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, Tidal Flat Morphodynamics 1

What does “Tidal Flat Morphodynamics” Mean? 2

Sediment Transport Tidal Flat Morphology Waves Orbital Velocity Tidal 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. 2

(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 3

(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 3

Where do tidal flats occur? 4

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) Mean tidal range (cm) Wave-Dominated 4

Where do tidal flats occur? In Spain too! 4 Tidal flats near the mouth of the Guadalquivir River estuary:

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, Tidal Flat Morphodynamics

What moves sediment across flats? 5

Answer: Tides plus concentration gradients 5

Higher sediment concentration Tidal advection High energy waves and/or tides Low energy waves and/or tides What moves sediment across flats? Answer: Tides plus concentration gradients; (i) Due to energy gradients: 5

High energy waves and/or tides Higher sediment concentration Lower sediment concentration Tidal advection High energy waves and/or tides Low energy waves and/or tides Low energy waves and/or tides What moves sediment across flats? Answer: Tides plus concentration gradients; (i) Due to energy gradients: 5

What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply: 6

Higher sediment concentration Tidal advection What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply: “High concentration boundary condition” Net settling of sediment Suspended sediment source from e.g., river, local runoff, bioturbation or easily eroded bed 6

Higher sediment concentration Lower sediment concentration Tidal advection What moves sediment across flats? Answer: Tides plus concentration gradients; (ii) Due to sediment supply: “High concentration boundary condition” Net settling of sediment “High concentration boundary condition” Net settling of sediment Suspended sediment source from e.g., river, local runoff, bioturbation or easily eroded bed 6

(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: 7

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. 5 km Fine sand Sandy mud Mud Photo location U max (m/s) 1 m/s (Reineck 1982) (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. 5 km Fine sand Sandy mud Mud Photo location U max (m/s) 1 m/s (Reineck 1982) (Grabemann et al. 2004) 8

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, Tidal Flat Morphodynamics

1 km Storm-Induced High Water (+5 m) Spring High Tide (+4 m) Spring Low Tide (0 m) (a) Response to Storms(b) Response to Tides Study Site 0 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) 9

xx = x f (t) Z(x) z = R/2 z = - R/2 x = 0 h(x,t)  (t) = (R/2) sin  t x = L z = x/L U T90 /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: 10

xx = x f (t) Z(x) z = R/2 z = - R/2 x = 0 h(x,t)  (t) = (R/2) sin  t x = L z = x/L U T90 /U T90 (L/2) U W90 /U W90 (L/2) Spatial variation in tidal current magnitude Landward Tide- Induced Sediment Transport Seaward Wave-Induced Sediment Transport Spatial variation in wave orbital velocity Maximum tide and wave orbital velocity distribution across a linearly sloping flat: 10

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) Wind Speed (meters/sec) Sediment Conc. (grams/liter) (Hartsuiker et al. 2009) Germany Netherlands 10 km Flat Channel Flat site Channel site 11

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) Wind Speed (meters/sec) Sediment Conc. (grams/liter) (Hartsuiker et al. 2009) Germany Netherlands 10 km Flat Channel Flat site Channel site 11

Elevation change (mm) Wave power supply (10 9 W s m -1 ) ACCRETION EROSION Significant wave height (m) Sediment flux ( mV m 2 s -1 ) LANDWARD SEAWARD 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) Depth (m) below LW Sampling location (Janssen-Stelder 2000) (Allen & Duffy 1998) 5 km 12

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, Tidal Flat Morphodynamics

(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 Elevation (m) Relative Area Eroding Accreting Eroding & concave-up Eroding & concave-up Accreting & convex-up 13

As tidal range increases (or decreases), flats become more convex (or concave) upward. Wetted area / High water area Elevation (m) Mean Tide Level Wetted area / High water area Mean Tide Level MTR = 1.8 m MTR = 2.5 m MTR = 3.3 m Elevation (m) German Bight tidal flats (Dieckmann et al. 1987) U.K. tidal flats (Kirby 2000) Convex Concave Convex Concave 14

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. 1.5 hours Envelope of max velocity Evolution of flat over 40 years Initial profile Last profile High water Low water Ex. Pritchard (2002): 6-m range, no waves, 100 mg/liter offshore, w s = 1 mm/s,  e = 0.2 Pa,  d = 0.1 Pa (Flood +) Convex 15

x = 0x = L Distance across tidal flat Equilibrium bathymetry between low and high tide 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 16

Model incorporating erosion, deposition & advection by tides plus waves favors concave upwards profile 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, w s = 1 mm/s,  e = 0.2 Pa,  d = 0.1 Pa, H b = h/2 Across-shore distance Elevation Equilibrium flat profiles (Roberts et al. 2000) Concave Convex 17

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, Tidal Flat Morphodynamics

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, Tidal Flat Morphodynamics

South San Francisco Bay Tidal Flats: 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 MLLW MLLW to m 18 (Bearman, Friedrichs et al. 2010)

San Mateo Bridge Dumbarton Bridge South San Francisco Bay MHW to MLLW MLLW to m Dominant mode of profile shape variability determined through eigenfunction analysis: Mean concave-up profile (scores < 0) Amplitude (meters) Across-shore structure of first eigenfunction Normalized seaward distance across flat Height above MLLW (m) Mean profile shapes Normalized seaward distance across flat First eigenfunction (deviation from mean profile) 90% of variability explained Mean + positive eigenfunction score = convex-up Mean + negative eigenfunction score = concave-up Mean tidal flat profile Mean convex-up profile (scores > 0) Profile regions 4 km 9 19 (Bearman, Friedrichs et al. 2010)

Profile regions 4 km 10-point running average of profile first eigenfunction score Convex Concave Convex Concave Eigenfunction score Tidal flat profiles Regionally-averaged score of first eigenfunction Significant spatial variation is seen in convex (+) vs. concave (-) eigenfunction scores: (Bearman, Friedrichs et al. 2010)

Profile regions 4 km Profile region Average fetch length (km) Convex Concave Eigenfunction score r = -.82 Fetch Length Profile region Mean tidal range (m) Convex Concave Eigenfunction score Tide Range r = (Bearman, Friedrichs et al. 2010)

Profile regions 4 km Profile region Average fetch length (km) Convex Concave Eigenfunction score r = -.82 Fetch Length Profile region Net 22-year deposition (m) Convex Concave Eigenfunction score Deposition r = +.92 Profile region Mean tidal range (m) Convex Concave Eigenfunction score Tide Range r = (Bearman, Friedrichs et al. 2010)

-- Tide range & deposition are positively correlated to eigenvalue score (favoring convexity). -- Fetch & grain size are negatively correlated to eigenvalue score (favoring concavity) Profile regions 4 km Profile region Average fetch length (km) Convex Concave Eigenfunction score r = -.82 Fetch Length Profile region Mean grain size (  m) Convex Concave Eigenfunction score r = -.61 Grain Size Profile region Net 22-year deposition (m) Convex Concave Eigenfunction score Deposition r = +.92 Profile region Mean tidal range (m) Convex Concave Eigenfunction score Tide Range r =

Tide + Deposition Fetch Explains 89% of Variance in Convexity/Concavity Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity Profile regions r = +.94 r 2 =.89 Profile region Observed Score Modeled Score Eigenfunction score Modeled Score = C 1 + C 2 x (Deposition) + C 3 x (Tide Range) – C 4 x (Fetch) Convex Concave San Mateo Bridge Dumbarton Bridge South San Francisco Bay MHW to MLLW MLLW to m 22 (Bearman, Friedrichs et al. 2010)

Tide + Deposition Fetch Explains 89% of Variance in Convexity/Concavity Tide + Deposition – Fetch Explains 89% of Variance in Convexity/Concavity Profile regions r = +.94 r 2 =.89 Profile region Observed Score Modeled Score Eigenfunction score Modeled Score = C 1 + C 2 x (Deposition) + C 3 x (Tide Range) – C 4 x (Fetch) Convex Concave San Mateo Bridge Dumbarton Bridge South San Francisco Bay MHW to MLLW MLLW to m Increased tide range Increased deposition Increased fetch Increased grain size Convex-upwards Concave-upwards Seaward distance across flat 22 (Bearman, Friedrichs et al. 2010)

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, Tidal Flat Morphodynamics

(Jaffe et al. 2006) 23

Regions 4 km Eigenfunction score Eigenfunction score 10-point running average of profile first eigenfunction score Regionally-averaged score of first eigenfunction 24 (Bearman, unpub.)

Regions 4 km Eigenfunction score Eigenfunction score 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

San Mateo Bridge Dumbarton Bridge South San Francisco Bay MHW to MLLW MLLW to m Central Valley San Jose Variation of External Forcings in Time: (Ganju et al. 2007) 25 (Bearman, unpub.)

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Year 26 (Bearman, unpub.) - Trend of Scores in Time (+ = more convex, - = more concave) Inner Outer

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region 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

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Sediment Disch. (MT) Sediment Disch. (MT) Sediment Disch. (MT) Sediment Disch. (MT) Year Inner regions Outerregions Outerregions * * * * * * * * SIGNIFICANT - Trend of Scores in Time (+ = more convex, - = more concave) CENTRAL VALLEY SEDIMENT DISCHARGE CENTRAL VALLEY SEDIMENT DISCHARGE - Outer regions become more concave as sediment discharge decreases sediment discharge decreases 27 (Bearman, unpub.) Inner Outer

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Year PDO Index Inner regions Outerregions Outerregions - Trend of Scores in Time (+ = more convex, - = more concave) PACIFIC DECADAL OSCILLATION PACIFIC DECADAL OSCILLATION - No significant relationship to changes in shape in shape 28 (Bearman, unpub.) Inner Outer

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Year Bed change (m) Bed change (m) Bed change (m) Bed change (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 erosion, more convex after deposition * * * * * * 29 (Bearman, unpub.) Inner Outer

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Year San Jose Rainfall (in) San Jose Rainfall (in) San Jose Rainfall (in) San Jose Rainfall (in) Inner regions Outerregions Outerregions * SIGNIFICANT - Trend of Scores in Time (+ = more convex, - = more concave) SAN JOSE RAINFALL SAN JOSE RAINFALL - Inner regions more convex when San Jose rainfall increases San Jose rainfall increases * * * SanJose 30 (Bearman, unpub.) Inner Outer

Regions 4 km Score Region 1 Region 4 Region 7 Region 8 Region 5 Region 2 Region 3 Region 6 Region 9 Region 12 Region 11 Region Year Tidal Range (m) Tidal Range (m) Tidal Range (m) Tidal Range (m) Inner regions Outerregions Outerregions - Trend of Scores in Time (+ = more convex, - = more concave) CHANGES IN TIDAL RANGE THROUGH TIME CHANGES IN TIDAL RANGE THROUGH TIME - No significant relationships to temporal changes in tidal range changes in tidal range 31 (Bearman, unpub.) Inner Outer

Significance (slope/std err) RegionMult Reg RsqCV SedsSJ RainfallDep/Eros r ––– r ––– r ––– r ––– r –––3.43 r60.53––– 1.51 r70.35–––1.39––– r80.47––– r –––2.4 r –––7.77 r –––1.37 r ––– 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) San Jose 32 (Bearman, unpub.)

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, Tidal Flat Morphodynamics