Ocean Tides and Sea Level - tide – “daily rise and fall of sea level” (C&D) - tide – distortions of sea by gravitational attraction of Moon and Sun on every part of Earth - tidal currents - small gravitational forces give rise to horizontal water movement - horizontal movement of water causes rise and and fall of sea level Geography “Physical Geography of the World’s Oceans”

first order explanation of tidal patterns gravitational attraction

daily tidal patterns - horizontal movement of water causes rise and and fall of sea level - can be represented as “waves” (periods ~12 or ~24 hours) - classified by period - diurnal tide (~1 cycle/day = 1 high, 1 low) - semidiurnal tide (~2 cpd = 2 highs, 2 lows) - mixed semidiurnal (2 highs and 2 lows not equal) - tidal day – time for one complete revolution of Earth beneath tidal bulges, ~24 hrs and 50 minutes

diurnal tide tidal range = high tide water height – low tide water height

semi-diurnal tide

mixed tide reference level for navigation: mean lower low water

tidal components diurnal tide + semidiurnal tide mixed tide mixed tide

Tab. 11.1

tidal patterns

Fig

daily tidal pattern details - actual tides depend on response of ocean to forcing - tidal currents can be very strong (~5 knots) - strongest currents typically near mouth of bays (i.e. SF Bay)

20 Jan Feb Mar Jan – 11 Mar spring-neap tides Santa Barbara (tidal currents a few cm/s) diurnal tide semi-diurnal tide

tide generating and raising forces - tides caused by gravitational attraction (tide generating force) - mostly by moon, but also by sun, negligible contribution from other bodies in solar system - technically, difference between gravitational force at Earth’s surface and Earth’s center gives rise to tides (tide raising forces) - gravitational force between two masses F G = G m 1 m 2 /d 2 F G - gravitational force between two masses G - gravitational constant m 1, m 2 - masses d - distance

earth & moon comparison

earth & moon distance

barycenter - the center of gravity where two or more celestial bodies orbit each other. For example, the moon does not orbit the exact center of the earth, instead orbiting a point outside the earth's center (but well below the surface of the Earth) where their respective masses balance each other.

acceleration of earth due to moon’s gravity Centripetal acceleration

centripetal acceleration and gravitational force Centripetal acceleration

centripetal acceleration and gravitational force apparent force due to centripetal acceleration Centripetal acceleration

C tide raising force = G + C G C TRF tide raising force

distribution of tide raising forces Centripetal acceleration tide raising force

Centripetal acceleration tide raising force -Tide Raising Force (due to moon) TRF m = 2 r G m m m e /d 3 (equation on page 227) F G - gravitational force between two masses G - gravitational constant m m, m e - masses d - earth-moon distance r - difference in earth-moon distance from Earth’s center

distribution of tide raising forces Centripetal acceleration tide raising force

horizontal component of tide raising force tide raising force

horizontal component of tide raising force local horizontal plane

horizontal component of tide raising force vertical component horizontal component

horizontal component of tide raising force earth’s gravitational force >> vertical component

horizontal component of tide raising force horizontal component unbalanced – produces water movement

pattern of horizontal components of tide raising forces

Tides are caused by the gravitational attraction between the Earth and other planetary bodies; primarily between the Earth and Moon, and the Earth and Sun.

maximum tide generating force a midlatitudes

equilibrium lunar tides

at equator velocity = 442 m/s to remain under moon tide wave would have to propagate 442 m/s eastward at equator

lunar day lunar day = 24 hours + 53 minutes - 2 high & 2 low tides per lunar day - called the M 2 tide with period of hours (see Table 11.1)

example of semi-diurnal tide

effect of moon’s declination (zero declination) - moon’s declination causes unequal tide heights

tidal inequality

lunar hours = large tidal inequality – diurnal tides small tidal inequality - semi-diurnal tides

example of diurnal tide

synodic month time between new moons - 2 spring-neap tide cycles/ synodic month

solar tide & spring neap cycle spring tide neap tide

earth-moon system center of mass of earth-moon system center of mass of earth (moon’s orbit around earth)

earth, moon, & sun

around sun Path of moon around earth

earth, moon, & sun around sun Path of moon around earth Path of earth around sun

earth, moon, & sun around sun Path of moon around earth Path of earth around sun

29.53 days = lunar month earth, moon, & sun around sun Path of moon around earth Path of earth around sun

earth, moon, & sun monthly (29.53 days) cycle

20 Jan Feb Mar Jan – 11 Mar spring-neap tides Santa Barbara diurnal tide semi-diurnal tide

d A = 405,800 km d P = 375,200 changing earth-moon distance TRF at perigee TRF at apogee = dAdA dPdP () 3 = 1.07 = 1.21  21% variation in TRF due to changing earth-moon distance 3

declination of moon & tidal inequality = max. angle above equator (always changing)

0 years 18.6 years 4.65 years 9.3 years moon’s changing declination

Earth

0 years moon’s changing declination (blue) (yellow)

0 years 4.65 years moon’s changing declination

153x10 6 km 149x10 6 km  ~8% variation in TRF due to changing earth-sun distance changing earth-sun distance

tidal components

distribution of tide raising forces

global distribution of tide types

consideration of ocean basin geometry and the Coliolis force results in amphidromic systems co-tidal lines amphidromic M 2 tide

M 2 amphidromic systems CCW CW tidal amplitude tidal phase

amphidromic system – M2 tide

Kelvin Wave – northern hemisphere

Kelvin waves and amphidromic systems

tidal current Coriolis pressure

Tides for Santa Monica, Municipal Pier starting with December 5, Day High Tide Height % Moon /Low Time Feet Visible F 5 High 3:37 AM Low 9:09 AM High 2:01 PM Low 9:00 PM 1.0 Tides for Santa Barbara starting with December 5, Day High Tide Height % Moon /Low Time Feet Visible F 5 High 3:57 AM Low 9:27 AM High 2:21 PM Low 9:18 PM 1.0 F 12 Low 1:50 AM High 8:16 AM Low 3:38 PM High 10:16 PM minute difference; 150km/20 min = 125 m/s; sqrt(9.8m/sx1500m = 121 m/s)

The End

Class Summary (it really does all fit together) : - position on earth, navigation - water properties - bathymetry (water depth; Geology) - sea water, solubility (Chemistry) - gasses & nutrients (oxygen & primary production; Biology) - seawater density, temperature and salinity effects - vertical structure of ocean (mixed layer, pycno, halo, and thermo –clines) - specific heat of water - solar radiation (where ocean circulation begins) - air-sea heat budget (heat from ocean drives atmosphere) - atmospheric circulation - Coriolis force - tropical cyclones and El Nino - direct wind driven Ekman flow (upper ocean mixed layer) - large scale wind driven circulation, sea level set up, subtropical gyres - western and eastern boundary currents (coastal upwelling/downwelling) - thermohaline circulation - waves (development, propagation, dissipation) - tides (forces, time scales, amphidromic systems, Kelvin waves)