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Carl Friedrichs

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.

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Carl Friedrichs

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  1. 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

  2. What does “Tidal Flat Morphodynamics” Mean? 2

  3. 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 Tidal Currents Waves Orbital Velocity External Sediment Sources/Sinks Sediment Transport Tidal Flat Morphology 2

  4. Tidal Flat Definition and General Properties e.g., Yangtze mouth (a) Open coast tidal flat Tidal flat = low relief, unvegetated, unlithified region between highest and lowest astronomical tide. e.g., Dutch Wadden Sea (b) Estuarine or back-barrier tidal flat (Sketches from Pethick, 1984) 3

  5. Tidal Flat Definition and General Properties e.g., Yangtze mouth (a) Open coast tidal flat Tidal flat = low relief, unvegetated, unlithified region between highest and lowest astronomical tide. Note there are no complex creeks or bedforms on these simplistic flats. e.g., Dutch Wadden Sea (b) Estuarine or back-barrier tidal flat (Sketches from Pethick, 1984) 3

  6. Where do tidal flats occur? 4

  7. Where do tidal flats occur? 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.) Tide-Dominated (High) Tide-Dominated (Low) Mixed Energy (Tide-Dominated) Mean tidal range (cm) Mixed Energy (Wave-Dominated) Wave-Dominated Mean wave height (cm) 4

  8. Where do tidal flats occur? In Spain too! http://www.iberia-natur.com/en/reise/201009_Montijo.html Tidal flats near the mouth of the Guadalquivir River estuary: http://www.iberia-natur.com/en/reise/201009_Montijo.html 4

  9. 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

  10. What moves sediment across flats? 5

  11. What moves sediment across flats? Answer: Tides plus concentration gradients 5

  12. 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

  13. 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

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

  15. 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

  16. 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

  17. Typical sediment grain size and tidal velocity pattern across tidal flats: e.g., Yangtze mouth (a) Open coast tidal flat Mud is concentrated near high water line where tidal velocities are lowest e.g., Dutch Wadden Sea (b) Estuarine or back-barrier tidal flat (Sketches from Pethick, 1984) 7

  18. 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 Photo location 1 m/s 0.25 0.50 1.00 1.50 Fine sand Sandy mud Mud Umax (m/s) (Grabemann et al. 2004) (Reineck 1982) 8

  19. 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 Photo location 1 m/s 0.25 0.50 1.00 1.50 Fine sand Sandy mud Mud Umax (m/s) (Grabemann et al. 2004) (Reineck 1982) 8

  20. 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

  21. 1 km 1 km 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) Study Site 0 20 km (Yang, Friedrichs et al. 2003) Spring High Tide (+4 m) Storm-Induced High Water (+5 m) Spring Low Tide (0 m) Spring Low Tide (0 m) (a) Response to Storms (b) Response to Tides 9

  22. 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 1.4 1.2 1.0 0.8 0.6 0.4 0.2 UT90/UT90(L/2) Landward Tide-Induced Sediment Transport 0 0.2 0.4 0.6 0.8 1 x/L 10

  23. 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) Seaward Wave-Induced Sediment Transport UW90/UW90(L/2) Landward Tide-Induced Sediment Transport 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L 10

  24. Wind events cause concentrations on flat to be higher than channel (Ridderinkof et al. 2000) 15 10 5 0 Germany Wind Speed (meters/sec) 10 km Netherlands Flat site Channel site 1.0 0.5 0.0 (Hartsuiker et al. 2009) Flat Channel Sediment Conc. (grams/liter) 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

  25. Wind events cause concentrations on flat to be higher than channel (Ridderinkof et al. 2000) 15 10 5 0 Germany Wind Speed (meters/sec) 10 km Netherlands Flat site Channel site 1.0 0.5 0.0 (Hartsuiker et al. 2009) Flat Channel Sediment Conc. (grams/liter) 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

  26. Larger waves tend to cause sediment export and tidal flat erosion 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) (Janssen-Stelder 2000) (Allen & Duffy 1998) 40 30 20 10 0 -10 -20 -30 200 0 -200 -400 -600 -800 LANDWARD ACCRETION Wave power supply (109 W s m-1) Sediment flux (mV m2 s-1) Elevation change (mm) 2 3 4 1 SEAWARD 0 0.1 0.2 0.3 0.4 0.5 Significant wave height (m) EROSION Depth (m) below LW Flat sites 5 km (Xia et al. 2010) Depth (m) below LW Sampling location 20 km 12 0 10 20

  27. 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

  28. Accreting flats are convex upwards; Eroding flats are concave upwards Accreting & convex-up Accreting & convex-up Eroding & concave-up Elevation (m) Severn, UK, Macrotidal Jiangsu Province, China, Mesotidal (Kirby 1992) Relative Area (Ren1992 in Mehta 2002) Accreting Eroding & concave-up Eroding Louisiana, USA, Microtidal (Lee & Mehta 1997 in Woodroffe 2000) 13

  29. As tidal range increases (or decreases), flats become more convex (or concave) upward. German Bight tidal flats (Dieckmann et al. 1987) U.K. tidal flats (Kirby 2000) MTR = 1.8 m MTR = 2.5 m MTR = 3.3 m Convex Elevation (m) Elevation (m) Concave Mean Tide Level Convex Mean Tide Level Concave 0 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 Wetted area / High water area 14

  30. 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 4.5 3 Initial profile 1.5 hours 6 Last profile Low water 7.5 10.5 9 Evolution of flat over 40 years Ataccretionary near-equilibrium without waves, maximum tidal velocity is nearly uniform across tidal flat. 15

  31. Analytical results for equilibrium profiles with spatially uniform maximum tidal or wave orbital velocity: Tides only Convex Lobate shoreline Embayed shoreline Embayed Equilibrium bathymetry between low and high tide Waves only Embayed Concave (Friedrichs & Aubrey 1996) x = 0 x = L Distance across tidal flat 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

  32. Model incorporating erosion, deposition & advection by tides plus waves favors concave upwards profile Equilibrium flat profiles (Roberts et al. 2000) Convex Convex Concave Elevation 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

  33. 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

  34. 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

  35. South San Francisco Bay Tidal Flats: 700 tidal flat profiles in 12 regions, separated by headlands and creek mouths. South San Francisco Bay MHW to MLLW MLLW to - 0.5 m 0 4 km San Mateo Bridge 12 Dumbarton Bridge 1 11 2 3 10 4 9 8 5 7 Semi-diurnal tidal range up to 2.5 m 6 18 (Bearman, Friedrichs et al. 2010)

  36. Dominant mode of profile shape variability determined througheigenfunction analysis: Across-shore structure of first eigenfunction South San Francisco Bay San Mateo Bridge MHW to MLLW MLLW to - 0.5 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) Dumbarton Bridge Normalized seaward distance across flat 4 km Mean profile shapes 12 Profile regions 1 11 2 3 Mean convex-up profile (scores > 0) 10 Height above MLLW (m) 4 Mean tidal flat profile 9 8 5 7 6 Mean concave-up profile (scores < 0) Normalized seaward distance across flat 19 (Bearman, Friedrichs et al. 2010)

  37. Significant spatial variation is seen in convex (+) vs. concave (-) eigenfunction scores: 8 4 0 -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 8 Regionally-averaged score of first eigenfunction 4 km 4 2 0 -2 5 Convex Concave 8 7 10 6 9 6 5 2 11 12 4 1 3 Tidal flat profiles 20 (Bearman, Friedrichs et al. 2010)

  38. 12 Profile regions 11 1 2 3 10 9 4 8 5 (Bearman, Friedrichs et al. 2010) 7 6 2.5 2.4 2.3 2.2 2.1 4 2 0 -2 Tide Range r = + .87 Mean tidal range (m) Eigenfunction score 4 km 1 3 5 7 9 11 Profile region 3 2 1 0 Convex Concave Convex Concave 4 2 0 -2 Fetch Length Average fetch length (km) Eigenfunction score r = - .82 1 3 5 7 9 11 21 Profile region

  39. 12 Profile regions 11 1 2 3 10 9 4 8 5 (Bearman, Friedrichs et al. 2010) 7 6 1 .8 .6 .4 .2 0 -.2 -.4 2.5 2.4 2.3 2.2 2.1 4 2 0 -2 4 2 0 -2 Tide Range Deposition r = + .92 r = + .87 Mean tidal range (m) Eigenfunction score Eigenfunction score Net 22-year deposition (m) 4 km 1 3 5 7 9 11 1 3 5 7 9 11 Profile region Profile region 3 2 1 0 Convex Concave Convex Concave Convex Concave 4 2 0 -2 Fetch Length Average fetch length (km) Eigenfunction score r = - .82 1 3 5 7 9 11 21 Profile region

  40. -- Tide range & deposition are positively correlated to eigenvalue score (favoring convexity). 12 Profile regions 11 1 2 3 10 -- Fetch & grain size are negatively correlated to eigenvalue score (favoring concavity). 9 4 8 5 7 6 1 .8 .6 .4 .2 0 -.2 -.4 2.5 2.4 2.3 2.2 2.1 4 2 0 -2 4 2 0 -2 Tide Range Deposition r = + .92 r = + .87 Mean tidal range (m) Eigenfunction score Eigenfunction score Net 22-year deposition (m) 4 km 1 3 5 7 9 11 1 3 5 7 9 11 Profile region Profile region 3 2 1 0 Convex Concave Convex Concave Convex Concave Convex Concave 40 30 20 10 0 4 2 0 -2 4 2 0 -2 Fetch Length Grain Size Mean grain size (mm) Average fetch length (km) Eigenfunction score Eigenfunction score r = - .82 r = - .61 1 3 5 7 9 11 1 3 5 7 9 11 21 Profile region Profile region

  41. Tide + Deposition –Fetch Explains 89% of Variance in Convexity/Concavity 12 Profile regions 11 1 2 3 10 4 South San Francisco Bay 9 8 5 4 2 0 -2 MHW to MLLW MLLW to - 0.5 m Observed Score Modeled Score 7 Convex Concave 6 San Mateo Bridge r = + .94 r2 = .89 Eigenfunction score Dumbarton Bridge Modeled Score = C1 + C2x (Deposition) + C3x (Tide Range) – C4x (Fetch) 1 3 5 7 9 11 Profile region 22 (Bearman, Friedrichs et al. 2010)

  42. Tide + Deposition –Fetch Explains 89% of Variance in Convexity/Concavity 12 Profile regions 11 1 2 3 10 4 South San Francisco Bay 9 8 5 4 2 0 -2 MHW to MLLW MLLW to - 0.5 m Observed Score Modeled Score 7 Convex Concave 6 San Mateo Bridge r = + .94 r2 = .89 Eigenfunction score Dumbarton Bridge Modeled Score = C1 + C2x (Deposition) + C3x (Tide Range) – C4x (Fetch) 1 3 5 7 9 11 Profile region Increased tide range Convex-upwards Increased deposition Increased fetch Concave-upwards Increased grain size Seaward distance across flat 22 (Bearman, Friedrichs et al. 2010)

  43. 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

  44. (Jaffe et al. 2006) 23

  45. 12 Regions 11 1 4 km 2 3 10 9 4 8 5 10-point running average of profile first eigenfunction score 7 Eigenfunction score 6 Regionally-averaged score of first eigenfunction Eigenfunction score 24 (Bearman, unpub.)

  46. 12 Regions 11 1 4 km 2 3 10 9 4 8 5 10-point running average of profile first eigenfunction score 7 Eigenfunction score 6 Inner regions (5-10) tend to be more convex Inner regions Regionally-averaged score of first eigenfunction Eigenfunction score 24 (Bearman, unpub.)

  47. Variation of External Forcings in Time: Central Valley South San Francisco Bay MHW to MLLW MLLW to - 0.5 m (Ganju et al. 2007) San Mateo Bridge Dumbarton Bridge San Jose 25 (Bearman, unpub.)

  48. - Trend of Scores in Time (+ = more convex, - = more concave) Outer 12 Regions 11 1 4 km 2 3 10 9 4 8 5 7 Inner Region 2 Region 1 Region 3 6 -1 0 -1 1 0 -1 0 -2 0 -2 -1 -2 0 -2 4 2 0 2 1 Score Region 6 Region 4 Region 5 Score Region 7 Region 9 Region 8 4 2 0 0 -1 2 1 0 1 -1 Score Region 12 Region 11 Region 10 Score 1900 1950 2000 1900 1950 2000 1900 1950 2000 26 (Bearman, unpub.) Year Year Year

  49. - 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 12 Regions 11 1 4 km 2 3 10 9 4 8 5 7 Inner Region 2 Region 1 Region 3 6 -1 0 -1 1 0 -1 0 -2 0 -2 -1 -2 0 -2 4 2 0 2 1 Score Region 6 Region 4 Region 5 Outer regions Score Inner regions Region 7 Region 9 Region 8 4 2 0 0 -1 2 1 0 1 -1 Score Outer regions Region 12 Region 11 Region 10 Score 1900 1950 2000 1900 1950 2000 1900 1950 2000 26 (Bearman, unpub.) Year Year Year

  50. Outer • - Trend of Scores in Time (+ = more convex, - = more concave) • CENTRAL VALLEY SEDIMENT DISCHARGE • Outer regions become more concave as • sediment discharge decreases 12 Regions 11 1 4 km 2 3 10 9 4 8 5 7 Inner Region 2 Region 1 Region 3 6 -1 0 -1 1 0 -1 0 -2 0 -2 * * * -1 -2 0 -2 4 2 0 2 1 6 4 2 6 4 2 6 4 2 Sediment Disch. (MT) Score Region 6 Region 4 Region 5 Outer regions * * 6 4 2 6 4 2 6 4 2 Sediment Disch. (MT) Score Inner regions *SIGNIFICANT Region 7 Region 9 Region 8 4 2 0 0 -1 2 1 0 1 -1 * 6 4 2 6 4 2 6 4 2 Sediment Disch. (MT) Score Outer regions Region 12 Region 11 Region 10 * 6 4 2 6 4 2 6 4 2 Sediment Disch. (MT) Score 1900 1950 2000 1900 1950 2000 1900 1950 2000 27 (Bearman, unpub.) Year Year Year

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