Monday is an awful way to spend 1 7 of your week A clear conscience is usually a sign of a bad memory I used to have an open mind but my brains kept falling out The Surface of the Ocean 2 Tides a Equilibrium tidal theory Earth covered with a uniform and ideal layer of water geoid simplification of the relationships between the Oceans and the tiderising bodies the Moon and the Sun The Earth Moon System The system orbits the Sun around a common center of mass the barycenter within the Earth Earth s mantle radius from center OCNG 251 Oceanography Tuesday Nov 18 2008 The surface of the Ocean 2 Tides Tides a Equilibrium tidal theory b Dynamical tidal theory a Equilibrium tidal theory The rotation of the Earth Moon System creates a motion that is equal at all points within and upon the Earth Each point will also have the same angular velocity and hence a similar centrifugal force CF CF a Equilibrium tidal theory The total centrifugal force within the Earth Moon system exactly balances the forces of gravitational attraction between the two bodies so that the system as a whole is in equilibrium We should neither lose the Moon nor collide with it Tidal Producing Force TPF The tidal producing force at A is equal to the TPF at B but of opposite sign TPFx Which is approximately equal to Therefore GMm Fg CF D2 TPFA GMm2r TPFB D3 How does it compare to the Earth Earth s gravitational force Where G Universal gravity cst M Mass of the Earth m Mass of the Moon D Distance between M E Let Let s work it out GMm GMm 2 D r D2 TPF Fg GMm2r Gm2r D3 10 7 3 gM gD The Tidal Force is 10 million times smaller than Earth Earth s gravitational pull There is therefore no possible vertical movement of water Tidal Producing Force TPF Gravitational attraction and centrifugal force produce two tidal bulges bulges of water of approximately the same size positioned on opposite sides of the Earth Tidal Producing Force TPF The effects of tides are due to horizontal components tractive tractive forces forces of the tidal producing force It is the tractive forces that cause the water to move because this horizontal component is unopposed by any other lateral force Formation of the tidal bulge bulge Production of unequal tides Tide inequalities Tidal Producing Force TPF What about the Sun TPF Mass Distance 3 Sun 27 106 M Sun 390 D 3 27 106 59 106 0 46 Thus the sun has 46 the tide generating force of the Moon Tide inequalities Spring Tides Tides and Neap Tides Tides The Moon orbits the Earth 29 days and the Earth Moon system orbits the Sun 365 days 1 Tidal Day Day While the Earth rotates upon its axis the Moon is moving in the same direction along its orbit about the Earth After 24 hours the Earth point that began directly under the Moon is no longer under the Moon The Earth must turn an additional 50 minutes to bring the starting point back in line with the Moon Therefore a tidal day is not 24 hours but 24hrs and 50 min Tides arrive at locations an hour later each day Tide inequalities 2 Spring Tides Tides and Neap Tides Tides The Moon orbits the Earth 29 days and the EarthMoon system orbits the Sun 365 days Tide inequalities Tide inequalities The Moon Moon s and Earth Earth s elliptical orbits REM TPF 1 D3 Perigee vs Apogee 13 difference 27 5 days Perihelion vs aphelion 4 difference a year 3 Additional Tidal variations The Moon Moon s declination Maximum tides Moon at Perigee Sun at Perihelion Sun and Moon at zero declination Full or new Moon This condition occurs only every 1600 yrs Next time is in 3300 b Dynamical tide theory A more accurate depiction of tides is possible if we assume that the Oceans are dynamic active rather than static still Dynamical model of tides 1 Water is assumed to respond actively to the tide generating force No longer have stationary tidal bulge bulge of water that stay aligned with the Moon as the Earth rotates 2 Consider the effects due to the presence of continents and shapes of basins horizontal and vertical In the Dynamic model the Ocean basins drag drag the tidal bulges with them each day as they rotate with the Earth b Dynamical tide theory The propagation of the tidal wave is deflected due to the Coriolis Force North to the right South to the left rotary wave wave 1 The rotary wave creates high tides the crest and low tides the trough each day 2 The water surface moves up and down about a node in the center of the basin the antinodes where amplitude is greatest are located furthest away from the node The amphidromic system system a Cotidal lines lines connect points at which any given tide level is simultaneous b Corange lines lines connect points on the water surface that have equal tidal range Global Amphidromic System Lines are cotidal lines that converge on nodes amphidromic points Cotidal lines are not evenly spaced Tides are shallow water waves C gh gh 1 2 Ocean basins have uneven shapes and depths wave refraction Combined effect of all these factors produces considerable regional variation in type and range of tides Standing waves Resonance Standing waves do not move horizontally but remain stationary Guitar string The water oscillates back and forth about a fixed point Node The properties of a standing wave depend on the geometry of the basin The larger the container the longer its characteristic standing wave will take to oscillate In an open basin seiche Tides in coastal basins Tides in coastal basins will differ from large amphidromic systems Broad and symmetrical basin i e Gulf of St Lawrence Narrow elongated basin i e Bay of Fundy Comparison of Actual and Forecasted Water Levels for Galveston Spring 97 Galveston Pleasure Pier during the spring of 1999 Cox Tissot Michaud Neural Network Forecasting of Water Levels Water Level History Wind Stress History Wind Stress Forecast Barometric Pressure History Input Layer a1 ixi X1 b1 X3 b3 b1 a2 ixi a3 ixi b3 X2 b2 H t i Water Level Forecast b2 Hidden Layer Output Layer Philippe Tissot 2000 Measures water levels black Tidal chart forecasts blue 24 hour neural network forecasts red The neural network model was trained for a period of 90 days during the spring of 1997 and is applied here to a frontal passage during the spring of 1999 The accuracy of the 24 hour neural network forecast shows the ability to predict the timing and the intensity of frontal passages