1. Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Spatial and Temporal Trends in Tidal Flat
Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy

2. Spatial and Temporal Trends in Tidal Flat Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Visit Josh at TheHotSeats.net
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy

3. South Bay Salt Pond Project
First ponds leveed in 1854
Currently 26,000 acres of salt ponds in South Bay
October, 2000
61% of ponds sold to large conglomerate of GOs, NGOs, private foundations.

4. What moves sediment across flats?
Ans: 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 1

5. What moves sediment across flats?
Ans: Tides plus concentration gradients; (ii) Due to sediment supply:
Tidal advection
Sediment source from
river or local runoff
Low energy waves
and/or tides
Higher sediment concentration
“High concentration
boundary condition”
Net settling of
sediment
Tidal advection
Lower sediment concentration
“High concentration
boundary condition”
Net settling of
sediment 2

6. Landward Tide-Induced Sediment Transport
Maximum tide and wave orbital velocity distribution across a linearly sloping flat:
z = R/2
h(t) = (R/2) sin wt
x = L
Z(x)
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
2.5
2.0
1.5
1.0
0.5
1.4
1.2
1.0
0.8
0.6
0.4
0.2
UT90/UT90(L/2)
UW90/UW90(L/2)
Seaward Wave-Induced
Sediment Transport
Landward Tide-Induced Sediment Transport
x/L
x/L 3

8. Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Spatial and Temporal Trends in Tidal Flat
Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy

9. Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Spatial and Temporal Trends in Tidal Flat
Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy

10. South San Francisco Bay Tidal Flats:
San Mateo Bridge
Dumbarton Bridge
South San Francisco Bay
MHW to MLLW
MLLW to m
700 tidal flat profiles in 12 regions, separated by headlands and creek mouths.
4 km 12 1 11 2 3 10 4 9 5 8 7
Semi-diurnal tidal range up to 2.5 m 6 6

11. 7 Dominant mode of profile shape variability
determined through eigenfunction analysis:
Across-shore structure of first eigenfunction
San Mateo Bridge
Dumbarton Bridge
South San Francisco Bay
MHW to MLLW
MLLW to m
First eigenfunction
(deviation from mean profile)
90% of variability explained
Mean + positive eigenfunction score = convex-up
Mean + negative eigenfunction score = concave-up
Amplitude (meters)
Normalized seaward distance across flat
Mean concave-up profile (scores < 0)
Height above MLLW (m)
Mean profile shapes
Normalized seaward distance across flat
Mean tidal flat profile
Mean convex-up profile (scores > 0) 12
Profile regions 1 11 2 3 10 4 9 8 5
4 km 7 6 7

12. Significant spatial variation is seen in convex (+) vs
Significant spatial variation is seen in convex (+) vs. concave (-) eigenfunction scores: 8 4 -4
10-point running average of profile first eigenfunction score
Convex
Concave 12
Profile regions 1 11 2 3 10
Eigenfunction score 7 4 9
Regionally-averaged score of first eigenfunction 8 4 2 -2 5
Convex
Concave 8
4 km 10 7 6 9 6 5 2 11 12 1 4 3
Tidal flat profiles 8

13. Average fetch length (km) Net 22-year deposition (m)
-- Tide range & deposition are positively correlated to eigenvalue score (favoring convexity). 1 2 3 4 5 6 7 8 9 10 11 12
Profile regions
4 km
-- Fetch & grain size are negatively correlated to eigenvalue score (favoring concavity).
Profile region 4 2 -2 3 1
Average fetch length (km)
Convex
Concave
Eigenfunction score
r = - .82
Fetch Length
Profile region 4 2 -2
2.5
2.4
2.3
2.2
2.1
Mean tidal range (m)
Convex
Concave
Eigenfunction score
Tide Range
r = + .87 1 .8 .6 .4 .2
-.2
-.4 4 2 -2
Profile region
Net 22-year deposition (m)
Convex
Concave
Eigenfunction score
Deposition
r = + .92 4 2 -2 40 30 20 10
Profile region
Mean grain size (mm)
Convex
Concave
Eigenfunction score
r = - .61
Grain Size 9

14. Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity
San Mateo Bridge
Dumbarton Bridge
South San Francisco Bay
MHW to MLLW
MLLW to m 4 2 -2
Observed Score
Modeled Score
Convex
Concave
r = + .94
r2 = .89
Eigenfunction
score
Modeled Score
= C1 + C2 x (Deposition)
+ C3 x (Tide Range) – C4 x (Fetch)
Profile region
Increased tide range
Convex-upwards 1 2 3 4 5 6 7 8 9 10 11 12
Profile regions
Increased deposition
Flat elevation
Increased fetch
Concave-upwards
Increased grain size
Seaward distance across flat 10

15. Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Spatial and Temporal Trends in Tidal Flat
Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy

16. (Jaffe et al. 2006) 11

17. 10-point running average of profile first eigenfunction score2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Regionally-averaged score of first eigenfunction
Eigenfunction
score 12

18. 10-point running average of profile first eigenfunction score2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Regionally-averaged score of first eigenfunction
Eigenfunction
score
Inner regions (5-11) tend to be more convex 12

19. South San Francisco Bay
Variation of External Forcings in Time:
Sed load at delta
(Ganju et al. 2008)
San Mateo Bridge
Dumbarton Bridge
South San Francisco Bay
MHW to MLLW
MLLW to m
San Jose 13

20. - Trend of Scores in Time (+ = more convex, - = more concave)1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 -1 1 -2 -1 -2 4 2 1
Score
Region 4
Region 5
Region 6
Score
Region 7
Region 8
Region 9 4 2 -1 2 1 -1
Score
Region 10
Region 11
Region 12
Score 14
Year
Year
Year

21. - 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) 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 -1 1 -2 -1 -2 4 2 1
Score
Region 4
Region 5
Region 6
Outer
regions
Score
Inner regions
Region 7
Region 8
Region 9 4 2 -1 2 1 -1
Score
Region 10
Region 11
Region 12
Outer
regions
Score 14
Year
Year
Year

22. - Trend of Scores in Time (+ = more convex, - = more concave)
CENTRAL VALLEY SEDIMENT DISCHARGE
Outer regions become more concave as
sediment discharge decreases 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 -1 1 * * -2 * -1 -2 4 2 1 6 4 2 6 4 2
Sediment
Disch. (MT) 6 4 2
Score
Region 4
Region 5
Region 6
Outer
regions * * 6 4 2 6 4 2 6 4 2
Sediment
Disch. (MT)
Score
Inner regions
*SIGNIFICANT
Region 7
Region 8
Region 9 4 2 -1 2 1 -1 * 6 4 2 6 4 2 6 4 2
Sediment
Disch. (MT)
Score
Region 10
Region 11
Region 12
Outer
regions * 6 4 2 6 4 2 6 4 2
Sediment
Disch. (MT)
Score 15
Year
Year
Year

23. - Trend of Scores in Time (+ = more convex, - = more concave)
PACIFIC DECADAL OSCILLATION
No significant relationship to changes in shape 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 1 -1 -1 1 1 -1 -2 1 -1 -1 -2 4 2 1
Score
PDO Index
Region 4
Region 5
Region 6
Outer
regions 1 -1 1 -1 1 -1
Score
PDO Index
Inner regions
Region 7
Region 8
Region 9 1 -1 4 2 -1 1 -1 2 1 -1 1 -1
Score
PDO Index
Region 10
Region 11
Region 12
Outer
regions 1 -1 1 -1 1 -1
Score
PDO Index 16
Year
Year
Year

24. - 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 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 -1 1 -2 .3
-.3
-.4
-.2
-.4 -1 -2 4 2 1
change (m)
Bed
Score
Region 4
Region 5
Region 6
Outer
regions * .2
-.2 .4 * .3
-.3
change (m)
Bed
Score
Inner regions
*SIGNIFICANT
Region 7
Region 8
Region 9 4 2 -1 * .6 .3 * 2 1 -1 1 .5 .6 .3
Score
change (m)
Bed
Region 10
Region 11
Region 12
Outer
regions * .6 .3 * .2
-.2
-.3
change (m)
Bed
Score 17
Year
Year
Year

25. - Trend of Scores in Time (+ = more convex, - = more concave)
SAN JOSE RAINFALL
Inner regions more convex when
San Jose rainfall increases 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3 20 15 10 -1 1 20 15 10 -2 20 15 10 -1 -2 4 2 1
Rainfall (in)
San Jose
San
Jose
Score
Region 4
Region 5
Region 6
Outer
regions 20 15 10 20 15 10 20 15 10 *
Rainfall (in)
San Jose
Score
Inner regions
*SIGNIFICANT
Region 7
Region 8
Region 9 20 15 10 4 2 -1 20 15 10 2 1 -1 20 15 10 * *
Score
Rainfall (in)
San Jose
Region 10
Region 11
Region 12
Outer
regions 20 15 10 20 15 10 20 15 10
Rainfall (in)
San Jose
Score 18
Year
Year
Year

26. - Trend of Scores in Time (+ = more convex, - = more concave)
CHANGES IN TIDAL RANGE THROUGH TIME
No significant relationships to temporal changes in tidal range 1 2 3 4 5 6 7 8 9 10 11 12
Regions
4 km
Region 1
Region 2
Region 3
1.8
1.7 -1 1
1.8
1.7 -2
1.8
1.7 -1 -2 4 2 1
Range (m)
Tidal
Score
Region 4
Region 5
Region 6
Outer
regions
1.8
1.7
1.8
1.7
1.8
1.7
Range (m)
Tidal
Score
Inner regions
Region 7
Region 8
Region 9
1.8
1.7 4 2 -1
1.8
1.7 2 1 -1
1.8
1.7
Score
Range (m)
Tidal
Region 10
Region 11
Region 12
Outer
regions
1.8
1.7
1.8
1.7
1.8
1.7
Range (m)
Tidal
Score 19
Year
Year
Year

27. Significance (slope/std err)
Temporal Analysis: Multiple Regression
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)
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 12 1 2 11 3
San Jose 10 4 9 5 8 7 6 20

28. Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Spatial and Temporal Trends in Tidal Flat
Shape in San Francisco Bay
Josh Bearman, Carl Friedrichs, Bruce Jaffe, Amy Foxgrover
Main Points
1) On tidal flats, sediment (especially mud) moves away from high concentration
areas and towards areas of weaker energy.
2) Tides and/or abundant sediment supply favor a convex upward profile;
waves and/or sediment loss favor a concave upward profile.
3) South San Francisco Bay provides a case study supporting these trends,
both in space and in time.
Aerial Photo of flats near Dumbarton Bridge, South San Francisco Bay
Courtesy