Signals of sea-level rise
Signals of of sea-level sea-level rise rise Signals in Delaware Delaware and and Chesapeake Chesapeake Bay Bay tides tides in Andrew Andrew C. C. Ross Ross and and Raymond Raymond G. G. Najjar Najjar Pennsylvania State State University University Pennsylvania
Also thanks thanks to to Also Ming Li, Serena Lee, Fan Zhang, Wei Liu
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations show tides are changing Flick et al. (2003):
2 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations show tides are changing Flick et al. (2003):
I
I
I I I
I
I
Redman (1877) Doodson (1924) Ray (2006) Jay (2009) Woodworth (2010) Müller et al. (2011) Feng et al. (2015)
2 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Tides control many estuarine processes I
I
I
I
Mixing and distribution of salinity, nutrients, and pollutants (e.g., Simpson et al., 1990; Prandle, 2004; Li and Zhong, 2009; Wei et al., 2016) Suspension, transportation, and deposition of sediment (e.g., Scully and Friedrichs, 2007) Growth and development of salt marshes (Friedrichs and Perry, 2001; Kirwan and Guntenspergen, 2010) and erosion of shorelines (Rosen, 1977) Flooding in coastal cities (Zhang and Sheng, 2013; Ezer and Atkinson, 2014)
3 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Questions for this talk
I
I
How are tides changing in Delaware and Chesapeake Bays? What is causing these changes and trends? I
I
Sea-level rise?
How might tides change in the future?
4 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Components of the tide 1.0
Water level (m)
M2
S2
K1
O1
0.0 0.5 1.0
01 02 Jul 1.52015
Water level (m)
N2
0.5
03
04
05
06
07
08
09
10
11
13
14
15
Observations
datetime
1.0
12
M2
0.5 0.0 0.5 1.0
01 02 Jul 2015
03
04
05
06
07
08
09
10
11
12
13
14
15
5 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Methods overview 1. Calculate trends in observed tidal properties 2. Determine sensitivity of tidal properties to mean sea level I
Compare observed sensitivity (from statistical model) with predicted sensitivity (from numerical model)
3. Calculate trends after removing effect of mean sea level
6 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: tide gauges Observation site 40°N
p
l
m q ba c n ed o f g hj ik r
38°N 36°N 34°N 32°N
76°W 2
8
74°W 32
72°W
70°W
a b c d e f g h i j k l m n o p q r
Tolchester Beach Baltimore Annapolis Cambridge Solomons Island Lewisetta Windmill Point Yorktown Sewells Point Kiptopeke CBBT Philadelphia Reedy Point Cape May Lewes Sandy Hook Atlantic City Duck
128 512 2048
Model depth (m)
7 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: data processing
I
I
Split each tide gauge time series into chunks by year. Use least squares harmonic analysis to calculate amplitudes and phases for each component of tides, for each year, for each site.
8 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Upper Chesapeake
20 Baltimore
Tolchester Beach Windmill Point Solomons Island
Lewisetta
15 Annapolis
1900
Amplitude (cm)
Cambridge
1920
1940
1960
1980
2000
Delaware Bay 80 Reedy Point Philadelphia
70
Cape May Lewes
60 1900
1920
1940
1960
1980
Type:
2000 Raw time series
40 Lower Chesapeake 38
Kiptopeke CBBT
Sewells Point
36 34 32 1900
Amplitude (cm)
Amplitude (cm)
25
Amplitude (cm)
Example: M2 amplitude time series
Yorktown
1920
1940
1960
1980
2000
70 Mid−Atlantic Bight 65
Sandy Hook
60 55
Atlantic City
50 45 1900
Duck
1920
1940
1960
1980
2000
Nodal cycle removed
9 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: statistical model for sensitivity y = βH H + βt t + β3 sin(ω) + β4 cos(ω) + β5 sin(2ω) + β6 cos(2ω) + β0 + I
I I I I
y is the time series of amplitude or phase (one value per year) H is the annual mean sea level t is the year βH is the sensitivity to sea level βt is the trend not explained by sea level 10 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: domain I
I
Finite Volume Coastal Ocean Model (FVCOM) (Chen et al., 2003, 2006) Resolution varies from less than 200 m in the bays to several kilometers in the deep ocean
Observation site 40°N
p
l
m q ba c n d o e f g hj ik r
38°N 36°N 34°N 32°N
76°W 2
8
74°W 32
72°W
70°W
a b c d e f g h i j k l m n o p q r
Tolchester Beach Baltimore Annapolis Cambridge Solomons Island Lewisetta Windmill Point Yorktown Sewells Point Kiptopeke CBBT Philadelphia Reedy Point Cape May Lewes Sandy Hook Atlantic City Duck
128 512 2048
Model depth (m)
11 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: configuation I
I
I I
Runs in full 3D mode with forcing from atmosphere, ocean boundary, and rivers. Tides specified at the ocean boundary using data from TPXO8. No inundation/wetting and drying of land. Model performance in Chesapeake is good; DE tides are too strong.
12 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: experiments Two main experiments, each one year long: I Control (present-day sea levels) I Historical (sea levels reduced by 25 cm) Sensitivity to sea level: ∆y /∆H I ∆y is the change in model-simulated amplitude or phase I ∆H is the change in mean sea level (imposed and simulated) 13 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 trends M2 amplitude 10
Chesapeake
Delaware
Mid−Atlantic ●
Trend (% / century)
● ●
0
● ●
●
●
●
●
●
●
●
●
−10 ●
●
●
−20
● ●
−30
Trend (min / century)
M2 phase 50 25 ●
●
0
●
●
● ● ●
● ●
● ●
●
●
● ●
●
●
●
−25
t t t s e ge tta nd BT wn oin ore ach ewes May Poin lphia Duck City Hook oli ek oin CB ptop lls P orkto ill P ewise s Isla mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc So To
14 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 sensitivity to sea level M2 amplitude Chesapeake
∆A/∆h (cm / m)
30
Delaware
20
Mid−Atlantic
●
●
●
10
0
● ●
●
●
●
●
●
● ● ●
● ●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
● ● ●
●
● ●
●
∆φ/∆h (min / m)
M2 phase 0 −50
●
● ●
● ●
● ● ●
● ●
● ●
● ●
● ●
● ●
●
● ●
● ●
● ● ●
●
●
● ●
●
●
−100 −150 t t t s a d ge wn oin BT eke oin ore ach ewes May Poin lphia Duck City Hook oli ett an CB ptop lls P orkto ill P ewis s Isl mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc o So T
Source:
●
Model
●
Observed
15 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 trends, removing sea level M2 amplitude
Trend (% / century)
10
Chesapeake
Delaware
●
Mid−Atlantic ●
0
●
●
●
●
● ● ●
●
−10
●
●
● ●
●
●
●
−20 ●
−30
Trend (min / century)
M2 phase 60 40 20 ●
0
●
● ●
● ●
● ●
●
●
●
●
●
●
● ●
●
●
−20 t t t s e ge tta nd BT wn oin ore ach ewes May Poin lphia Duck City Hook oli ek oin CB ptop lls P orkto ill P ewise s Isla mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc So To
16 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Sea-level rise and background trend are the best explanation for most observed tide changes Things that do not sufficiently explain tide changes: I Abrupt, large-scale tide trends I River discharge I Errors and instrument problems in tide gauge data I Dredging and channel deepening (known periods excluded from analysis) 17 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Sensitivity to sea level is nearly linear Toffolon and Savenije (2011) analytical model. ∂A/∂H (cm/m):
18 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
But, future changes might depend on inundation I
I
Past inundation of wetlands and low-lying areas is insignificant compared to future predictions. Future inundation increases friction, lowering amplitudes.
Hall et al. (2013):
19 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Conclusions How are tides changing in Delaware and Chesapeake Bays? I Different M2 amplitude trends; many negative M2 phase trends. What is causing these changes and trends? I Combination of sea-level rise and large-scale changes. How might tides change in the future? I Large increases possible if no new inundation; smaller changes with inundation. 20 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Chen, C., R. C. Beardsley, and G. Cowles, 2006: An unstructured grid, Finite-Volume Coastal Ocean Model (FVCOM) system. Oceanography, 19, 78–89. Chen, C., H. Liu, and R. C. Beardsley, 2003: An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries. Journal of Atmospheric and Oceanic Technology, 20, 159–186. Doodson, A. T., 1924: Perturbations of harmonic tidal constants. Proceedings of the Royal Society of London Series A, 106, 513–526. Ezer, T., and L. P. Atkinson, 2014: Accelerated flooding along the U.S. East Coast: On the impact of sea-level rise, tides, storms, the Gulf Stream, and the North Atlantic Oscillations. Earth’s Future, 2, 362–382. Feng, X., M. N. Tsimplis, and P. L. Woodworth, 2015: Nodal variations and long-term changes in the main tides on the coasts of China. Journal of Geophysical Research: Oceans, 120, 1215–1232. Flick, R. E., J. F. Murray, and L. C. Ewing, 2003: Trends in United States tidal datum statistics and tide range. Journal of Waterway, Port, Coastal, and Ocean Engineering, 129, 155–164. Friedrichs, C. T., and J. E. Perry, 2001: Tidal salt marsh morphodynamics: a synthesis. Journal of Coastal Research, (Special Issue No. 27), 7–37. Hall, G. F., D. F. Hill, B. Horton, S. E. Engelhart, and W. R. Peltier, 2013: A high-resolution study of tides in the Delaware Bay: Past conditions and future scenarios. Geophysical Research Letters, 40, 338–342. Jay, D. A., 2009: Evolution of tidal amplitudes in the eastern Pacific Ocean. Geophysical Research Letters, 36, doi:10.1029/2008GL036185. Kirwan, M. L., and G. R. Guntenspergen, 2010: Influence of tidal range on the stability of coastal marshland. Journal of Geophysical Research: Earth Surface, 115, doi:10.1029/2009JF001400. Li, M., and L. Zhong, 2009: Flood–ebb and spring–neap variations of mixing, stratification and circulation in Chesapeake Bay. Continental Shelf Research, 29, 4–14. Müller, M., B. K. Arbic, and J. X. Mitrovica, 2011: Secular trends in ocean tides: Observations and model results. Journal of Geophysical Research, 116, doi:10.1029/2010JC006387. Prandle, D., 2004: How tides and river flows determine estuarine bathymetries. Progress in Oceanography, 61, 1–26. Ray, R. D., 2006: Secular changes of the M2 tide in the Gulf of Maine. Continental Shelf Research, 26, 422–427. Redman, J. B., 1877: The River Thames. Proceedings of the Institution of Civil Engineers, 49, 67–157. Rosen, P. S., 1977: Increasing shoreline erosion rates with decreasing tidal range in the Virginia Chesapeake Bay. Chesapeake Science, 18, 383–386. Scully, M. E., and C. T. Friedrichs, 2007: Sediment pumping by tidal asymmetry in a partially mixed estuary. Journal of Geophysical Research, 112, doi:10.1029/2006JC003784. Simpson, J. H., J. Brown, J. Matthews, and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13, 125–132. 21 / 23 Toffolon, M., and H. H. G. Savenije, 2011: Revisiting linearized one-dimensional tidal propagation. Journal of
Also thanks thanks to to Also Ming Li, Serena Lee, Fan Zhang, Wei Liu
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations show tides are changing Flick et al. (2003):
2 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations show tides are changing Flick et al. (2003):
I
I
I I I
I
I
Redman (1877) Doodson (1924) Ray (2006) Jay (2009) Woodworth (2010) Müller et al. (2011) Feng et al. (2015)
2 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Tides control many estuarine processes I
I
I
I
Mixing and distribution of salinity, nutrients, and pollutants (e.g., Simpson et al., 1990; Prandle, 2004; Li and Zhong, 2009; Wei et al., 2016) Suspension, transportation, and deposition of sediment (e.g., Scully and Friedrichs, 2007) Growth and development of salt marshes (Friedrichs and Perry, 2001; Kirwan and Guntenspergen, 2010) and erosion of shorelines (Rosen, 1977) Flooding in coastal cities (Zhang and Sheng, 2013; Ezer and Atkinson, 2014)
3 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Questions for this talk
I
I
How are tides changing in Delaware and Chesapeake Bays? What is causing these changes and trends? I
I
Sea-level rise?
How might tides change in the future?
4 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Components of the tide 1.0
Water level (m)
M2
S2
K1
O1
0.0 0.5 1.0
01 02 Jul 1.52015
Water level (m)
N2
0.5
03
04
05
06
07
08
09
10
11
13
14
15
Observations
datetime
1.0
12
M2
0.5 0.0 0.5 1.0
01 02 Jul 2015
03
04
05
06
07
08
09
10
11
12
13
14
15
5 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Methods overview 1. Calculate trends in observed tidal properties 2. Determine sensitivity of tidal properties to mean sea level I
Compare observed sensitivity (from statistical model) with predicted sensitivity (from numerical model)
3. Calculate trends after removing effect of mean sea level
6 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: tide gauges Observation site 40°N
p
l
m q ba c n ed o f g hj ik r
38°N 36°N 34°N 32°N
76°W 2
8
74°W 32
72°W
70°W
a b c d e f g h i j k l m n o p q r
Tolchester Beach Baltimore Annapolis Cambridge Solomons Island Lewisetta Windmill Point Yorktown Sewells Point Kiptopeke CBBT Philadelphia Reedy Point Cape May Lewes Sandy Hook Atlantic City Duck
128 512 2048
Model depth (m)
7 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: data processing
I
I
Split each tide gauge time series into chunks by year. Use least squares harmonic analysis to calculate amplitudes and phases for each component of tides, for each year, for each site.
8 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Upper Chesapeake
20 Baltimore
Tolchester Beach Windmill Point Solomons Island
Lewisetta
15 Annapolis
1900
Amplitude (cm)
Cambridge
1920
1940
1960
1980
2000
Delaware Bay 80 Reedy Point Philadelphia
70
Cape May Lewes
60 1900
1920
1940
1960
1980
Type:
2000 Raw time series
40 Lower Chesapeake 38
Kiptopeke CBBT
Sewells Point
36 34 32 1900
Amplitude (cm)
Amplitude (cm)
25
Amplitude (cm)
Example: M2 amplitude time series
Yorktown
1920
1940
1960
1980
2000
70 Mid−Atlantic Bight 65
Sandy Hook
60 55
Atlantic City
50 45 1900
Duck
1920
1940
1960
1980
2000
Nodal cycle removed
9 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Observations: statistical model for sensitivity y = βH H + βt t + β3 sin(ω) + β4 cos(ω) + β5 sin(2ω) + β6 cos(2ω) + β0 + I
I I I I
y is the time series of amplitude or phase (one value per year) H is the annual mean sea level t is the year βH is the sensitivity to sea level βt is the trend not explained by sea level 10 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: domain I
I
Finite Volume Coastal Ocean Model (FVCOM) (Chen et al., 2003, 2006) Resolution varies from less than 200 m in the bays to several kilometers in the deep ocean
Observation site 40°N
p
l
m q ba c n d o e f g hj ik r
38°N 36°N 34°N 32°N
76°W 2
8
74°W 32
72°W
70°W
a b c d e f g h i j k l m n o p q r
Tolchester Beach Baltimore Annapolis Cambridge Solomons Island Lewisetta Windmill Point Yorktown Sewells Point Kiptopeke CBBT Philadelphia Reedy Point Cape May Lewes Sandy Hook Atlantic City Duck
128 512 2048
Model depth (m)
11 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: configuation I
I
I I
Runs in full 3D mode with forcing from atmosphere, ocean boundary, and rivers. Tides specified at the ocean boundary using data from TPXO8. No inundation/wetting and drying of land. Model performance in Chesapeake is good; DE tides are too strong.
12 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Numerical model: experiments Two main experiments, each one year long: I Control (present-day sea levels) I Historical (sea levels reduced by 25 cm) Sensitivity to sea level: ∆y /∆H I ∆y is the change in model-simulated amplitude or phase I ∆H is the change in mean sea level (imposed and simulated) 13 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 trends M2 amplitude 10
Chesapeake
Delaware
Mid−Atlantic ●
Trend (% / century)
● ●
0
● ●
●
●
●
●
●
●
●
●
−10 ●
●
●
−20
● ●
−30
Trend (min / century)
M2 phase 50 25 ●
●
0
●
●
● ● ●
● ●
● ●
●
●
● ●
●
●
●
−25
t t t s e ge tta nd BT wn oin ore ach ewes May Poin lphia Duck City Hook oli ek oin CB ptop lls P orkto ill P ewise s Isla mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc So To
14 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 sensitivity to sea level M2 amplitude Chesapeake
∆A/∆h (cm / m)
30
Delaware
20
Mid−Atlantic
●
●
●
10
0
● ●
●
●
●
●
●
● ● ●
● ●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
● ● ●
●
● ●
●
∆φ/∆h (min / m)
M2 phase 0 −50
●
● ●
● ●
● ● ●
● ●
● ●
● ●
● ●
● ●
●
● ●
● ●
● ● ●
●
●
● ●
●
●
−100 −150 t t t s a d ge wn oin BT eke oin ore ach ewes May Poin lphia Duck City Hook oli ett an CB ptop lls P orkto ill P ewis s Isl mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc o So T
Source:
●
Model
●
Observed
15 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
M2 trends, removing sea level M2 amplitude
Trend (% / century)
10
Chesapeake
Delaware
●
Mid−Atlantic ●
0
●
●
●
●
● ● ●
●
−10
●
●
● ●
●
●
●
−20 ●
−30
Trend (min / century)
M2 phase 60 40 20 ●
0
●
● ●
● ●
● ●
●
●
●
●
●
●
● ●
●
●
−20 t t t s e ge tta nd BT wn oin ore ach ewes May Poin lphia Duck City Hook oli ek oin CB ptop lls P orkto ill P ewise s Isla mbrid nap altim r Be L tic y y de pe m Y an and L B An Ki ewe Ca Reed Phila on ste Ca nd Atl e i m S h S o l W lc So To
16 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Sea-level rise and background trend are the best explanation for most observed tide changes Things that do not sufficiently explain tide changes: I Abrupt, large-scale tide trends I River discharge I Errors and instrument problems in tide gauge data I Dredging and channel deepening (known periods excluded from analysis) 17 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Sensitivity to sea level is nearly linear Toffolon and Savenije (2011) analytical model. ∂A/∂H (cm/m):
18 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
But, future changes might depend on inundation I
I
Past inundation of wetlands and low-lying areas is insignificant compared to future predictions. Future inundation increases friction, lowering amplitudes.
Hall et al. (2013):
19 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Conclusions How are tides changing in Delaware and Chesapeake Bays? I Different M2 amplitude trends; many negative M2 phase trends. What is causing these changes and trends? I Combination of sea-level rise and large-scale changes. How might tides change in the future? I Large increases possible if no new inundation; smaller changes with inundation. 20 / 23
Introduction
Background
Methods
Results
Discussion and conclusion
References
Chen, C., R. C. Beardsley, and G. Cowles, 2006: An unstructured grid, Finite-Volume Coastal Ocean Model (FVCOM) system. Oceanography, 19, 78–89. Chen, C., H. Liu, and R. C. Beardsley, 2003: An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries. Journal of Atmospheric and Oceanic Technology, 20, 159–186. Doodson, A. T., 1924: Perturbations of harmonic tidal constants. Proceedings of the Royal Society of London Series A, 106, 513–526. Ezer, T., and L. P. Atkinson, 2014: Accelerated flooding along the U.S. East Coast: On the impact of sea-level rise, tides, storms, the Gulf Stream, and the North Atlantic Oscillations. Earth’s Future, 2, 362–382. Feng, X., M. N. Tsimplis, and P. L. Woodworth, 2015: Nodal variations and long-term changes in the main tides on the coasts of China. Journal of Geophysical Research: Oceans, 120, 1215–1232. Flick, R. E., J. F. Murray, and L. C. Ewing, 2003: Trends in United States tidal datum statistics and tide range. Journal of Waterway, Port, Coastal, and Ocean Engineering, 129, 155–164. Friedrichs, C. T., and J. E. Perry, 2001: Tidal salt marsh morphodynamics: a synthesis. Journal of Coastal Research, (Special Issue No. 27), 7–37. Hall, G. F., D. F. Hill, B. Horton, S. E. Engelhart, and W. R. Peltier, 2013: A high-resolution study of tides in the Delaware Bay: Past conditions and future scenarios. Geophysical Research Letters, 40, 338–342. Jay, D. A., 2009: Evolution of tidal amplitudes in the eastern Pacific Ocean. Geophysical Research Letters, 36, doi:10.1029/2008GL036185. Kirwan, M. L., and G. R. Guntenspergen, 2010: Influence of tidal range on the stability of coastal marshland. Journal of Geophysical Research: Earth Surface, 115, doi:10.1029/2009JF001400. Li, M., and L. Zhong, 2009: Flood–ebb and spring–neap variations of mixing, stratification and circulation in Chesapeake Bay. Continental Shelf Research, 29, 4–14. Müller, M., B. K. Arbic, and J. X. Mitrovica, 2011: Secular trends in ocean tides: Observations and model results. Journal of Geophysical Research, 116, doi:10.1029/2010JC006387. Prandle, D., 2004: How tides and river flows determine estuarine bathymetries. Progress in Oceanography, 61, 1–26. Ray, R. D., 2006: Secular changes of the M2 tide in the Gulf of Maine. Continental Shelf Research, 26, 422–427. Redman, J. B., 1877: The River Thames. Proceedings of the Institution of Civil Engineers, 49, 67–157. Rosen, P. S., 1977: Increasing shoreline erosion rates with decreasing tidal range in the Virginia Chesapeake Bay. Chesapeake Science, 18, 383–386. Scully, M. E., and C. T. Friedrichs, 2007: Sediment pumping by tidal asymmetry in a partially mixed estuary. Journal of Geophysical Research, 112, doi:10.1029/2006JC003784. Simpson, J. H., J. Brown, J. Matthews, and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13, 125–132. 21 / 23 Toffolon, M., and H. H. G. Savenije, 2011: Revisiting linearized one-dimensional tidal propagation. Journal of
