A Parameter Space for Particle Trapping – Explorations in Two Estuaries David A. Jay, Philip M. Orton, Douglas J. Wilson, Annika M. V.Fain, Oregon Graduate Institute Daniel McDonald, and Wayne R. Geyer, Woods Hole Oceanographic Institute Research Supported by the National Science Foundation and Office of Naval Research

2 The Challenges -- Define a parameter space for estuarine turbidity maxima (ETM) Invent flexible observational and theoretical methods Understand SPM advection, which is critical to formation of an ETM Investigate potentially contradictory influence of riverflow on particle trapping

3 ETM-Ecological Perspective CRETM-LMER project-

4 Approach -- Use acoustical and optical methods to measure SPM properties by settling velocity (W s ) class Use scaling analysis of SPM equations to bring out the role of advection Understand how intratidal processes condition subtidal patterns Define the tidal monthly and seasonal patterns Use two estuaries (Fraser and Columbia) to increase dynamical range.

5 To Determine SPM from Data -- Single-frequency inverse method (Fain MS Thesis, 2000) for acoustic backscatter (ABS) data from moored ADP data Multiple frequency method for ABS (from vessel ADCP) plus optical (OBS) data

6 Single-Frequency Inverse Methods Define profiles (basis functions) for known W s classes (0.014, 0.3, 2, 14 mms -1 in Columbia) Use non-negative least squares to determine contribution of each basis function to each profile Advantages: works well with aggregates -- does NOT assume a scattering law Disadvantages: doesn’t account for size-variability of ABS or advection effects

7 Stage 1 Inverse Analysis: Calibrate and cor- rect ABS Fit W S classes to ABS profiles via non-negative least squares

8 Multi-Frequency Inverse Methods ABS vs. SPM & OBS vs. SPM calibrations Stage 1 consists of single-frequency analyses for ABS and OBS separately Stage 2 provides an empirical scattering law to calibrate each W s class for each sensor Advantages: works well with aggregates AND with a broad size range of particles Disadvantages: requires more input data, advection effects still problematic

9 Flow Chart -- Two-Stage, Multi-Frequency Inverse Analysis

10 Calibrating the Two-Stage Inverse -- C 1 to C 4, W s = 0.01, 3, 15, 45 mms -1 for Fraser Two-stage inverse recon- ciles OBS and ABS views of ETM OBS responds to all W s classes, ABS C 2 to C 4 only Note that theory and analysis are forced to agree on C 2 in table

11 Scaling Analysis -- Equations: –Local SPM conservation equation in 2-D (x and z), with boundary conditions –Integral SPM conservation over the ETM volume, averaged tidally (Jay and Musiak 1994) Determine the governing parameters Test relevance against data

12 Local SPM Conservation -- Non-Dimensional Parameters: > Rouse Number P = W s /(kU  ) ~ 1-4 (ETM particles) > Time-change m <0.1 (neglect) > Advection number A = P H m /H ~ H m is the height of the SPM max off bed; cf. H m /U  of Lynch et al. (1991) >Aggregation number  (neglect for now)

13 Integral SPM Conservation -- ETM extends from X 1 to X 2, overbar = tidal average, subscript V refers to vertical deviations, subscript R refers to river Tracks subtidal evolution of the SPM inventory on LHS, and supply, fluxes in and out, aggregation and erosion on RHS Non-dimensional numbers -- –Trapping efficiency E = C E /C R >1 ratio of estuarine to fluvial SPM –Supply number S R = const P U R /(  H) is the fluvial SPM input –Shear flux number F V = const E T P where: –Trapping potential T P =  U/(kU  ) is in F V

14 Summary of ETM Parameters: Rouse Number P = W s /(kU  ) Advection number A = P H m /H Trapping efficiency E = C E /C R Supply number S R = P U R /(  H) Trapping potential T P =  U/(kU  ) Not Considered here: lateral exchanges with peripheral areas, aggregation, erosion/deposition Salinity intrusion problem has only two non- dimensional numbers!

15 Overview of Columbia and Fraser River Systems and Analyses --

16 Columbia and Fraser Data -- Columbia: 7-8 mo data from four ADPs, largest spring freshet in 25 years (1997). Three 15d cruise for calibration data. Much aggregation. Fraser: 20 d of vessel data in 1999, during extreme high flow. Currents to 4.5 ms -1 (!), little aggregation. Calibration data for both: –gravimetric (bulk) SPM calibration –known W s spectra (Owen tube) –Coulter counter size spectraS

17 The Columbia River Basin Columbia basin spans >15° of latitude Timing of snow melt in the Canadian and Snake parts of the basin strongly influences duration of freshet

18 Columbia River Flow and SPM Supply 1997 La Niña year -- highest total flow of century. Largest daily flow: 20,000 m 3 s -1 in January -- a western basin rain-on-snow event (<2.7x mean) Spring freshet (interior basin snowmelt) peaked in May at 16,000 m 3 s -1 (2.1x mean) Natural freshet was ~25,000 m 3 s -1 (3x mean) Pre-release of water began in January to cut freshet

19 The Fraser River Basin A compact basin, spans <s10  of latitude

Fraser River Flow Peak Fraser flows were 4x times the mean Freshet lasted ~50 d because of late, cold spring Such flows have not occurred in the Columbia since 1948

21 Intratidal Processes --

22 Columbia River Stations - Tansy, Am169 and Am012 are in the ETM Red26 is on seaward edge of ETM

23 Velocity and Total SPM at Tansy Strong outward flow during freshet High SPM during freshet strong neap- spring SPM signal Biofouling days

24 Advection vs. Vertical Motion in Columbia Single-frequency inverse analysis; W s classes C 1 to C 4 : (washload), 0.3, 2, 14 (aggregate+sand) mms -1 Near-bed: advection +deposition/erosion of large particles Surface: mostly advection of fines with some advection Surface C 2 concentrationNear-bed C 4 concentration

25 Intratidal Processes In Columbia: A high on flood; ~0.3 on springs sand not impor- tant 2m off bed Peak SPM on ebb leads to SPM export single stage inversion Spring Tide

26 Intratidal Processes In Columbia: A higher than on springs; ~ Maximum SPM on flood, not ebb sand not impor- tant 2m off bed single stage inversion Neap Tide

27 Fraser River 1999 Stations -- All data here are from bD11, at entrance bL11 = upstream limits of salinity intrusion

28 Fraser Intratidal Processes, A and  - A >5 on flood, must include advection (under development) U  is very small P 3 large, except on greater ebb T P negative and sometimes very large (no trapping)

29 Fraser River Freshet Season Salt Wedge-- High stresses on ebb, U  > 0.1 ms -1, rapid response to changes Large particles on ebb, mostly sand, W s = 0.01,3, 15, 45 mms -1 Little stress on flood, SPM maximal at surface No ETM particle trapping -- all SPM removed on each ebb

30 Subtidal Processes --

31 Freshet and Post-Freshet Transports Freshet: outward transport at all stations-- SPM residence times short (<14 d) Post-freshet: recirculation from South to North Channels -- SPM residence times as long as d.

32 SPM Residence Time Index R T Low R T during the spring freshet, only ~14 d After freshet, R T increases with time since the freshet Since there is no seasonal storage on the channel bed, SPM is being supplied from peripheral areas North Channel R T is much longer -- lack of export.

33 Rouse Number P -- Station Tansy was in mid-ETM during the freshet Despite large variations in tides and Q R, minimum tidal P for C 4 is constrained within a narrow range P f > P e during freshet yielded little particle trapping; Spring values of P f and P e are closer toward the end of the record Maximum flood and ebb Rouse Numbers (P) in the Columbia over 8 mo. in 1997

34 Subtidal Processes: E and A vs P: E is lagged by 7 days -- SPM in water column on springs was trapped on the bed on neaps. Lagged E in Columbia is low on springs (P low) and high on neaps (P high), H m /H (therefore A) in- creases with P (on neaps) A=PH m /H vs. P E vs. P 0.18P

35 Subtidal Processes: E vs A and T P : E is maximal at inter- mediate A F /A E because max A occurs on weak tides, when SPM is on bed E is maximal at high T PF /T PE because max T P occurs on strong floods during periods of moderate stratification

36 Subtidal: E vs. Supply Number Paradox: increased Q R shortens estuary, but intensifies two-layer flow -- what happens? As Q R , E  0; all SPM is removed on each tide. As Q R  0, E  0, there is no shear to trap SPM Maximum E at moderate flows BUT: peripheral bay storage/supply partly determines E ! CR FR

37 Summary of Particle Trapping -- Columbia is near optimal particle trapping, with moderate shear and bedstress In Fraser, P is too small on ebb (washload limit) and too big on flood (bedload limit) with respect to flocs Hypothetical view of particle trapping with E as a function: P = W s /(kU  ) T P =  U/(kU  )

38 Conclusions -- Inverse methods: promising as tools to analyze estuarine SPM dynamics, but advection must be included Scaling analysis provides understanding of ETM dynamics; parameters need to be tested further Advection (A) is a very strong factor in river estuary ETM formations Moderate values of A, P and S R lead to max E Max T P is associated with maximal E

39 Subtidal W s -Class Distributions C 1 and C 2 dominant near surface, C 4 minimal C 3 and C 4 dominant at bed on springs, but more variable; low on neaps Near-bed time seriesSurface time series

40 Time Series of A (left) and E (right) -- A is consistently high on neap tides spatial variations in A and E are consistent with seasonal migration of ETM E is high in the North channel, sbecause Q R goes to South channel