Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
1
What does “Tidal Flat Morphodynamics” Mean?
2
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.
External
Hydrodynamic
Forcing
Waves Orbital
Velocity
Tidal Currents
External Sediment
Sources/Sinks
Sediment Transport
Tidal Flat
Morphology
2
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)
3
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)
3
Where do tidal flats occur?
4
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.
(Large sediment supply can push tidal
flat regime toward larger waves.)
Mixed Energy (Tide-Dominated)
Mixed Energy
(Wave-Dominated)
Wave-Dominated
Mean wave height (cm)
4
Where do tidal flats occur? In Spain too!
Tidal flats near the mouth of the Guadalquivir River estuary:
http://www.iberia-natur.com/en/reise/201009_Montijo.html
http://www.iberia-natur.com/en/reise/201009_Montijo.html
4
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
What moves sediment across flats?
5
What moves sediment across flats?
Answer: Tides plus concentration gradients
5
What moves sediment across flats?
Answer: Tides plus concentration gradients; (i) Due to energy gradients:
Tidal advection
High energy waves
and/or tides
Low energy waves
and/or tides
Higher sediment concentration
5
What moves sediment across flats?
Answer: Tides plus concentration gradients; (i) Due to energy 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
5
What moves sediment across flats?
Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
6
What moves sediment across flats?
Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
Suspended sediment source from
e.g., river, local runoff,
bioturbation or easily eroded bed
Tidal advection
Higher sediment concentration
“High concentration
boundary condition”
Net settling of
sediment
6
What moves sediment across flats?
Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
Suspended sediment source from
e.g., river, local runoff,
bioturbation or easily eroded bed
Tidal advection
Higher sediment concentration
“High concentration
boundary condition”
Net settling of
sediment
Tidal advection
Lower sediment concentration
“High concentration
boundary condition”
Net settling of
sediment
6
Typical sediment grain size and tidal velocity
pattern across tidal flats:
(a) Open coast
tidal flat
e.g., Yangtze mouth
Mud is concentrated near high water
line where tidal velocities are lowest
e.g., Dutch Wadden Sea
(b) Estuarine or backbarrier tidal flat
(Sketches from
Pethick, 1984)
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, mean
tide range 3.7 m; Spring tide range 3.9 m.
Photo
location
Fine sand
Sandy mud
Mud
5 km
1 m/s
Umax
(Reineck
1982)
(m/s)
0.25
0.50
1.00
1.50
(Grabemann
et al. 2004)
8
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
5 km
1 m/s
Umax
(Reineck
1982)
(m/s)
0.25
0.50
1.00
1.50
(Grabemann
et al. 2004)
8
Tidal Flat Morphodynamics
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,
both in space and time.
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)
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
9
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
z = - R/2
x=0
x
x=L
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
0.8
1
x/L
10
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
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
x=L
Z(x)
0
0.2
0.4
0.6
x/L
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
0.8
1
x/L
10
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
11
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
11
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
12
0
10
20
Sampling
location
20 km
4
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
Elevation (m)
Accreting flats are convex upwards; Eroding flats are concave upwards
Accreting &
convex-up
Accreting &
convex-up
Eroding &
concave-up
Severn, UK, Macrotidal
Jiangsu Province, China, Mesotidal
(Kirby 1992)
Relative Area
(Ren 1992 in
Mehta 2002)
Accreting
Eroding & concave-up
Eroding
Louisiana, USA, Microtidal
(Lee & Mehta 1997 in Woodroffe 2000)
13
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
1.0
Wetted area / High water area
14
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 near-equilibrium without waves, maximum tidal velocity is nearly
uniform across tidal flat.
15
Lobate shoreline
Embayed shoreline
Equilibrium bathymetry between low and high tide
Analytical results for equilibrium profiles with spatially uniform maximum tidal or wave orbital velocity:
Tides only
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.
16
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.
17
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
South San Francisco Bay Tidal Flats:
South San
Francisco Bay
700 tidal flat profiles in 12 regions,
separated by headlands and creek mouths.
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)
18
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
6
8
7
Normalized seaward distance across flat
(Bearman, Friedrichs et al. 2010)
19
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
1
Concave
-4
4
2
5
0
-2
8
9
4 km
10
6
8
7
6
11
3
9
5
Convex
2
1
10
4
7
Regionally-averaged
score of first
eigenfunction
11
2 3
4
Concave
12
Tidal flat profiles
(Bearman, Friedrichs et al. 2010)
20
Profile
regions
12
11
10
2 3
4
(Bearman, Friedrichs et al. 2010)
Tide
Range
2
2.4
r = + .87
2.3
0
2.2
-2
Concave
1
3
5
7
9
Profile region
11
2.1
3
Fetch
Length
2
2
r = - .82
0
1
-2
Concave
1
3
5
7
9
Profile region
11
8
7
6
Convex
4
Eigenfunction score
2.5
Mean tidal range (m)
Eigenfunction score
4 km
Convex
4
9
5
Average fetch length (km)
1
0
21
Profile
regions
12
11
10
2 3
4
(Bearman, Friedrichs et al. 2010)
2.3
0
2.2
-2
Concave
3
5
7
9
Profile region
11
.8
Deposition
2
.6
r = + .92
.4
.2
0
0
-2
-.2
Concave
1
3
5
7
9
Profile region
3
Fetch
Length
2
2
r = - .82
0
1
-2
Concave
1
3
5
7
9
Profile region
11
0
1
Convex
4
2.1
Eigenfunction score
r = + .87
Mean tidal range (m)
2
2.4
7
6
Convex
4
8
11
-.4
Net 22-year deposition (m)
Eigenfunction score
2.5
Tide
Range
1
Eigenfunction score
4 km
Convex
4
9
5
Average fetch length (km)
1
21
11
10
2 3
4
9
5
2.3
0
2.2
-2
Concave
3
5
7
9
Profile region
11
.6
r = + .92
.4
.2
0
0
-2
-.2
Concave
1
3
5
7
9
Profile region
11
-.4
2
r = - .82
0
1
-2
2.1
.8
Deposition
2
Fetch
Length
Concave
1
3
1
Convex
4
Eigenfunction score
r = + .87
3
2
5
7
9
Profile region
11
Convex
4
7
6
Convex
4
Eigenfunction score
2
2.4
Net 22-year deposition (m)
Eigenfunction score
Tide
Range
1
Eigenfunction score
2.5
Mean tidal range (m)
Convex
0
40
30
2
Grain
Size
0
20
r = - .61
-2
10
Concave
1
3
5
7
9
Profile region
11
8
Average fetch length (km)
1
4 km
4
Profile
regions
12
Mean grain size (mm)
-- Tide range & deposition are positively correlated
to eigenvalue score (favoring convexity).
-- Fetch & grain size are negatively correlated to
eigenvalue score (favoring concavity).
0
21
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
1
9
Profile
regions
12
11
10
2 3
4
9
5
6
22
MHW to MLLW
8
7
(Bearman, Friedrichs et al. 2010)
11
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
1
9
11
Profile
regions
12
11
10
2 3
4
9
5
6
22
MHW to MLLW
8
7
(Bearman, Friedrichs et al. 2010)
Seaward distance across flat
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org
(Jaffe et al. 2006)
23
Eigenfunction
score
10-point running average
of profile first
eigenfunction score
Regions
12
11
10
1
2 3
4
9
5
6
Eigenfunction
score
4 km
8
7
Regionally-averaged
score of first
eigenfunction
(Bearman, unpub.)
24
Eigenfunction
score
10-point running average
of profile first
eigenfunction score
Regions
12
11
10
1
Inner regions (5-10) tend
to be more convex
2 3
4
Eigenfunction
score
9
5
Inner
regions
4 km
6
8
7
Regionally-averaged
score of first
eigenfunction
(Bearman, unpub.)
24
Variation of External Forcings in Time:
Central Valley
(Ganju et al. 2007)
South San
Francisco Bay
MHW to MLLW
MLLW to - 0.5 m
San Mateo Bridge
Dumbarton Bridge
San Jose
(Bearman, unpub.)
25
- Trend of Scores in Time (+ = more convex, - = more concave)
Outer
1
11
10
2 3
4
Region 2
Region 1
Score
-1
-1
7
0
-2
-1
Region 4
Region 6
Region 5
0
Score
1
0
0
-2
-1
Region 7
-2
Region 8
4
Score
6
8
0
-2
2
0
4
2
2
1
0
0
Region 9
Region 12
Region 11
Region 10
Score
4 km
9
5
Inner
Region 3
Regions
12
0
2
1
-1
1
1900
1950
Year
2000
1900
1950
Year
2000
-1
1900
1950
Year
2000
(Bearman, unpub.)
26
- 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)
Outer
1
11
10
2 3
4
Region 2
Region 1
Score
-1
-1
7
0
-2
-1
Region 4
Region 6
Region 5
0
Outer
regions
Score
1
0
0
-2
Inner regions
-1
Region 7
-2
Region 8
4
Score
6
8
0
-2
2
0
4
2
2
1
0
0
Region 9
0
2
Outer
regions
Region 12
Region 11
Region 10
Score
4 km
9
5
Inner
Region 3
Regions
12
1
-1
1
1900
1950
Year
2000
1900
1950
Year
2000
-1
1900
1950
Year
2000
(Bearman, unpub.)
26
Outer
- Trend of Scores in Time (+ = more convex, - = more concave)
CENTRAL VALLEY SEDIMENT DISCHARGE
- Outer regions become more concave as
sediment discharge decreases
Region 2
4
4
2
-2
-1
Score
*
-2
2
0
2
-1
Region 8
4
4
Score
6
6
2
4
0
2
6
4
2
-2
Region 9
2
*
6
2
4
0
2
1
2
6
4
1
2
0
Region 12
0
6
*
1
2
1900
1950
Year
2000
6
4
4
-1
2
2000
6
4
Region 11
Region 10
1950
Year
0
4
Region 7
Score
Region 6
*
6
4
1900
2
Region 5
1
6
4
-2
2
Region 4
0
*
6
-1
2
1900
1950
Year
2000
4 km
9
5
6
8
7
Sediment
Disch. (MT)
*
0
Sediment
Disch. (MT)
6
0
2 3
Inner
Region 3
Sediment
Disch. (MT)
*
-1
-1
11
10
4
Sediment
Disch. (MT)
Score
Region 1
1
Regions
12
Outer
regions
Inner regions
*SIGNIFICANT
Outer
regions
(Bearman, unpub.)
27
Outer
- Trend of Scores in Time (+ = more convex, - = more concave)
PACIFIC DECADAL OSCILLATION
- No significant relationship to changes
in shape
Region 2
1
0
0
0
-2
-1
-1
1
Score
1
1
1
0
-2
0
0
-1
-1
1
4
1
2
1
2
0
2
0
1
0
0
-1
0
-1
0
-1
-1
-1 -2
Region 8
4
0
0
Region 7
Score
Region 6
Region 5
0
Region 12
1
1
1
0
2
1
0
0
0
-1
1
1900
1950
Year
2000
-1
1900
1950
Year
2000
7
-1 -1
Outer
regions
Inner regions
Region 9
Region 11
Region 10
6
8
-1
-1
Region 4
PDO Index
-2
Score
0
9
5
PDO Index
-1
1
0
4 km
PDO Index
-1
2 3
Inner
Region 3
1
11
10
4
-1
1900
1950
Year
2000
PDO Index
Score
Region 1
1
Regions
12
Outer
regions
(Bearman, unpub.)
28
Outer
- 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
Region 2
0
-.2
-.4 -2
Region 4
0
.2
Score
.3
0
0
Score
.6
*
.3
0
0
2
*
Score
2
.5
1
0
0
.6
.3
0
Region 12
Region 11
.6
*
*
0
.3
0
1
1950
Year
1
Region 9
0
Region 10
1900
0
-.3 -2
Region 8
4
*
0
2000
.4
0
-.2 -1
2
2
Region 6
1
Region 7
4
-.4
Region 5
*
-2
0
0
-.3 -1
-2
0
.2
0
1
0
-1
1900
1950
Year
2000
-.2 -1
-.3
1900
1950
Year
2000
6
8
7
Bed
change (m)
0
-1
4 km
9
5
Inner
Region 3
Bed
change (m)
-1
4
Bed
change (m)
.3
11
10
2 3
Bed
change (m)
Score
Region 1
1
Regions
12
Outer
regions
Inner regions
*SIGNIFICANT
Outer
regions
(Bearman, unpub.)
29
Outer
- Trend of Scores in Time (+ = more convex, - = more concave)
SAN JOSE RAINFALL
- Inner regions more convex when
San Jose rainfall increases
Region 2
0
15
-2
20
Score
15
-2
* 15
0
10 -1
Region 8
*
2
0
20
4
15
2
10
0
20
20
1
Region 7
Score
Region 6
Region 5
0
4
10
10
Region 4
*
0
15
10
10 -2
Region 9
20
2
20
15
1
15
10
0
10
Region 12
Region 11
Region 10
20
20
20
0
2
1
15
15
15
-1
1
1900
1950
Year
10
2000
1900
1950
Year
San Jose
Rainfall (in)
10 -1
-2
Score
15
San Jose
Rainfall (in)
15
20
0
10 -1
2000
10
1900
1950
Year
2000
4 km
9
5
Inner
San Jose
Rainfall (in)
20
-1
4
Region 3
20 -1
11
10
2 3
San Jose
Rainfall (in)
Score
Region 1
1
Regions
12
8
7
6
San
Jose
Outer
regions
Inner regions
*SIGNIFICANT
Outer
regions
(Bearman, unpub.)
30
Outer
- Trend of Scores in Time (+ = more convex, - = more concave)
CHANGES IN TIDAL RANGE THROUGH TIME
- No significant relationships to temporal
changes in tidal range
Region 2
0
-2
1.7 -1
-2
1.7
Region 4
Score
1.8
0
0
-2
1.7 -1
Region 7
Region 8
1.8
4
Score
Region 6
1.8
1
2
1.7
0
1.7 -2
4
1.8 2
2
1
0
1.7 0
1.7
1.8
1.8
1.7
Region 12
1.8
0
2
1.8
1
-1
1
1900
1950
Year
1.7
2000
1900
1950
Year
1.7 -1
2000
Outer
regions
Inner regions
Region 9
Region 11
Region 10
7
1.7
Region 5
1.8
0
Score
1.8
6
8
Tidal
Range (m)
1.8 0
9
5
Inner
Region 3
Tidal
Range (m)
-1
4
4 km
Tidal
Range (m)
Score
1.8 -1
11
10
2 3
1.7
1900
1950
Year
2000
Tidal
Range (m)
Region 1
1
Regions
12
Outer
regions
(Bearman, unpub.)
31
Temporal Analysis: Multiple Regression
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
–––
–––
Less 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)
12
1
2
11
San Jose
3
10
4
9
5
6
(Bearman, unpub.)
8
7
32
Tidal Flat Morphodynamics
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,
both in space and time.
Photo of Jade Bay tidal flats, Germany (spring tide range 3.8 m)
by D. Schwen, http://commons.wikimedia.org