carl friedrichs 1) on tidal flats, sediment (especially mud) moves toward areas of weaker energy. 2)...

Carl Friedrichs

1) On tidal flats, sediment (especially mud) moves toward areas of weaker energy.

2) Tides usually move sediment landward; waves usually move sediment seaward.

3) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave upward profile.

4) South San Francisco Bay provides a case study supporting these trends, both in space and time.

Virginia Institute of Marine Science, College of William and Mary

Main Points

Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)by D. Schwen, http://commons.wikimedia.org

Tidal Flat Morphodynamics

1

What does “Tidal Flat Morphodynamics” Mean?

2

Sediment Transport

Tidal Flat Morphology

Waves Orbital Velocity

Tidal Currents

External Hydrodynamic

Forcing

External Sediment Sources/Sinks

What does “Tidal Flat Morphodynamics” Mean?

Morphodynamics = the process by which morphology affects hydrodynamics in such a way as to influence the further evolution of the morphology itself.

2

(b) Estuarine or back-barrier tidal flat

(a) Open coast tidal flat

Tidal flat = low relief, unvegetated, unlithified region between highest and lowest astronomical tide.

Tidal Flat Definition and General Properties

(Sketches from Pethick, 1984)

e.g., Yangtze mouth

e.g., Dutch Wadden Sea

3



Tidal flat = low relief, unvegetated, unlithified region between highest and lowest astronomical tide.

Tidal Flat Definition and General Properties


Note there are no complex creeks or bedforms on these simplistic flats.

e.g., Yangtze mouth


3

Where do tidal flats occur?

4

Where do tidal flats occur?

Mixed Energy (Wave-Dominated)

Mixed Energy (Tide-Dominated)

Tide-Dominated (Low)

Tide-Dominated (High)

According to Hayes (1979), flats are likely in “tide-dominated” conditions, i.e., Tidal range > ~ 2 to 3 times wave height.

(Large sediment supply can push tidal flat regime toward larger waves.)

Mean wave height (cm)

Mea

n tid

al ra

nge

(cm

)

Wave-Dominated

4

http://www.iberia-natur.com/en/reise/201009_Montijo.html

Where do tidal flats occur? In Spain too!

4

Tidal flats near the mouth of the Guadalquivir River estuary:

http://www.iberia-natur.com/en/reise/201009_Montijo.html

Carl Friedrichs






Main Points



What moves sediment across flats?

5

What moves sediment across flats? Answer: Tides plus concentration gradients

5

Higher sediment concentration

Tidal advectionHigh energy waves

and/or tidesLow energy waves

and/or tides

What moves sediment across flats? Answer: Tides plus concentration gradients; (i) Due to energy gradients:

5

High energy wavesand/or tides


Lower sediment concentration

Tidal advection

Tidal advectionHigh energy waves

and/or tidesLow energy waves

and/or tides

Low energy wavesand/or tides

What moves sediment across flats? Answer: Tides plus concentration gradients; (i) Due to energy gradients:

5

What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply:

6


Tidal advection


“High concentrationboundary condition”

Net settling of sediment

Suspended sediment source from e.g., river, local runoff,

bioturbation or easily eroded bed

6


Lower sediment concentration

Tidal advection

Tidal advection






Suspended sediment source from e.g., river, local runoff,

bioturbation or easily eroded bed

6



Mud is concentrated near high water line where tidal velocities are lowest


e.g., Yangtze mouth


Typical sediment grain size and tidal velocity pattern across tidal flats:

7

Typical sediment grain size and tidal velocity pattern across tidal flats:

Mud is concentrated near high water line where tidal velocities are lowest.

Ex. Jade Bay, German Bight, meantide range 3.7 m; Spring tide range 3.9 m.

5 km

Fine sandSandy mudMud

Photo location

0.250.501.001.50

Umax

(m/s)

1 m/s

(Reineck1982)

(Grabemannet al. 2004)

8

Carl Friedrichs






Main Points



1 km 1 km

Storm-Induced High Water (+5 m)

Spring High Tide (+4 m)

Spring Low Tide (0 m)Spring Low Tide (0 m)

(a) Response to Storms (b) Response to Tides

StudySite0 20

km(Yang, Friedrichs et al. 2003)

Following energy gradients: Storms move sediment from flat to sub-tidal channel; Tides move sediment from sub-tidal channel to flat

Ex. Conceptual model for flats at Yangtze River mouth (mean range 2.7 m; spring 4.0 m)

9

x x = xf(t)

Z(x)

z = R/2

z = - R/2x = 0

h(x,t)

h(t) = (R/2) sin wtx = L

z = 0

0 0.2 0.4 0.6 0.8 1

1.4

1.2

1.0

0.8

0.6

0.4

0.2

x/L

UT9

0/U

T90(L

/2)

Spatial variation in tidal current magnitude

Landward Tide-Induced Sediment

Transport

Maximum tide and wave orbital velocity distribution across a linearly sloping flat:

10

x x = xf(t)

Z(x)

z = R/2

z = - R/2x = 0

h(x,t)

h(t) = (R/2) sin wtx = L

z = 0

0 0.2 0.4 0.6 0.8 1

1.4

1.2

1.0

0.8

0.6

0.4

0.20 0.2 0.4 0.6 0.8 1

3.0

2.5

2.0

1.5

1.0

0.5

x/L x/L

UT9

0/U

T90(L

/2)

UW

90/U

W90

(L/2

)

Spatial variation in tidal current magnitude

Landward Tide-Induced Sediment

Transport

Seaward Wave-InducedSediment Transport

Spatial variation in wave orbital velocity

Maximum tide and wave orbital velocity distribution across a linearly sloping flat:

10

Ems-Dollard estuary, The Netherlands, mean tidal range 3.2 m, spring range 3.4 m

Day of 1996

Wind events cause concentrations on flat to be higher than channel

(Ridderinkof et al. 2000)

Win

d Sp

eed

(met

ers/

sec)

Se

dim

ent C

onc.

(gra

ms/

liter

)

(Hartsuiker et al. 2009)

Germany

Netherlands

10 km

15

10

5

0

1.0

0.5

0.0250 260 270 280 290

Flat

Channel

Flat siteChannel site

11

Elev

ation

cha

nge

(mm

)

Wave power supply(109 W s m-1)

ACCRETION

EROSIONSignificant wave height (m)

Sedi

men

t flux

(mV

m2 s

-1)

LANDWARD

SEAWARD

0 0.1 0.2 0.3 0.4 0.5

200

0

-200

-400

-600

-800

40

30

20

10

0

-10

-20

-30

3 42

1

Wadden Sea Flats, Netherlands(mean range 2.4 m, spring 2.6 m)

Severn Estuary Flats, UK(mean range 7.8 m, spring 8.5 m)

Larger waves tend to cause sediment export and tidal flat erosion

Flat sites

20 km

(Xia et al. 2010)

0 10 20

Depth (m) below LW

Depth (m) below LW

Samplinglocation

(Janssen-Stelder 2000) (Allen & Duffy 1998)

5 km

12

Carl Friedrichs






Main Points



(Ren 1992 in Mehta 2002)

(Lee & Mehta 1997 in Woodroffe 2000)

(Kirby 1992)

Accreting flats are convex upwards; Eroding flats are concave upwards

Severn, UK, Macrotidal

Louisiana, USA, Microtidal

Jiangsu Province, China, Mesotidal

Accreting &convex-up

Elev

ation

(m)

Relative Area

Eroding

AccretingEroding & concave-up

Eroding &concave-up

Accreting &convex-up

13

As tidal range increases (or decreases), flats become more convex (or concave) upward.

Wetted area / High water area0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Elev

ation

(m)

Mean TideLevel

Wetted area / High water area

Mean TideLevel

MTR = 1.8 m

MTR = 2.5 m

MTR = 3.3 m

Elev

ation

(m)

German Bight tidal flats (Dieckmann et al. 1987)

U.K. tidal flats(Kirby 2000)

Convex

Concave

Convex

Concave

14

Models incorporating erosion, deposition & advection by tides produce convex upwards profiles

At accretionary near-equilibrium without waves, maximum tidal velocity is nearly uniform across tidal flat.

1.5hours

3 4.56

7.5910.5

Envelope of max velocity

Evolution of flat over 40 years

Initial profileLast profile

High water

Low water

Ex. Pritchard (2002): 6-m range, no waves, 100 mg/liter offshore, ws = 1 mm/s, te = 0.2 Pa, td = 0.1 Pa

(Flood +)

Convex

15

x = 0 x = L

Distance across tidal flat

Eq

uili

bri

um

bath

ym

etr

y b

etw

een low

and h

igh

tid

e

Tides only

Waves only

Analytical results for equilibrium profiles with spatially uniform maximum tidal or wave orbital velocity:

Lobate shoreline Embayed shoreline

Uniform tidal velocity favors convex-up profile; uniform wave orbital velocity favors concave-up profile.Embayed shoreline enhances profile convexity; lobate shoreline (slightly) enhances profile concavity.

(Friedrichs & Aubrey 1996)

Convex

Concave

Embayed

Embayed

16

Model incorporating erosion, deposition & advection by tides plus waves favors concave upwards profile

Tidal tendency to move sediment landward is balanced by wave tendency to move sediment seaward.

4-m range, 100 mg/liter offshore, ws = 1 mm/s, te = 0.2 Pa, td = 0.1 Pa, Hb = h/2

Across-shore distance

Elev

ation

Equilibrium flat profiles (Roberts et al. 2000)

Concave

Concave

ConvexConvex

17

Carl Friedrichs






Main Points



South San Francisco Bay Tidal Flats:

1

23

4

5

6

7

89

10

11

12

0 4 km

700 tidal flat profiles in 12 regions, separated by headlands and creek mouths.

Semi-diurnal tidal range up to 2.5 m

San Mateo Bridge

Dumbarton Bridge

South San Francisco Bay

MHW to MLLW

MLLW to - 0.5 m

18(Bearman, Friedrichs et al. 2010)

San Mateo Bridge

Dumbarton Bridge

South San Francisco Bay MHW to MLLW

MLLW to - 0.5 m

Dominant mode of profile shape variability determined through eigenfunction analysis:

Mean concave-up profile (scores < 0)

Ampl

itude

(met

ers)

Across-shore structure of first eigenfunction

Normalized seaward distance across flat

Hei

ght a

bove

MLL

W (m

)

Mean profile shapes

Normalized seaward distance across flat

First eigenfunction (deviation from mean profile)90% of variability explained

Mean + positive eigenfunction score = convex-upMean + negative eigenfunction score = concave-up

Mean tidal flat profile

Mean convex-up profile (scores > 0)

12 3

45

6 7

8

10

11

12 Profile regions

4 km

9

19(Bearman, Friedrichs et al. 2010)

12 3

45

6 7

8

10

11

12 Profile regions

4 km

10-point running average of profile first

eigenfunction score

Convex

Concave

Convex

Concave

8

4

0

-4

Eige

nfun

ction

sco

re

Tidal flat profiles

4

2

0

-2

Regionally-averaged score of first

eigenfunction

9

12

3 4

5 6

7

8

9 10

1112

20

Significant spatial variation is seen in convex (+) vs. concave (-) eigenfunction scores:

(Bearman, Friedrichs et al. 2010)

12 3

45

6 7

8910

11

12 Profile regions

4 km

Profile region1 3 5 7 9 11

4

2

0

-2

3

2

1

0

Aver

age

fetc

h le

ngth

(km

) Convex

Concave

Eige

nfun

ction

sco

re

r = - .82

Fetch Length


4

2

0

-2

2.5

2.4

2.3

2.2

2.1

Mea

n tid

al ra

nge

(m)

Convex

Concave

Eige

nfun

ction

sco

re

Tide Ranger = + .87

21


12 3

45

6 7

8910

11

12 Profile regions

4 km


4

2

0

-2

3

2

1

0

Aver

age

fetc

h le

ngth

(km

) Convex

Concave

Eige

nfun

ction

sco

re

r = - .82

Fetch Length

1

.8

.6

.4

.2

0

-.2

-.41 3 5 7 9 11

4

2

0

-2

Profile region

Net

22-

year

dep

ositi

on (m

) Convex

Concave

Eige

nfun

ction

sco

re

Depositionr = + .92


4

2

0

-2

2.5

2.4

2.3

2.2

2.1

Mea

n tid

al ra

nge

(m)

Convex

Concave

Eige

nfun

ction

sco

re

Tide Ranger = + .87

21


-- Tide range & deposition are positively correlated to eigenvalue score (favoring convexity).-- Fetch & grain size are negatively correlated to eigenvalue score (favoring concavity).

12 3

45

6 7

8910

11

12 Profile regions

4 km


4

2

0

-2

3

2

1

0

Aver

age

fetc

h le

ngth

(km

) Convex

Concave

Eige

nfun

ction

sco

re

r = - .82

Fetch Length

1 3 5 7 9 11

4

2

0

-2

40

30

20

10

0

Profile region

Mea

n gr

ain

size

(mm

) Convex

Concave

Eige

nfun

ction

sco

re

r = - .61

Grain Size

1

.8

.6

.4

.2

0

-.2

-.41 3 5 7 9 11

4

2

0

-2

Profile region

Net

22-

year

dep

ositi

on (m

) Convex

Concave

Eige

nfun

ction

sco

re

Depositionr = + .92


4

2

0

-2

2.5

2.4

2.3

2.2

2.1

Mea

n tid

al ra

nge

(m)

Convex

Concave

Eige

nfun

ction

sco

re

Tide Ranger = + .87

21

Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity

12 3

45

6 7

8910

11

12 Profile regions

1 3 5 7 9 11

4

2

0

-2

r = + .94r2 = .89

Profile region

Observed ScoreModeled Score

Eige

nfun

ction

scor

e

Modeled Score = C1 + C2 x (Deposition)+ C3 x (Tide Range) – C4 x (Fetch)

Convex

Concave

San Mateo Bridge

Dumbarton Bridge


MHW to MLLW

MLLW to - 0.5 m

22 (Bearman, Friedrichs et al. 2010)

Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity

12 3

45

6 7

8910

11

12 Profile regions

1 3 5 7 9 11

4

2

0

-2

r = + .94r2 = .89

Profile region

Observed ScoreModeled Score

Eige

nfun

ction

scor

e

Modeled Score = C1 + C2 x (Deposition)+ C3 x (Tide Range) – C4 x (Fetch)

Convex

Concave

San Mateo Bridge

Dumbarton Bridge


MHW to MLLW

MLLW to - 0.5 m

Increased tide

range

Increased

deposition

Increased

fetch

Increased

grain size

Convex-upwards

Concave-upwards

Seaward distance across flat22 (Bearman, Friedrichs et al. 2010)

Carl Friedrichs






Main Points



(Jaffe et al. 2006)23

12 3

45

6 7

8910

11

12 Regions

4 km

Eige

nfun

ction

scor

eEi

genf

uncti

onsc

ore


eigenfunction score


eigenfunction

24(Bearman, unpub.)

12 3

45

6 7

8910

11

12 Regions

4 km

Eige

nfun

ction

scor

eEi

genf

uncti

onsc

ore


eigenfunction score


eigenfunction

24(Bearman, unpub.)

Inner regions (5-10) tend to be more convex

Inner regions

San Mateo Bridge

Dumbarton Bridge


MHW to MLLW

MLLW to - 0.5 m

Central Valley

San Jose

Variation of External Forcings in Time:

(Ganju et al. 2007)

25(Bearman, unpub.)

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9

Region 12Region 11Region 10

1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year 26(Bearman, unpub.)

- Trend of Scores in Time (+ = more convex, - = more concave)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year

- Trend of Scores in Time (+ = more convex, - = more concave)- Outer regions are getting more concave in time (i.e., eroding)- Inner regions are not (i.e., more stable)

Inner regions

Outerregions

Outerregions

26(Bearman, unpub.)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

6

4

2

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000S

edim

ent

Dis

ch. (

MT

)S

edim

ent

Dis

ch. (

MT

)S

edim

ent

Dis

ch. (

MT

)S

edim

ent

Dis

ch. (

MT

)Year Year Year

Inner regions

Outerregions

Outerregions

* * *

* *

*

*

*SIGNIFICANT

- Trend of Scores in Time (+ = more convex, - = more concave) CENTRAL VALLEY SEDIMENT DISCHARGE- Outer regions become more concave as sediment discharge decreases

27(Bearman, unpub.)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

PD

O In

dex

PD

O In

dex

PD

O In

dex

PD

O In

dex

Inner regions

Outerregions

Outerregions

- Trend of Scores in Time (+ = more convex, - = more concave) PACIFIC DECADAL OSCILLATION- No significant relationship to changes in shape

28(Bearman, unpub.)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year

.3

0

-.3

.2

0

-.2

.6

.3

0

0

-.4

.3

0

-.3

0

-.2

-.4

.4

0

.6

.3

0

1

.5

0

.6

.3

0

.2

0

-.2

0

-.3

B

edch

ang

e (m

)

Bed

chan

ge

(m)

B

edch

ang

e (m

)

Bed

chan

ge

(m)

Inner regions

Outerregions

Outerregions

*SIGNIFICANT

- Trend of Scores in Time (+ = more convex, - = more concave)Relationship to preceding deposition or erosion- Inner and outer regions more concave after erosion, more convex after deposition

* *

* *

**

29(Bearman, unpub.)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

20

15

10

San

Jo

seR

ain

fall

(in

) S

an J

ose

Rai

nfa

ll (i

n)

San

Jo

seR

ain

fall

(in

) S

an J

ose

Rai

nfa

ll (i

n)

Inner regions

Outerregions

Outerregions

*SIGNIFICANT

- Trend of Scores in Time (+ = more convex, - = more concave) SAN JOSE RAINFALL- Inner regions more convex when San Jose rainfall increases

*

* *

SanJose

30(Bearman, unpub.)

Inner

Outer

12 3

45

6 7

8910

11

12 Regions

4 km

Sco

reS

core

Sco

reS

core

-1

-2

0

-2

4

2

0

2

1

-1

0

-1

1

0

-1

4

2

0

0

-1

0

-2

0

-2

2

1

0

1

-1

Region 1

Region 4

Region 7 Region 8

Region 5

Region 2 Region 3

Region 6

Region 9


1900 1950 2000 1900 1950 2000 1900 1950 2000Year Year Year

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

1.8

1.7

T

idal

Ran

ge

(m)

T

idal

Ran

ge

(m)

T

idal

Ran

ge

(m)

T

idal

Ran

ge

(m)

Inner regions

Outerregions

Outerregions

- Trend of Scores in Time (+ = more convex, - = more concave) CHANGES IN TIDAL RANGE THROUGH TIME- No significant relationships to temporal changes in tidal range

31(Bearman, unpub.)

Inner

Outer

12

3

4

5

67

89

10

11

12

Significance (slope/std err)

Region Mult Reg Rsq CV Seds SJ Rainfall Dep/Eros

r1 0.82 4.21 ––– –––

r2 0.73 3.19 ––– –––

r3 0.71 3.07 ––– –––

r4 0.55 2.10 ––– –––

r5 0.95 8.18 ––– 3.43

r6 0.53 ––– ––– 1.51

r7 0.35 ––– 1.39 –––

r8 0.47 ––– 1.29 1.12

r9 0.66 2.03 ––– 2.4

r10 0.94 3.41 ––– 7.77

r11 0.46 1.05 ––– 1.37

r12 0.51 1.39 ––– –––

Temporal Analysis: Multiple RegressionLess Central Valley sediment discharge: Outer regions more concave.

More San Jose Rains: Inner regions more convex.

Recent deposition (or erosion): Middle regions more convex (or concave)

San Jose

32(Bearman, unpub.)

Carl Friedrichs






Main Points



carl friedrichs 1) on tidal flats, sediment (especially mud) moves toward areas of weaker energy. 2)...

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