Tides
Tides:
longest waves
Tides
Simulated & observed tides, Cook Inlet, Alaska
• Definition: The rise and fall of sea level due to the
gravitational forces of the Moon and Sun and the
rotation of the Earth.
• Why tides are important?
- ship navigation in harbors
- coastal morphology (sediments motion)
- tidal currents impact ocean mixing
• How to predict tides?
- mechanical tide calculating machines
since 1880s, tidal charts and analysis
- computer models, tide gauges, satellite
altimetry, etc.
• Largest tides: 17m range: Bay of Fundy &
Ungava Bay (Canada); ~10m: Cook Inlet (Alaska)
Tidal Terminology • Spring tide- (from old English Springere- to rise, not season) high tide
range when sun and moon are inline at full or new moon. – MHWS : Mean High Water Spring
– MLWS : Mean Low Water Spring
• Neap tide- (Near Even As Possible) low tide range when moon & sun effect cancel each other
– MHWN : Mean High Water Neap
– MLWN : Mean Low Water Neap
MSL : Mean Sea Level (need a reference level)
• Semi-diurnal Tide- The most common tidal pattern, featuring two highs and two lows each day
• Diurnal Tide- Only a single high and a single low during each tidal day
• Flood- The tidal current when it is coming from the sea to the shore
• Ebb- The tidal current when it is coming from shore and returning to the sea
• Slack- The point between flood and ebb (or ebb and flood) currents when there is no flow.
Why we have
these different
tides?
Later…
Tidal
Range Tidal
Amplitude
Tidal water level and biological zonation along the shore
(supratidal) • never covered by
water (maybe
splash from waves)
• covered/ exposed
with the tidal cycle
• always covered by
water
(intertidal)
shore
Deep ocean
Neap
tid
e r
an
ge
Sp
rin
g t
ide r
an
ge
Why do we need to predict tides?
Example: ship navigation and access to harbor
(Cairns Harbour, Australia)
water level too low,
danger for grounding
of ships
u
Ebb Tide
Flood Tide
t
t
Low Tide
Slack water before flood
High Tide
Slack water after flood
tAt fcos)(Tide water level can be described by:
A = tidal amplitude (tidal range=2A)
= tidal frequency
= tidal phase
A
2cos)( tUtu f
The relation between tidal water level () and tidal current (u)
max & max u are “out of phase”
EQUILIBRIUM TIDE
The forces between two moving bodies (Moon & Earth)
• Centrifugal forces: push bodies away from each other
• Gravitational forces: push bodies toward each other- stronger on the side
facing the moon
• The difference between the two forces is uneven over the earth
• generate tides (if forces are in equilibrium)
Moon
Earth
What are the physical forces of tides?
Balance of forces:
2234
2
22 2
2)(
)( RPRPP
RPRGmM
P
mMG
RP
mMGFF
aatforcelcentrifuga
aatattractionnalgravitatio
ca
M
Since the Moon is relatively far compared to Earth’s radius, P>>R
33
2)(;
2)(
P
RGmMFF
P
RGmMFF cbca
m
Since F~M/P3, effect of Sun vs. Moon:
Msun=2.5x107Mmoon ; Psun=400Pmoon
Fsun ~ (2.5x107)/(400)3Fmoon ~ 0.4Fmoon
Tides in average: 60% moon and 40% sun
Gravitational Constant
G = 6.67×10-11 N m2/kg2
P=distance between center of Earth and center of Moon
R= radius of Earth
EQUILIBRIUM TIDE
However, the combined effects of lunar and solar, diurnal and
semidiurnal is more complex in the real ocean…
Why tides are different at different latitudes?
Declination (tilt) angle between the moon
and earth axis.
a useful way to characterize the tide is:
The Form factor
F = [ K1 + O1 ] / [ M2 + S2 ]
0.25 < F < 1.25 the tide is mixed
- mainly semidiurnal
F > 3 the tide is diurnal
F < 0.25 the tide is semidiurnal
1.25 < F < 3.00 the tide is mixed
- mainly diurnal
F=0.1
F=0.9
F=2.1
F=19
Equilibrium vs. Dynamic theories of tides Equilibrium theory of tides: If the entire globe
is covered with water and we sum up the forces
along the surface, the maximum “Spring Tide”
when the Moon & Sun are in line would be
always 55cm (M)+24cm(S)=79cm
However, in reality tides in different places are
very different!
Dynamic theory of tides: shallow-water waves
driven by periodic forcing- amplified when basin
in resonant with dominant periods, affected by
coastline topography and Coriolis.
Actual tides in Chesapeake Bay
The tide propagation involve both,
progressive free waves in the open
ocean and waves running along
coasts (mostly Kelvin Waves):
- long waves that travel parallel to
the coastline
- geostrophic balance with higher
sea level near the coast
- in N. Hemisphere generate
counterclockwise propagation
direction-in x decays lev-sea
direction-yin propagates wave
0 )cos(),,(gh
fx
etkytyx
Pressure
Gradient
Coriolis
x
y
Kelvin waves
propagating in opposite
direction would create a
rotating Amphidrome
Semidiurnal tide in the North Sea (“Amphidromic System”)
Amphidromic
point
Tidal propagation
(anti-clockwise in
N. Hemisphere)
Co-tidal lines: points with the same
tidal stage (phase)
Co-range lines: points with the same
tidal range (amplitude)
Tidal Patterns Vary with Ocean Basin
Shape and Size: shallow-wide basin
(a) An amphidromic system in a broad, shallow basin.
(b) The amphidromic system for the Gulf of St. Lawrence
Tidal Patterns Vary with Ocean Basin
Shape and Size: narrow basin
(a) True amphidromic systems do not develop in narrow basins because there is no space for rotation. (b) Tides in the Bay of Fundy, Nova Scotia (one of the largest tides)
How can tides be predicted? Most common: Harmonic Method
• For shallow water:
– Use long-term tide gauge
data
– Do harmonic analysis of
basic tidal constituents
(i.e., find the amplitude and
phase of each component)
– Use astronomical tables or
tidal calculators for future
tides at each location
...)sin()sin()(
12
222111 KM
tAtAt
http://tidesonline.nos.noaa.gov/
Useful resources for tidal data: NOAA Tides Online
(Data: http://tidesonline.nos.noaa.gov/)
Why are the predicted and observed tides different?
How well can we predict tides?
What about wind-driven (storm surge) variations?
November-09
Nor’Easter
Water Level:
Tides+ storm surge
Tides only
Wind:
Floods in Hague area (Nowbray St., Norfolk, VA) Minor flood: high tide (~4ft; 8-25-2012) Major flood: Hurricane Sandy (~7ft; 10-29-2012)
M2
http://www.esr.org/polar_tide_models/Model_TPXO62_load.html
useful tools for global tide prediction:
TPXO6.2 Load Tide: Global Inverse Tide Model 1/4x1/4 developed at Oregon State University, based on
assimilation of T/P altimetry with corrections for coastal oceans.
(code available in Fortran and Matlab)
Run Matlab Tide
Model simulations in Cook Inlet, Alaska,
where the inlet size creates a perfect
resonant with the tidal period (M2)
(Oey & Ezer et al., 2007)
H=50m depth; L=250km long
C=(gH)½ = 22 m/s propagation speed
Resonant: T=4L/C = ~12h
(M2 period=12.42h)
The amplification of the tides in the inlet are simulated quite well
Kodiak Island
Seldovia
Nikiski
Anchorage
mod
obs
Tidal Bores over the mud flats in
Turnagain Arm of Cook Inlet:
big tourist attraction (and a
challenge for surfers…)
2m high, 3-5 m/s propagation speed
ebb
flood
m/s
Velocity and tide level in Turnagain Arm
Cook Inlet, Alaska Low Tide
High Tide
Bay of Fundy: Max. Spring Tide: 17 m
•Shape of basin
•Oscillation period close to tidal period
•Shoals and narrows to north
•Basin oriented toward right (Coriolis
moves water toward right)
finished with waves and tides…
Next Classes:
• Monday 25-November
– Coastal processes and estuarine circulation
• Wednesday 27-November: Happy Thanksgiving
• Monday 02-December: Review for Final Exam
• Wednesday 04-December 5:00pm Final Exam?
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