberg, G. C. Kineke (1997) The variability of suspended aggregates on the Amazon continental shelf. Continental Shelf Research, 17, Burchard H. and H. Baumert (1998) The formation of estuarine turbidity maxima due to density effects in the salt wedge: A hydrodynamic process study. Journal of Physical Oceanography, 28,

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33 Kostachuk R. A., J. L. Lutenauer, and M. A. Church (1989) Suspended sediment hysteresis in a salt-wedge estuary, Fraser River, Canada. Marine Geology, 87, Kranck K., E. Pettigrew, T. G. Milligan, and I. G. Droppo (1993) In situ particle size distributions resulting from flocculation of suspended sediment. In: Nearshore and Estuarine Cohesive Sediment Transport, A. J. Mehta, editor, AGU, pp Lee H. T. and D. M. Hanes (1995) Direct inversion method to measure the concentration profile of suspended particles using backscattered sound. Journal of Geophysical Research, 100, Lynch J. F. and Y. C. Agrawal (1991) A model-dependent method for inverting vertical profiles of scattering to obtain size spectra in boundary layers. Marine Geology, 99, Lynch J. F., T. F. Gross, B. H. Brumley and R. A. Filyo (1991) Sediment concentration profiling in HEBBLE using a 1-MHz acoustic backscatter system. Marine Geology, 99, Lynch J.F, J.D Irish, C.R. Sherwood, and Y.C. Agrawal (1994) Determining suspended sediment particle size information from acoustical and optical backscatter measurements. Continental Shelf Research, 14, Ma Y., V. K. Varadan, V. V. Varadan, and K. W. Bedford (1983) Multifrequency remote sensing of suspended materials in water. Journal of the Acoustical Society of America, 74, Middleton J. F. and J. W. Loder (1989). Skew fluxes in polarized wave fields. Journal of Physical Oceanography, 19, Naik P. K. and D. A. Jay (2001) Distinguishing human and climate influences on the Columbia River: Part 1: changes in mean flow and sediment transport. To be submitted to Water Resources Research. 33

34 Orton P.M., D.J. Wilson, D.A. Jay, and A.M.V. Fain (2001) High resolution sediment dynamics in salt-wedge estuaries. In: Southwest Washington Coastal Erosion Workshop Report 2000, G. Gelfenbaum, and G. Kaminsky, editors, U.S. Geological Survey, in press. Orton P.M. and G. C. Kineke (2001) Comparing calculated and observed vertical suspended sediment distributions from a Hudson River Estuary turbidity maximum. In press Estuarine, Coastal and Shelf Science. Partheneides E. (1993) Turbulence, flocculation and cohesive sediment dynamics. In: Nearshore and Estuarine Cohesive Sediment Transport, A. J. Mehta, editor, AGU, pp Reed D. J. and J. Donovan (1995) The character and composition of the Columbia River estuarine turbidity maximum. In: Changing Particle Fluxes in Estuaries: Implications from Science to Management, ECSAERF22 Symposium, K. Dyer and R. Orth, editors, Olsen & Olsen Press, Friedensborg. pp Schubel J. R., R. E. Wilson, A. Okubo (1978) Vertical transport of suspended sediment in upper Chesapeake Bay. In: Estuarine Transport Processes, B. J. Kjerfve, editor, University of South Carolina Press, pp Sherwood C. R., D. A. Jay, R. B. Harvey, P. Hamilton and C. A. Simenstad (1990) Historical changes in the Columbia River estuary. Progress in Oceanography, 25, Simenstad C. A., D. A. Jay, and C. R. Sherwood (1992) Impacts of watershed management on land-margin ecosystems: the Columbia River Estuary as a case study. In: New Perspectives for Watershed Management - Balancing Long-term Sustainability with Cumulative Environmental Change, R. Naimen, editor, Springer-Verlag, New York, pp Simenstad C.A., D. Reed, D.A. Jay, F. Prahl, L. Small and J.A. Baross (1995) LMER in the Columbia River Estuary: an interdisciplinary approach to investigating couplings between hy- 34

35 drological, geochemical and ecological processes. In: Changing Particle Fluxes in Estuaries: Implications from Science to Management, K.R. Dyer and R. J. Orth, editors, Olsen and Olsen, Friedensborg, pp Small L. F., C. D. McIntire, K.B. Macdonald, J. R. Lara-Lara, B.E. Frey, M. C. Amspoker and T. Winfield (1990) Primary production, pland and detrital biomass, and particle transport in the Columbia River Estuary. Progress in Oceanography, 25, Thevenot M. and N. C. Kraus (1993) Comparison of acoustical and optical measurements of suspended material in the Chesapeake Bay. Journal of Marine Environmental Engineering, 1, Van Leussen W. (1996) Erosion/sedimentation cycles in the Ems estuary. Advances in Limnology, 47, Appendix A The analyses described in the text rely upon functional definitions of the five nondimensional parameters defined by the scaling of (2) and (3). These variables were calculated for the Columbia and Fraser as follows: Rouse number P = W s /(ku ): P was calculated using the W s value for the most rapid-settling W s -class (C 4 ) in the inverse analysis. U is determined from the velocity (U b ) in the bottom ADP bin as U = C ½ D U b. C D was taken as 10-3, based on the analysis of Giese and Jay (1989), a value typical for stratified estuarine conditions in the Columbia. The U estimate used here is that related to the total bedstress (skin friction plus form drag), as it is the total stress that is related to the SPM distribution in the portion of the water column (elevations > 35

36 2-3 m) sampled here. To understand intertidal variations, a running 7-hr window was used to select the minimum P characteristic of each flood and each ebb. P was then given a sign (positive for flood, negative for ebb). Advection Number A = P H m /H: H is total depth below mean sea level, and H m (the elevation of maximum SPM concentration) was taken from the total SPM profiles. Because the deepest valid ADP bin is typically 2-3 m off the bed, the tabulated H m /H cannot go to zero as it does in reality there is an instrumentally imposed floor. Maximal values of A were tabulated separately for flood (A f ) and ebb (A e ), using a moving 7-hr window. Supply number S R = A f U R /(ϖh): Values of S R were tabulated from daily river flow (U R ) for the station closest to the estuary. US Geological Survey flow data for Beaver, OR, a location about 85 km landward of the mouth of the estuary, were used for the Columbia. Similar values are provided by Environment Canada for the Fraser at Hope. Flood values (A f ) of the Advection number were used in calculating S R. Trapping Potential T P = U/(k U ): U is taken to be the maximum velocity difference between H m and the bed over a moving 7-hr window. T P has the sign of U, and U is taken at the time of the maximum U. Flood and ebb values are tabulated separately (T Pf and T Pe ). Trapping Efficiency E= C Emax /C R : The concentration of trapped material (C Emax ) is the maximum near-bed concentration of the three largest W s -classes (results of the inverse analysis) in a running 13-hr window. This is calculated using brackish water periods only, corresponding to SPM within the salt-wedge. Fluvial source concentration (C R ) was taken as the daily fluvial SPM concentration predicted from river flow (Naik and Jay, 2001), based on

37 data provided by the US Geological Survey (Haushild et al., 1966; These non-dimensional numbers were then low-pass filtered to remove any remaining tidal variability. For the other systems considered, values of S R and E were calculated from the literature to be as similar as possible to those for the Fraser and Columbia. It is also important to note that the numbers were formulated to be as robust as possible against inverse analysis calibration difficulties. Given a W s value for a particular settling velocity class, P is a function of the flow alone. A depends (through H m /H) on SPM properties only through the assumption that total SPM concentration increases monotonically (after all necessary corrections have been made for beam spreading and absorption by water and particulates) with acoustic backscatter. S R and T P do not depend on sediment parameters, aside from the dependence of A on H m /H. E does depend on inverse analysis results. 37

38 Table 1: Trapping Parameters for Selected Estuaries System or station River Flow Tide W s U Q R 10 3 mms -1 mms -1 m 3 s -1 Width km H m /H e C R mg l -1 C Emax E S R mg l -1 Columbia b medium spring (Am012) medium neap high spring high neap Columbia b medium spring (Tansy) medium neap high spring high neap Fraser high neap Weser f low spring 5 h i 250 i high neap 5 h i 200 i Hudson c,d low interm 5 i i 500 i high neap 5 h i 250 i Elbe g low spring 5 h i 200 i high neap 5 h i 400 i b c d e f g h i Unlike Figure 10, values for the Columbia pertain to individual tidal cycles, not tidal monthly averages. Orton and Kineke (2001), the seaward of two distinct ETM, not associated with the head of the salt wedge Geyer (1995) If specific, observed values of H m were not available, a nominal value of 0.25 m was assumed. Grabemann and Krause (1989) Grabemann and Krause (1996) Estimate based on Dyer (1989). Ws-specific SPM data were not available. Total riverine and estuarine concentrations were used to calculate E. 38

39 Latitude Baker Bay Red26 Tansy Youngs Bay Am012 Am169 Grays Bay Cathlamet Bay Longitude 10km N Beaver Figure 1a: Map of CORIE moored ADP stations in the Columbia River Estuary for Red26 and Am169 had 0.5 MHz ADPs, while Tansy and Am012 had 1.5 MHz ADPs. The north and south channel ETM s are depicted by black outlines (modified from Simenstad et al., 1990). Maximum salinity intrusion during the study period probably did not reach the seaward end of Cathlamet Bay. Figure 1b: Vessel stations in the Fraser River estuary. Results shown below stem from bd11 at the mouth of the estuary. Maximum salinity intrusion extended only to about bl11, about 10 km from the mouth. There is only one small peripheral bay, southeast of bl11. There are, however, also extensive tidal flats north of the jetty and south of the channel between bl11 and bd11. 39

40 Figure 2a: River flow (Q R ) at Beaver, and predicted total SPM and sand supply for the Columbia during Figure 2b: River flow (Q R ) for the Fraser River during Also shown (shaded) is the range covered by the mean plus and minus one standard deviation. 40

41 Figure 3: Scaleograms of near bed SPM concentration amplitude calculated by continuous wavelet transform analyses of acoustically determined hourly average total SPM concentration, for (top to bottom) Tansy, AM012 and Red26. Time in d is on the x-axis. Log 2 of frequency (d -1 ) is on the y-axis; equivalent periods range from ~29 d to 3 hr. Biofouling invalidated some data between ~d 240 to 320 at each station. Note the differences in the concentration scales.