Tides or ripples or seas Tides: longest waves
Tides 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 - fishing, marine biology, etc. 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) Simulated & observed tides, Cook Inlet, Alaska
Tide measurements old mechanical recorder satellite transmitter acoustic sensor solar panel today s tide and meteorological station old mechanical float electronics box
Useful resources for tidal data: NOAA Tides Online http://tidesonline.nos.noaa.gov/
Global Tide Gauge Data (longest records ~200 years; PSMSL used mostly for studies of sea level rise)
(Physics Today, 2011)
Tides are important for fishermen Note that while weather can only be predicted for a few days, because of the cyclical nature of tides, they can be predicted many days and years in advance
Tidal charts and ship navigation (Cairns Harbour, Australia)
NOS/NOAA education
Berkley Bridge over the Elizabeth River (picture by T. Ezer, Nov-2017)
Neap tide range Spring tide range Tides are important for biological zonation along the shore shore (supratidal) never covered by water (maybe splash from waves) (intertidal) covered/ exposed with the tidal cycle Deep ocean always covered by water
Elizabeth River Low Tide High Tide (pictures by T. Ezer, Nov-2017)
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.
Tidal Range Tidal Amplitude Why we have these different tides? Later
The relation between tidal water level ( ) and tidal current (u) Tide water level can be described by: A = tidal amplitude (tidal range=2a) = tidal frequency = tidal phase A u max & max u are out of phase Low Tide Slack wat er before flood Flood T ide ( t) High T ide Slack wat er after flood Acos t f Ebb T ide u( t) U cos t 2 f t t
What are the physical forces of tides? Earth EQUILIBRIUM TIDE Moon 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)
F a F c Balance of forces: gravitational attraction at a centrifugal force at a Gravitational Constant G = 6.67 10-11 N m 2 /kg 2 2 mm mm 2PR R G G ( GmM) 2 2 4 3 2 ( P R) P P 2P R P R 2 F Since the Moon is relatively far compared to Earth s radius, P>>R a F c 2R ( GmM) ; 3 P F b F c 2R ( GmM) 3 P m P=distance between center of Earth and center of Moon R= radius of Earth Since F~M/P 3, effect of Sun vs. Moon: M M sun =2.5x10 7 M moon ; P sun =400P moon F sun ~ (2.5x10 7 )/(400) 3 F moon ~ 0.4F moon Tides in average: 60% moon and 40% sun
EQUILIBRIUM TIDE
Why tides are different at different latitudes? Declination (tilt) angle between the moon and earth axis. However, the combined effects of lunar and solar, diurnal and semidiurnal is more complex in the real ocean
F=0.1 a useful way to characterize the tide is: The Form factor F = [ K 1 + O 1 ] / [ M 2 + S 2 ] F < 0.25 the tide is semidiurnal F=0.9 0.25 < F < 1.25 the tide is mixed - mainly semidiurnal F=2.1 1.25 < F < 3.00 the tide is mixed - mainly diurnal F=19 F > 3 the tide is diurnal
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
y 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 Coriolis Pressure Gradient x ( x, y, t) 0 cos( ky t) wave propagates in y-direction fx gh e sea-lev decays in x-direction
Semidiurnal tide in the North Sea ( Amphidromic System ) Co-tidal lines: points with the same tidal stage (phase) Co-range lines: points with the same tidal range (amplitude) Amphidromic point Tidal propagation (anti-clockwise in N. Hemisphere)
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)
For shallow water: How can tides be predicted? Most common: Harmonic Method 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 ( t) M 2 1 A1 sin( 1t 1) A2 sin( 2t 2)... K
Useful resources for tidal data: NOAA Tides Online http://tidesonline.nos.noaa.gov/
(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)
useful tools for global tide prediction: TPXO6.2 Load Tide: Global Inverse Tide Model 1/4 x1/4 developed at Oregon State University, based on assimilation of T/P altimetry with corrections for coastal oceans. (code available in Fortran and Matlab) http://www.esr.org/polar_tide_models/model_tpxo62_load.html M2 Run Matlab Tide
Model simulations in Cook Inlet, Alaska, where the inlet size creates a perfect resonant with the tidal period (M 2 ) (Oey & Ezer et al., 2007) H=50m depth; L=250km long C=(gH) ½ = 22 m/s propagation speed Resonant: T=4L/C = ~12h (M 2 period=12.42h)
The amplification of the tides in the inlet are simulated quite well Anchorage Nikiski Seldovia Kodiak Island 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
flood m/s Velocity and tide level in Turnagain Arm ebb
Low Tide Cook Inlet, Alaska 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: Tuesday 21-November: Coastal processes I (homework#5 due) Thursday 23-November: Happy Thanksgiving Tuesday 28-November: Coastal processes II Thursday 30-November: Estuaries and models Tuesday 5-December: Review for exam Thursday 07-December: Exam#3