Download - Carl Friedrichs
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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
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What does “Tidal Flat Morphodynamics” Mean?
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Sediment Transport
Tidal Flat Morphology
Waves Orbital VelocityTidal 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.
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(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
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(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)
Note there are no complex creeks or bedforms on these simplistic flats.
e.g., Yangtze mouth
e.g., Dutch Wadden Sea
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Where do tidal flats occur?
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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
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http://www.iberia-natur.com/en/reise/201009_Montijo.html
Where do tidal flats occur? In Spain too!
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Tidal flats near the mouth of the Guadalquivir River estuary:
http://www.iberia-natur.com/en/reise/201009_Montijo.html
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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
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What moves sediment across flats?
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What moves sediment across flats? Answer: Tides plus concentration gradients
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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:
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High energy wavesand/or tides
Higher sediment concentration
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:
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What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
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Higher sediment concentration
Tidal advection
What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
“High concentrationboundary condition”
Net settling of sediment
Suspended sediment source from e.g., river, local runoff,
bioturbation or easily eroded bed
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Higher sediment concentration
Lower sediment concentration
Tidal advection
Tidal advection
What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply:
“High concentrationboundary condition”
Net settling of sediment
“High concentrationboundary condition”
Net settling of sediment
Suspended sediment source from e.g., river, local runoff,
bioturbation or easily eroded bed
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(b) Estuarine or back-barrier tidal flat
(a) Open coast tidal flat
Mud is concentrated near high water line where tidal velocities are lowest
(Sketches from Pethick, 1984)
e.g., Yangtze mouth
e.g., Dutch Wadden Sea
Typical sediment grain size and tidal velocity pattern across tidal flats:
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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)
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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)
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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
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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)
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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:
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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:
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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
FlatChannel
Flat siteChannel site
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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
FlatChannel
Flat siteChannel site
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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
3 421
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
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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
![Page 28: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/28.jpg)
(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
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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
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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
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x = 0 x = L
Distance across tidal flat
Equi
libriu
m b
athy
met
ry b
etwe
en lo
w an
d hi
gh ti
de 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
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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
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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
![Page 34: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/34.jpg)
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
![Page 35: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/35.jpg)
South San Francisco Bay Tidal Flats:
1
23
4
5
67
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 MLLWMLLW to - 0.5 m
18(Bearman, Friedrichs et al. 2010)
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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
Heig
ht 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)
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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
scor
e
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)
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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
scor
e
r = - .82
Fetch Length
Profile region1 3 5 7 9 11
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
scor
e Tide Ranger = + .87
21
(Bearman, Friedrichs et al. 2010)
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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
scor
e
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
scor
e
Depositionr = + .92
Profile region1 3 5 7 9 11
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
scor
e Tide Ranger = + .87
21
(Bearman, Friedrichs et al. 2010)
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-- 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
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
scor
e
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
scor
e
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
scor
e
Depositionr = + .92
Profile region1 3 5 7 9 11
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
scor
e Tide Ranger = + .87
21
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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
South San Francisco Bay
MHW to MLLWMLLW to - 0.5 m
22 (Bearman, Friedrichs et al. 2010)
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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
South San Francisco Bay
MHW to MLLWMLLW 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)
![Page 43: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/43.jpg)
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
![Page 44: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/44.jpg)
(Jaffe et al. 2006)23
![Page 45: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/45.jpg)
12 3
45
6 7
8910
11
12 Regions
4 km
Eige
nfun
ction
scor
eEi
genf
uncti
onsc
ore
10-point running average of profile first
eigenfunction score
Regionally-averaged score of first
eigenfunction
24(Bearman, unpub.)
![Page 46: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/46.jpg)
12 3
45
6 7
8910
11
12 Regions
4 km
Eige
nfun
ction
scor
eEi
genf
uncti
onsc
ore
10-point running average of profile first
eigenfunction score
Regionally-averaged score of first
eigenfunction
24(Bearman, unpub.)
Inner regions (5-10) tend to be more convex
Inner regions
![Page 47: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/47.jpg)
San Mateo Bridge
Dumbarton Bridge
South San Francisco Bay
MHW to MLLWMLLW to - 0.5 m
Central Valley
San Jose
Variation of External Forcings in Time:
(Ganju et al. 2007)
25(Bearman, unpub.)
![Page 48: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/48.jpg)
12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
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12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
- 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
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12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
Region 12Region 11Region 10
1900 1950 2000 1900 1950 2000 1900 1950 2000Se
dim
ent
Dis
ch. (
MT)
Sedi
men
tD
isch
. (M
T)Se
dim
ent
Dis
ch. (
MT)
Sedi
men
tD
isch
. (M
T)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
![Page 51: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/51.jpg)
12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
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
PDO
Inde
xPD
O In
dex
PDO
Inde
xPD
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
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12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
.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
ange
(m)
B
edch
ange
(m)
B
edch
ange
(m)
B
edch
ange
(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
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12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
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
Jos
eR
ainf
all (
in)
San
Jos
eR
ainf
all (
in)
San
Jos
eR
ainf
all (
in)
San
Jos
eR
ainf
all (
in)
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
![Page 54: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/54.jpg)
12 3
45
6 7
8910
11
12 Regions
4 km
Scor
eSc
ore
Scor
eSc
ore
-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
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
)
Tid
alR
ange
(m)
T
idal
Ran
ge (m
)
Tid
alR
ange
(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
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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.)
![Page 56: Carl Friedrichs](https://reader035.vdocuments.us/reader035/viewer/2022062323/568165f5550346895dd91a95/html5/thumbnails/56.jpg)
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