Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
In: B.W. Flemming and J.D. Hansom (eds.), Treatise
on Estuarine and Coastal Science: Vol. 3,
Sedimentology and Geology. Elsevier, pp. 137-170.
Today’s talk =
Friedrichs (2011)
+ new literature
SINCE 2011
Tidal Flat Definition, General Properties, and Distribution
(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)
Tidal Flat Definition, General Properties, and Distribution
(a) Open coast tidal
flat
Note there are no complex creeks or bedforms
on these simplistic flats.
This lecture focuses mainly on “sheet flow”
over flats, not flow in channels.
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)
SINCE 2011
Larger Tidal Range and/or More Sediment
Red =
Barrier Island
Barrier Island
OCEAN
OCEAN
Tidal Flats
UPLAND
UPLAND
Yellow =
Tidal Flats
UPLAND
UPLAND
UPLAND
Tidal
Marsh
Tidal Marsh
OCEAN
OCEAN
OCEAN
Tidal Flats
Decreasing Exposure to Waves
Green =
Tidal Marsh
Tidal Marsh
(Fan et al. 2013)
Tidal Marsh
Tidal Flats
OCEAN
UPLAND
SINCE 2011
Larger Tidal Range and/or More Sediment
Red =
Barrier Island
Barrier Island
OCEAN
OCEAN
Tidal Flats
UPLAND
UPLAND
Yellow =
Tidal Flats
UPLAND
UPLAND
UPLAND
Tidal
Marsh
Tidal Marsh
OCEAN
OCEAN
OCEAN
Tidal Flats
Large tidal range + sediment supply
= Dynamic Equilibrium for tidal flats
(Friedrichs 2011, Hu, Wang et al. 2015)
Decreasing Exposure to Waves
Green =
Tidal Marsh
Tidal Marsh
(Fan et al. 2013)
Tidal Marsh
Focus of this lecture
Tidal Flats
OCEAN
UPLAND
SINCE 2011
Larger Tidal Range and/or More Sediment
Red =
Barrier Island
Barrier Island
OCEAN
OCEAN
Tidal Flats
UPLAND
UPLAND
Yellow =
Tidal Flats
UPLAND
UPLAND
UPLAND
Tidal
Marsh
Tidal Marsh
OCEAN
OCEAN
OCEAN
Tidal Flats
Small tidal range + wave-based erosion
= instability likely
for area of marsh vs. tidal flats
Decreasing Exposure to Waves
Green =
Tidal Marsh
Tidal Marsh
(Fan et al. 2013)
Tidal Marsh
(Mariotti & Fagherazzi 2010; Walters et al. 2014)
Tidal Flats
Not the focus of this lecture
OCEAN
UPLAND
Tidal Flat Definition, General Properties, and Distribution (cont.)
With all these restrictions, are there relevant environments left for this lecture?
(Flemming 2012)
Answer: Yes! All coastal environments except for microtidal (light yellow on above map)
commonly include tidal flats subject to dynamic equilibrium.
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
What moves sediment across flats? Ans: Tides acting on concentration gradients
(Friedrichs, 2011)
What moves sediment across flats? Ans: Tides acting on concentration gradients
(Friedrichs, 2011)
Often the cause of the suspended concentration gradient is energy gradients
What moves sediment across flats? Ans: Tides acting on concentration gradients
(Hu, Wang et al. 2015)
- DET ESTMORF model calculates tides, waves, and
resulting suspended sediment concentration.
- Suspended sediment is then diffused toward areas of
lower bed stress and associated lower concentration.
- Diffusion coefficient scales with strength of tidal velocity.
SINCE 2011
Another common cause of sediment concentration gradients is sources/sinks
(Friedrichs, 2011)
(Friedrichs, 2011)
Another common cause of sediment concentration gradients is sources/sinks
Example sediment
source: Varying
concentration in
Seine River
estuary drives
elevation changes
on adjacent tidal
flats.
River + Tidal
Height
= High River
Flow Period
(Deloffre et al., 2005)
River
Discharge
River
Suspended
Sediment
Concentration
Tidal Flat
Elevation
Another common cause of sediment concentration gradients is sources/sinks
1 km
SINCE
2011
(Nittrouer et al.
2013)
Example sediment sink:
Seasonal absence/growth of
vegetation (seagrass and
microphytobenthos) on tidal
flats of Willapa Bay (spring
TR 4 m), causes mud to
move to (1) from flats to
channel in winter and (2)
from channel to flats in
summer.
(Boldt et al. 2013)
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
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)
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
Analytical sol’n for maximum tidal current 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 & Aubrey 1996;
Friedrichs 2011)
z = - R/2
x=0
x
x = xf(t)
Spatial variation in tidal current magnitude
1.4
U/U(L/2)
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
0.8
1
Numerical sol’n for maximum tidal current velocity distribution across a linearly sloping flat:
SINCE 2011
Non-hydrostatic, Reynolds-averaged Navier-Stokes equations with a k-e turbulence closure.
Nearly identical result for maximum tidal velocity over tidal cycle as analytical solution.
Main difference is slight flood dominant velocity asymmetry at tidal front.
Depth-averaged tidal velocity (m/s)
(Hsu et al. 2013)
Tidal
Range
=4m
Friedrichs &
Aubrey (1996)
analytical solution
Distance across tidal flat (m)
Analytical 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 & Aubrey 1996;
Friedrichs 2011)
z = - R/2
x=0
x
x = xf(t)
Spatial variation in tidal current magnitude
Spatial variation in wave orbital velocity
3.0
1.4
2.5
U/U(L/2)
U/U(L/2)
1.2
1.0
0.8
Landward TideInduced Sediment
Transport
0.6
Seaward Wave-Induced
Sediment Transport
1.5
1.0
0.4
0.2
2.0
0
0.2
0.4
0.6
x/L
0.8
1
0.5
0
0.2
0.4
0.6
x/L
0.8
1
Numerical maximum tide and wave stress distribution across more realistic 1-D topography
SINCE 2011
Model forced with realistic tide and winds.
Tidal stress decreases landward across tidal flat.
Wave-induced stress increases landward across flat.
Sum of tidal + wave stress is nearly constant with
distance across flat
Vlie Basin, Wadden Sea
Inter-tidal flats
Distance landward in terms of surface area
(van Prooijen & Z. Wang 2013)
Wind events cause concentrations on flat to be higher than in 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
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)
40
(Janssen-Stelder 2000)
200
LANDWARD
0
-200
-400
-600
SEAWARD
-800
0
0.1
0.2
0.3
Significant wave height (m)
0.4
Elevation change (mm)
Sediment flux (mV m2 s-1)
Larger waves tend to cause sediment export and tidal flat erosion;
Tides without waves cause sediment important and flat deposition
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
0
10
20
Sampling
location
20 km
4
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
Accreting flats are convex upwards; Eroding flats are concave upwards
(Ren 1992 in
Mehta 2002)
(Kirby 1992)
(Lee & Mehta 1997 in Woodroffe 2000)
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Wetted area / High water area
1.0
Analytical results for equilibrium profiles with spatially uniform maximum tidal or wave orbital velocity:
Embayed shoreline
Tides only
Equilibrium bathymetry between low and high tide
Lobate shoreline
Convex
Embayed
Waves only
Embayed
Concave
(Friedrichs & Aubrey 1996)
x=0
Distance across tidal flat
x=L
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.
Semi-analytical results for equilibrium profiles with spatially uniform tidal or wave induced bed stress:
Tidal stress determined from total velocity,
including along-estuary component.
Wave height estimated from wind fetch and
wave-induced stress included at low tide.
Uniform tidal stress favors convex-up profile;
uniform wave stress favors concave-up profile.
(Townend, 2010)
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
7.5
Evolution of flat over 40 years
At accretionary equilibrium (shape) without waves, maximum tidal velocity is nearly
uniform across tidal flat.
Diffusion-driven transport model incorporating waves, tides and different offshore concentrations
Equilibrium shape more convex-up with increasing sediment concentration.
Equilibrium shape more concave-up with increasing wave height.
(Hu, Wang et al. 2015)
SINCE 2011
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
Typical sediment grain size and tidal velocity
pattern across tidal flats:
Finest sediment is typically concentrated near high water
line where tidal velocities are lowest.
Zonated sorting of sediment suggest complete
equilibrium in tide plus wave stress is rarely reached.
Ex. Jade Bay, German Bight, mean tide range 3.7 m; Spring
tide range 3.9 m.
5 km
1 m/s
Fine sand
Sandy mud
Mud
Umax
(Reineck
1982)
(m/s)
0.25
0.50
1.00
1.50
(Grabemann
et al. 2004)
Sediment muddy floc size pattern across tidal flat:
Willapa Bay, USA (spring TR = 4 m)
Muddy flocs are sorted
across tidal flat in manner
analagous to typical sand
vs. mud sorting.
Larger/faster settling sand
and flocs are concentrated
on lower flat.
Finer/slower settling nonflocculated mud is
concentrated on upper flat.
Zonated sorting of
sediment again suggests
complete equilibrium in
tide plus wave stress is
rarely reached.
SINCE 2011
(Law et al. 2013)
Wave events rapidly change local grain size on flats along with elevation:
Complete equilibrium in tide plus
wave stress is rarely reached.
Tendency to always be moving
toward dynamic equilibrium without
ever reaching it.
(Yang et al. 2008)
Luchaogang tidal flat, Yangtze Delta, China
Wave seasonally change (and slightly reverse) across-flat grain size trend on exposed flats:
SINCE
2011
(Choi 2014)
Approaching “dynamic equilibrium” without ever reaching it.
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
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
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
12 Profile regions
1
11
2 3
10
4
9
5
4 km
Normalized seaward distance across flat
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)
1
-- Fetch & grain size are negatively
correlated to eigenvalue score (favoring
convexity).
2
.4
.2
0
0
-.4
-2
Concave
1
3
5
7
9
Profile region
4
Convex
Fetch
Length
2
r = - .82
0
1
Concave
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
7
5
7
9
Profile region
-2
11
Eigenfunction score
4
3
2
2.4
8
6
Convex
Tide
Range
2.5
2.1
11
Mean grain size (mm)
-.2
Mean tidal range (m)
4
r = + .92
9
5
4 km
Eigenfunction score
Average fetch length (km)
.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
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
Profile
regions
12
1
9
11
10
2 3
4
9
5
6
11
Flat elevation
Eigenfunction
score
Convex
MHW to MLLW
8
7
(Bearman, Friedrichs et al. 2010)
Seaward distance across flat
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
Conclusions:
(Friedrichs, 2011)
Conclusions (cont):
(Friedrichs, 2011)
Independent Forcings:
Increased tide range;
Decreased wave height;
Increased external sediment supply;
Bioadhesion.
Properties of Tidal Flat Profiles
Dependent Responses:
Tidal elevation
Net shoreward sediment transport;
Increased deposition;
Decreased grain size;
Increasingly convex-up profile;
Prograding profile.
Independent Forcings:
Decreased tide range;
Increased wave height;
Decreased external sediment supply;
Human disturbance.
Dependent Responses:
Landward distance across flat
Net seaward sediment transport;
Increased erosion;
Increased grain size;
Increasingly concave-up profile;
Retreating profile.
Tidal Flat Morphodynamics: A Synthesis
Carl Friedrichs
Virginia Institute of Marine Science
Main Points/Outline
1) Definition of tidal flats. Focus = non-channelized, non-marsh intertidal areas w/TR ≥ 1.0 m.
2) Tides acting on suspended conc. gradients are main cause of sediment transport across flats.
3) Tides usually move sediment landward; waves usually move sediment seaward.
4) Tides and/or deposition favor a convex upward profile; waves and/or erosion favor a concave
upward profile.
5) Ever changing grain size patterns across flats are partly a response to dynamic equilibrium.
6) South San Francisco Bay provides a case study supporting these trends.
7) Conclusions.
Potential importance of tidal asymmetry in enhancing sediment transport across tidal flat:
Example of asymmetric tidal
bore rising across tidal flat.
(Dronkers 1986)
(Friedrichs 2011)
Local temporal
asymmetry in
(a) peak velocity
(b) peak stress
Local temporal
asymmetry at
high tide slack in
(a) slack velocity
(b) slack stress
Models incorporating erosion, deposition & advection including tides and waves produce
sensible but complex profiles and grain size patterns
SINCE
2011
(Zhou et al. 2015)
However, 100 years of steady forcing is not like reality.
Real tidal flats approach “dynamic equilibrium” without ever reaching it.
SINCE 2011
(cont.)
(Hu, Wang et al. 2015,
cont.)
Tide or tide plus wave
each evolve to distinct
equilbrium shape.
Stable equilibrium has
nearly uniform sediment
concentration and stress
over intertidal area.
Tide dominated profile is
convex-up; tide+wave
profile is concave up.
Tide dominated equilibrium
shape continues to
advance seaward.
Tide+wave equilibrium
shape becomes fixed in
space.
Another cause of fine sediment transport off tidal flats is precipitation on flats
SINCE 2011 (cont.)
1) Willapa Bay, USA (spring TR = 4 m)
(Nowacki & Ogston 2013)
2) Gyeonggi Bay, Korea
(spring TR = 9 m)
(Choi & Jo 2015)