2011

The explanationof tides in 11 stepsMarc PhilippartRijkswaterstaat

2011Rijkswaterstaat

Generation of tides

• main drivers are Moon and Sun• explaining the tides in 11 steps

2011Rijkswaterstaat

Step 1: gravity force of moon

• No continents, just water (equilibrium tide)• Only influenced by attraction of the moon

moonearth

2011Rijkswaterstaat

Step 2: centrifugal force

• If this was the only force, the moon would crash on the earth• Also centrifugal force due to rotation around centre of gravity

2011Rijkswaterstaat

Step 3: combined forces

gravity

centrifugal

combination

2011Rijkswaterstaat

Step 4: twice a day?

• twice a day would mean every 12 hour• however, we see 12 hour and 25 minutes• where is this ‘error’ of 50 minutes a day ?• moon travels around earth in 27.32 days• after one full earth rotation• moon travels also 13 dgr

t=24h5023h56

t=o

13º

54 min.

2011Rijkswaterstaat

Step 5: the sun

• sun acts the same as moon• amplitude ca 25% of moon• rotation of earth: 23 h 56 minutes

t=o

(by definition)t=24h00

1º = 4 min.23h56

eg. at 12h, sun in South

after 23h56 + 4 min, sun in South

2011Rijkswaterstaat

Step 6: the sun moon interaction

• effect of tide by moon

2011Rijkswaterstaat

Step 6: the sun moon interaction

• sun and moon work together: Spring Tide• during full moon and during new moon

2011Rijkswaterstaat

Step 6: the sun moon interaction

• sun and moon work opposite: Neap Tide• firts quarter and last quarter of the moon

2011Rijkswaterstaat

Step 7: diurnal inequality

• inequality due to the declination of earth axis

23,5ºdeclination

equator

rotationof earth

h2

h1

equator

rotationof earth

2011Rijkswaterstaat

Step 7: diurnal inequality

• spring tide neap tide cycle sensitive

2011Rijkswaterstaat

Step 8: variation in driving forces

• distance moon to earth varies (ellipsoid, 27,55 day)• direction ellipsoid varies in 8,85 yr.• distance sun to earth varies• plane of moon varies 5 degrees around 23,5 (18,61 yr.)• plane of sun varies with the precession (25.765 yr.)

2011Rijkswaterstaat

Step 9: continents & coriolis

• the equilibrium tide runs around the southern hemisphere• further it travels around the world with a delay• tides in the north sea are more than 2 days old• the coriolis force (due to rotation of the earth) influences the tides

2011Rijkswaterstaat

Step 9: continents & coriolis

2011Rijkswaterstaat

Step 10: non-lineair effects

• due to bottom friction the tide will deform• allthough the driving forces consist of 2 forces, called M2 (moon) and S2 (sun), at our coast a set of nearly 200

components are needed to reconstruct the tide

2011Rijkswaterstaat

Step 11: wind effects

• due to meteorological influences the actual tide differs• surge bij NW storm• negative surge by Easterly winds

2011Rijkswaterstaat

2011Rijkswaterstaat

Forecast of tides

• there are two ways of forecasting (predicting)• 1: harmonical analyse and composing• observed tide > decomposing > reconstruction• 2: modelling• calibrating model > meteo input > result

2011Rijkswaterstaat

harmonic analyse of tideobservedpredicted

decomposition continuation of decomposition