Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science, College of William and Mary
Main Points
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.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
Tidal Flat Definition and General Properties
(a) Open coast
tidal flat
e.g., Yangtze mouth
Tidal flat = low relief, unvegetated,
unlithified region between highest
and lowest astronomical tide.
e.g., Dutch Wadden Sea
(b) Estuarine or backbarrier tidal flat
(Sketches from
Pethick, 1984)
1/17
Tidal Flat Definition and General Properties
e.g., Yangtze mouth
(a) Open coast
tidal flat
Note there are no complex creeks or
bedforms on these simplistic flats.
Tidal flat = low relief, unvegetated,
unlithified region between highest
and lowest astronomical tide.
e.g., Dutch Wadden Sea
(b) Estuarine or backbarrier tidal flat
(Sketches from
Pethick, 1984)
1/17
Where do tidal flats occur?
Mean tidal range (cm)
Tide-Dominated (High)
Tide-Dominated (Low)
According to Hayes (1979), flats are
likely in “tide-dominated” conditions,
i.e., Tidal range > ~ 2 to 3 times wave
height.
Mixed Energy (Tide-Dominated)
Mixed Energy
(Wave-Dominated)
Wave-Dominated
Mean wave height (cm)
2/17
What moves sediment across flats?
Tidal advection
High energy waves
and/or tides
Low energy waves
and/or tides
Higher sediment concentration
3/17
What moves sediment across flats? Ans: Tides plus energy-driven concentration gradients
Tidal advection
High energy waves
and/or tides
Low energy waves
and/or tides
Higher sediment concentration
Tidal advection
High energy waves
and/or tides
Low energy waves
and/or tides
Lower sediment concentration
3/17
<
What moves sediment across flats? Ans: Tides plus energy-driven concentration gradients
Tidal advection
or supply-driven
High energy waves
and/or tides
Low energy waves
and/or tides
Higher sediment concentration
Tidal advection
High energy waves
and/or tides
Low energy waves
and/or tides
Lower sediment concentration
3/17
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, mean
tide range 3.7 m; Spring tide range 3.9 m.
Photo
location
Fine sand
Sandy mud
Mud
4/17
5 km
1 m/s
Umax
(Reineck
1982)
(m/s)
0.25
0.50
1.00
1.50
(Grabemann
et al. 2004)
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, mean
tide range 3.7 m; Spring tide range 3.9 m.
Photo
location
Fine sand
Sandy mud
Mud
4/17
5 km
1 m/s
Umax
(Reineck
1982)
(m/s)
0.25
0.50
1.00
1.50
(Grabemann
et al. 2004)
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs and Josh Bearman
Virginia Institute of Marine Science, College of William and Mary
Main Points
1) On tidal flats, sediment (especially mud) moves toward areas of weaker energy.
2) Tides usually move sediment landward; waves usually move it 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.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
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)
0
(Yang, Friedrichs et al. 2003)
5/17
km
Spring Low Tide (0 m)
Spring Low Tide (0 m)
(a) Response to Storms
Study
Site
Spring High Tide (+4 m)
Storm-Induced
High Water (+5 m)
1 km
20
1 km
(b) Response to Tides
Maximum tide and wave orbital velocity distribution across a linearly sloping flat:
z = R/2
h(t) = (R/2) sin wt
Z(x)
h(x,t)
z=0
x=L
(Friedrichs, in press)
z = - R/2
x=0
x
x = xf(t)
Spatial variation in tidal current magnitude
UT90/UT90(L/2)
1.4
1.2
1.0
0.8
Landward TideInduced Sediment
Transport
0.6
0.4
0.2
0
0.2
0.4
0.6
x/L
6/17
0.8
1
Maximum tide and wave orbital velocity distribution across a linearly sloping flat:
z = R/2
h(t) = (R/2) sin wt
h(x,t)
z=0
x=L
Z(x)
(Friedrichs, in press)
z = - R/2
x=0
x
x = xf(t)
Spatial variation in tidal current magnitude
Spatial variation in wave orbital velocity
3.0
1.2
UW90/UW90(L/2)
UT90/UT90(L/2)
1.4
1.0
0.8
Landward TideInduced Sediment
Transport
0.6
0.4
0.2
0
0.2
0.4
0.6
x/L
6/17
0.8
1
2.5
2.0
Seaward Wave-Induced
Sediment Transport
1.5
1.0
0.5
0
0.2
0.4
0.6
x/L
0.8
1
Wind events cause concentrations on flat to be higher than channel
Wind Speed
(meters/sec)
15
(Ridderinkof et al. 2000)
Germany
10
10 km
Netherlands
5
Flat site
Channel site
Sediment Conc.
(grams/liter)
0
1.0
(Hartsuiker et al. 2009)
Flat
Channel
0.5
0.0
250
260
270
280
290
Day of 1996
Ems-Dollard estuary, The Netherlands, mean tidal range 3.2 m, spring range 3.4 m
7/17
Wind events cause concentrations on flat to be higher than channel
Wind Speed
(meters/sec)
15
(Ridderinkof et al. 2000)
Germany
10
10 km
Netherlands
5
Flat site
Channel site
Sediment Conc.
(grams/liter)
0
1.0
(Hartsuiker et al. 2009)
Flat
Channel
0.5
0.0
250
260
270
280
290
Day of 1996
Ems-Dollard estuary, The Netherlands, mean tidal range 3.2 m, spring range 3.4 m
7/17
Wadden Sea Flats, Netherlands
Severn Estuary Flats, UK
(mean range 2.4 m, spring 2.6 m)
(mean range 7.8 m, spring 8.5 m)
200
LANDWARD
0
-200
-400
-600
-800
40
(Janssen-Stelder 2000)
Elevation change (mm)
Sediment flux (mV m2 s-1)
Larger waves tend to cause sediment export and tidal flat erosion
SEAWARD
0
0.1
0.2
0.3
0.4
Significant wave height (m)
30
(Allen & Duffy 1998)
ACCRETION
20
Wave power supply
(109 W s m-1)
10
2
0
3
1
-10
0.5
-20
EROSION
-30
Depth (m) below LW
Flat sites
5 km
(Xia et al. 2010)
Depth (m) below LW
8/17
0
10
20
Sampling
location
20 km
4
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs and Josh Bearman
Virginia Institute of Marine Science, College of William and Mary
Main Points
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.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
Accreting flats are convex upwards; Eroding flats are concave upwards
(Ren 1992 in
Mehta 2002)
(Kirby 1992)
(Lee & Mehta 1997 in Woodroffe 2000)
9/17
As tidal range increases (or decreases), flats become more convex (or concave) upward.
German Bight tidal flats
U.K. tidal flats
(Dieckmann et al. 1987)
(Kirby 2000)
MTR = 1.8 m
Convex
Elevation (m)
Elevation (m)
MTR = 2.5 m
MTR = 3.3 m
Convex
Mean Tide
Level
Mean Tide
Level
Concave
Concave
0
Wetted area / High water area
10/17
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Wetted area / High water area
Models incorporating erosion, deposition & advection by tides produce convex upwards profiles
Ex. Pritchard (2002): 6-m range, no waves, 100 mg/liter offshore, ws = 1 mm/s, te = 0.2 Pa, td = 0.1 Pa
Envelope of max velocity
(Flood +)
High water
Convex
Initial profile
Last profile
1.5
hours
4.5
3
6
Low water
10.5
9
Evolution of flat over 40 years
At accretionary equilibrium without waves, maximum tidal velocity is nearly uniform
across tidal flat.
11/17
7.5
Model incorporating erosion, deposition & advection by tides plus waves favors
concave upwards profile
Equilibrium flat profiles
(Roberts et al. 2000)
Elevation
Convex
Convex
Concave
Concave
Across-shore distance
4-m range, 100 mg/liter offshore, ws = 1 mm/s, te = 0.2 Pa, td = 0.1 Pa, Hb = h/2
Tidal tendency to move sediment landward is balanced by wave tendency to move sediment seaward.
12/17
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs and Josh Bearman
Virginia Institute of Marine Science, College of William and Mary
Main Points
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.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
South San Francisco Bay case study:
766 tidal flat profiles in 12 regions,
separated by headlands and creek mouths.
Data from 2005 and 1983 USGS surveys.
South San
Francisco Bay
MHW to MLLW
MLLW to - 0.5 m
San Mateo Bridge
0
4 km
Dumbarton Bridge
12
1
11
2
3
10
4
9
8
5
Semi-diurnal tidal
range up to 2.5 m
13/17
7
6
(Bearman, Friedrichs et al. 2010)
Dominant mode of profile shape variability determined through eigenfunction analysis:
Amplitude (meters)
Across-shore structure of first eigenfunction
South San
Francisco Bay
MHW to MLLW
First eigenfunction
(deviation from mean profile)
90% of variability explained
MLLW to - 0.5 m
San Mateo Bridge
Mean + positive eigenfunction score = convex-up
Mean + negative eigenfunction score = concave-up
Dumbarton Bridge
Normalized seaward distance across flat
Height above MLLW (m)
Mean profile shapes
1
11
2 3
10
4
9
5
4 km
Normalized seaward distance across flat
14/17
12 Profile regions
6
8
7
(Bearman, Friedrichs et al. 2010)
Significant spatial variation is seen in convex (+) vs. concave (-) eigenfunction scores:
8
4
10-point running average
of profile first
eigenfunction score
Convex
Eigenfunction score
12 Profile regions
0
Concave
1
-4
4
2
Regionally-averaged
score of first
eigenfunction
11
2 3
10
4
9
5
Convex
4 km
6
8
7
0
Concave
-2
Tidal flat profiles
(Bearman, Friedrichs et al. 2010)
15/17
1
-- Fetch & grain size are negatively
correlated to eigenvalue score (favoring
convexity).
0
0
-.2
-.4
-2
Concave
1
3
5
7
9
Profile region
3
Fetch
Length
2
r = - .82
0
1
0
1
3
5
7
Profile region
9
-2
11
4
2
r = + .87
2.3
0
2.2
-2
Concave
1
3
5
7
Profile region
40
Grain
Size
30
r = - .61
9
11
Convex
4
2
20
0
10
Concave
0
1
(Bearman, Friedrichs et al. 2010)
3
5
7
9
Profile region
-2
11
Eigenfunction score
4
Concave
2.4
8
7
6
Convex
Tide
Range
2.5
2.1
11
Convex
2
Mean tidal range (m)
.2
Eigenfunction score
Average fetch length (m)
2
.4
4
16/17
4
r = + .92
9
5
4 km
Mean grain size (mm)
.6
Convex
2 3
Eigenfunction score
Deposition
.8
11
10
4
Eigenfunction score
Net 22-year deposition (m)
1
Profile
regions
12
-- Deposition & tide range are positively correlated
to eigenvalue score (favoring convexity).
Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity
South San
Francisco
Bay
4
Observed Score
Modeled Score
Eigenfunction
score
Convex
MLLW to - 0.5 m
San Mateo Bridge
r = + .94
r2 = .89
2
0
Dumbarton Bridge
Modeled Score
= C1 + C2 x (Deposition)
+ C3 x (Tide Range) – C4 x (Fetch)
Concave
-2
1
3
5
7
Profile region
9
11
Profile
regions
12
11
10
1
2 3
4
9
5
6
8
7
(Bearman, Friedrichs et al. 2010)
17/17
MHW to MLLW
Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity
South San
Francisco
Bay
4
Observed Score
Modeled Score
San Mateo Bridge
r = + .94
r2 = .89
2
0
Dumbarton Bridge
Modeled Score
= C1 + C2 x (Deposition)
+ C3 x (Tide Range) – C4 x (Fetch)
Concave
-2
1
3
5
7
Profile region
9
Profile
regions
12
11
10
1
2 3
4
9
5
6
11
8
7
(Bearman, Friedrichs et al. 2010)
17/17
MLLW to - 0.5 m
Flat elevation
Eigenfunction
score
Convex
MHW to MLLW
Seaward distance across flat
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs and Josh Bearman
Virginia Institute of Marine Science, College of William and Mary
Main Points
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.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org