A Parameter Space for Particle A Parameter Space for Particle Trapping – Explorations in Trapping – Explorations in

Two EstuariesTwo EstuariesDavid 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 --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

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ETM-Ecological PerspectiveETM-Ecological Perspective

CRETM-LMER project-http://depts.washington.edu/cretmweb/

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Approach --Approach --• Use acoustical and optical methods to measure

SPM properties by settling velocity (Ws) 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.

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To Determine SPM from Data --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

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Single-Frequency Inverse MethodsSingle-Frequency Inverse Methods

• Define profiles (basis functions) for known Ws 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

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Stage 1 Inverse Stage 1 Inverse

Analysis:Analysis:• Calibrate and cor-

rect ABS

• Fit WS classes to ABS profiles via non-negative least squares

0 20 40 60 80 100 120 140 1602

4

6

8

10

12

14

16

spm in mg/l

heig

ht abo

ve b

ed in m

ete

rs Am169 fit on May 5th(102)

total spmspm(0.02 mm/s Ws)spm(0.3 mm/s Ws)spm(2 mm/s Ws)spm(14 mm/s Ws)total fitted spm

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

4

6

8

1 0

1 2

1 4

1 6

he

igh

t a

bo

ve

be

d i

n m

ete

rs

d b

c o r b s

r a w b s

- D e c a y

o c o r

c o r b s + o c o r

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Multi-Frequency Inverse MethodsMulti-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 Ws 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

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

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Calibrating the Two-Stage Inverse --Calibrating the Two-Stage Inverse --

• C1 to C4, Ws = 0.01, 3, 15, 45 mms-1 for Fraser

• Two-stage inverse recon-ciles OBS and ABS views of ETM

• OBS responds to all Ws classes, ABS C2 to C4 only

• Note that theory and analysis are forced to agree on C2 in table

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Scaling Analysis --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

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Local SPM Conservation --Local SPM Conservation --

• Non-Dimensional Parameters:

> Rouse Number P = Ws /(kU) ~ 1-4 (ETM particles)

> Time-change m <0.1 (neglect)

> Advection number A = P Hm/H ~ 0.1- 500. Hm is the height of the SPM max off bed; cf. Hm/U of Lynch et al. (1991)

>Aggregation number (neglect for now)

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Integral SPM Conservation --Integral SPM Conservation --

• ETM extends from X1 to X2, 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 = CE/CR >1 ratio of estuarine to fluvial SPM – Supply number SR = const P UR/( H) is the fluvial SPM input– Shear flux number FV = const E TP where: – Trapping potential TP = U/(kU) is in FV

2

1

2

1

2

11

0

X

X

X

X

n

i viviVVVRR

X

X H

dxnaggregatioerosionT

HCUCUFCQSdxdzCt

E

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Summary of ETM Parameters:Summary of ETM Parameters:• Rouse Number P = Ws /(kU)

• Advection number A = P Hm/H

• Trapping efficiency E = CE/CR

• Supply number SR = P UR/( H)

• Trapping potential TP =U/(kU)• Not Considered here: lateral exchanges with peripheral

areas, aggregation, erosion/deposition• Salinity intrusion problem has only two non-

dimensional numbers!

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

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Columbia and Fraser Data --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 Ws spectra (Owen tube)– Coulter counter size spectraS

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The Columbia River BasinThe 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

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Columbia River Flow and SPM SupplyColumbia River Flow and SPM Supply• 1997 La Niña year -- highest

total flow of century.

• Largest daily flow: 20,000 m3s-1 in January -- a western basin rain-on-snow event (<2.7x mean)

• Spring freshet (interior basin snowmelt) peaked in May at 16,000 m3s-1 (2.1x mean)

• Natural freshet was ~25,000 m3s-1 (3x mean)

• Pre-release of water began in January to cut freshet

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The Fraser The Fraser River BasinRiver BasinA compact basin, spans <s10 of latitude

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1999 Fraser River Flow1999 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

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Intratidal Processes --Intratidal Processes --

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Columbia River Stations -Columbia River Stations -

• Tansy, Am169 and Am012 are in the ETM

• Red26 is on seaward edge of ETM

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Velocity and Total SPM at TansyVelocity and Total SPM at Tansy

• Strong outward flow during freshet

• High SPM during freshet

• strong neap-spring SPM signal

• Biofouling days 230- 290

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Advection vs. Vertical Motion in ColumbiaAdvection vs. Vertical Motion in Columbia

• Single-frequency inverse analysis; Ws classes C1 to C4 : 0.014 (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

150 200 250 300 350Time, days from 7198- 4

- 3

- 2

- 1

0

1

2

3

_g

ol

2,

qe

rF

.,

d^-1

Tansy Surf C2, mgl- 1

0

7.5

Surface C2 concentration

150 200 250 300 350Time, days from 1197- 4

- 3

- 2

- 1

0

1

2

3

_g

ol

2,

qe

rF

.,

d^-1

AM012 Bed C4, mgl- 1

.01

25

Near-bed C4 concentration

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Intratidal Intratidal ProcessesProcessesIn 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

50100150

mg/

l Total SPMTotal fit

0

200

mg/

l sand aggregateC

3+C

4

-30-20-10

010

mm

/s U*

0

0.2

0.4

A

141.5 142 142.5 1430

10

20

Days from 1/1/1997

sal P

4

Spring Tide

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Intratidal Intratidal ProcessesProcesses

In Columbia:• A higher than on

springs; ~0.4-0.6

• Maximum SPM on flood, not ebb

• sand not impor-tant 2m off bed

• single stage inversion

50100150

mg/

l Total SPMTotal fit

0

100

200

mg/

l sand aggregateC

3+C

4

-20-10

010

mm

/s U*

0

0.2

0.4

A

121.5 122 122.5 1230

10

Days from 1/1/1997

sal P

4

Neap Tide

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Fraser River 1999 Stations --Fraser River 1999 Stations --

• All data here are from bD11, at entrance

• bL11 = upstream limits of salinity intrusion

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Fraser Intratidal Processes, A and Fraser Intratidal Processes, A and - -

• A >5 on flood, must include advection (under development)

• U is very small P3 large, except on greater ebb

• TP negative and sometimes very large (no trapping)

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Fraser River Freshet Season Salt Wedge--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, Ws = 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

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Subtidal Processes --Subtidal Processes --

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Freshet and Post-Freshet TransportsFreshet 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 60-100 d.

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SPM Residence Time Index SPM Residence Time Index RRTT

• Low RT during the spring freshet, only ~14 d

• After freshet, RT 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 RT is much longer -- lack of export.

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Rouse Rouse Number Number PP -- --

• Station Tansy was in mid-ETM during the freshet

• Despite large variations in tides and QR, minimum tidal P for C4 is constrained within a narrow range

• Pf > Pe during freshet yielded little particle trapping;

• Spring values of Pf and Pe are closer toward the end of the record

Maximum flood and ebb Rouse Numbers (P) in the Columbia over 8 mo. in 1997

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Subtidal Processes: Subtidal Processes: EE and A vs and A vs PP::• 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),

• Hm/H (therefore A) in-creases with P (on neaps)

1 2 3Rouse Number P_f

0.5

0.9

noitcevdA

rebmuN

f_A

A=PHm/H vs. P

E vs. P

0.18P

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Subtidal Processes: Subtidal Processes: EE vs vs A A and and TTPP::

• E is maximal at inter-mediate AF/AE because max A occurs on weak tides, when SPM is on bed

• E is maximal at high TPF/TPE because max TP occurs on strong floods during periods of moderate stratification

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Subtidal: E vs. Subtidal: E vs. Supply NumberSupply Number

Paradox: increased QR shortens estuary, but intensifies two-layer flow -- what happens?

• As QR , E 0; all SPM is removed on each tide. As QR 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

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Summary of Particle Trapping --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 = Ws/(kU) TP=U/(kU)

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Conclusions --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 SR lead to max E

• Max TP is associated with maximal E

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Subtidal WSubtidal Wss-Class Distributions-Class Distributions

• C1 and C2 dominant near surface, C4 minimal

• C3 and C4 dominant at bed on springs, but more variable; low on neaps

150 200 250 300 350Days from 11970

20

40

lg

m-1

AM012 Subtidal Ws Classes

C3+C4

C1+C2

Near-bed time series

150 200 250 300 350Days from 11970

5

10

15

20

25

lg

m-1

Tansy Surface Subtidal Ws Classes

C3+C4

C1+C2

Surface time series

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Time Series of Time Series of AA (left) and (left) and EE (right) -- (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 QR goes to South channel