# Time of day with most and least land?

1. Apr 9, 2014

### snorkack

What is the time of day when Earth´s land area is largest, and what time of day is it smallest? Or more importantly, at which position of Moon is land largest and when is it smallest?

The volume of ocean is conserved by waves and tides. The water volume that rises in high tide can only come from low tide somewhere else in the ocean at the same time.
But there is no reason for ocean to conserve area! If there is a high tide on a gently shelving coast which floods broad tidal flats, there might be at the same time low tide at the opposite coast being steep cliffs and exposing no projected area. Or depending on the width and depth of the oceans, there might be high tides on both coasts at the same time while low tide happens in deep midocean and has no shores or shoals to expose.

The phase of tide is different around the oceans - while some places have high tide, others have low tide but yet others are in middle of flood and yet others in the middle of ebb. So the area of the ocean and land should be continuously changing depending on the distribution of tidal phases and ranges around the coasts and the distribution of ground at various altitudes between low and high tides.

What is the total area of Earth surface between low and high tide?
And what is the largest and smallest amount of ground exposed by tides at any phase of tide?

2. Apr 10, 2014

### Staff: Mentor

I'm confused.

You seem to be ignoring the fact that, using your model of tidally exposed/unexposed land, that high tide happens one one side of the earth, and you forget the other side is low tide (simplified take on this). Only a small contiguous fraction of the ocean is at any full high tide at any one time, the same idea holds for low tide.

Also, tides are cyclic neap tides -> spring tides -> neap tides. So only at the height of a spring tide can the most land area be exposed by low tide on two "sides" of the Earth (actually a band), while least land area is exposed at high tide (two bulges: sublunar and antipodal). Is this what you are driving at in your question?

Plus "time" has nothing in particular to do with the biggest spring tide - just the position of the earth relative to sun and moon, plus the moon at apogee. A new moon at lunar apogee and earth apogee (closest to the sun) would be the strongest possible spring tide.

Maybe what I said is not relevant to what you are asking, so please try again.... and I just do not get it.

This explains things with pictures. http://en.wikipedia.org/wiki/Tide

Last edited: Apr 10, 2014
3. Apr 11, 2014

### micromass

Is that true? I thought the other side was on high tide too?

Anyway, are you suggesting that the tides preserve area? Because this is clearly not true. Consider an earth with an ocean of 10 km deep everywhere with only one mountain that barely sticks out of the ocean at low tide. Then as the tides change, the entire earth is covered with water. So in this earth, the area of land covered by water does change during the day. So I see no reason as to why the area of land does not change during the day in this earth.

4. Apr 11, 2014

### Staff: Mentor

No, I cited the same picture. High tides are two bulges. I thought I conveyed that idea, my bad if not.

I do not know a really good answer. My attempt at an answer:

An answer is to look for an aggregation of geographic locations like Minas Bay http://www.thehighesttides.com/ and use tide charts to figure out when low and or high tides are in majority of them. Your island example is correct in an abstract sense, but tides around islands are minimal. The Bay of Fundy can, in your abstract sense, be likened to water sloshing in a bathtub.

What we are discussing is the delta in the exposed area of the littoral (intertidal zone) http://en.wikipedia.org/wiki/Intertidal_zone worldwide.

What snorkack is actually asking I think: is there a way to determine a worlwide exposed littoral maximum and minimum and how to predict the UTC time? I cannot find an authoritative answer, but this is a really interesting question. He would require the largest possible spring tide.

Anybody?

Note:
From http://en.wikipedia.org/wiki/Tide#Phase_and_amplitude

Last edited: Apr 11, 2014
5. Apr 11, 2014

### micromass

Ah yes, then I just misinterpreted your previous answer. I already thought I misinterpreted you, but I wanted to make sure

6. Apr 12, 2014

### AlephZero

It would be interesting (and challenging) to try to estimate this for a smaller region where all the data (maps showing mean high and low water around the coast, plus relative times of high and low water) is available - e.g. the UK.

As Jim mcnamara implied, the simple model of tides on a planet completely covered with deep water is completely irrelevant to this question. For example on the east coast of the UK, the high tide is essentially a traveling wave of water traveling south into the relatively shallow water of the North Sea, and there is 5 or 6 hours time difference between high tide at the north and south ends of the coastline, over a distance of only about 1000 miles.

Not to mention the fact that at some places on earth and at some phases of the moon, there are not even two high tides per day. There may only be one, or (for example at Southampton on the south coast of the UK) four.

7. Apr 12, 2014

### Staff: Mentor

8. Apr 12, 2014

### D H

Staff Emeritus
That isn't true. There is no such thing as a tidal bulge. That was Newton's idea, and it is one of the few places where Newton was wrong. It's Laplace's dynamic theory of the tides that provides a much more accurate picture of how the tides work.

At any given time of day, one can always find a spot somewhere along the coast of the North Sea where it's high tide, and some other spot where it's low tide. The same applies to New Zealand, Patagonia, and Hudson Bay.

9. Apr 12, 2014

### micromass

Then why do you see Newton's theory everywhere? Including wikipedia and in classrooms where children are actually taught that? This is very much a surprise for me.

10. Apr 12, 2014

### D H

Staff Emeritus
Lies to children, maybe?

Newton's tidal theory does yield the correct tidal forcing functions. It does not yield the correct responses to these forcings. I've posted on this before, multiple times. Here's one:

11. Apr 12, 2014

### AlephZero

I wonder if the experimental data Newton quoted in "Principia" was selectively chosen to support his theory, or whether being honest with the limited amount of data he actually new. An uncritical reading certainly gives you the idea that he had explained "everything".

Of course the seafarers of that time would have known a lot of accurate empirical data about tides (especially around an area like the North Sea), but scientists didn't have much access to that level of information.

12. Apr 15, 2014

### abitslow

DH. thanks for tutorial! I didn't realize the extent of the mismatch between tidal forcing and real world results.
How significant are the contributions of SST, wind and currents to the resulting water level? Surely, ice-pack complicates this; are seasonal influences significant? In my ignorance, I don't even know how wave action on the shoreline is incorporated into determination of the tide "line".
I got my info from Wikipedia, it is too bad that that presentation isn't as clear about how poorly the Newton mean depth model fits.
-=-=-=-
Would the most correct answer to snorkack's question be that the total area exposed at a given instant is most likely chaotic and unpredictable? Would it be better to consider the (19 year) mean lower low and higher high?

13. Apr 15, 2014

### davenn

DH
Also a thankyou from me
I had no idea there was a better explanation

cheers
Dave

14. Apr 16, 2014

### D H

Staff Emeritus
The tidal forcing functions that Newton derived are correct. It's the overly simplistic two bulge equilibrium response to those forcings that is incorrect.

With regard to understanding the tides, here are a couple of online resources. There are plenty more.
http://www.oberlin.edu/faculty/swojtal/SFWpage/161Stuff/161Lect17/sld001.htm
http://faculty.washington.edu/luanne/pages/ocean420/notes/tidedynamics.pdf

With regard to how tides are measured, see http://tidesandcurrents.noaa.gov/levelhow.html.

Physicists and engineers study the response of a damped oscillator to oscillating inputs. Did you ever make waves in the bath tub when you were a kid? (I got in a good deal of trouble for soaking the floor.) The oceans are big huge bathtubs with complicated responses to driving inputs, and the driving inputs have a number of different characteristic frequencies. The response to any one of these input frequencies will be an amphidromic system. For example, here's the response to the M2 (principal lunar semi-diurnal) component of the tidal forcing function:

There are curved white lines emanating from the the centers of the dark blue areas in this image. Those centers are "amphidromic points", places where the response to the roughly twice daily component of the tidal forcing function due to the Moon is zero. Those curved white lines are cotidal lines, places where the phase delay to the M2 tidal component are equal. If the M2 tidal component was the only thing that caused the tides, high and low tide would occur at the same time along points on one of those cotidal lines. The response to other driving frequencies (there are a number of them) will be rather different, but it's the twice daily response to the Moon, that governs the tides at most places on the Earth covered by water.

Here's the M2 tidal response in the North Sea:

The red points in this image are the amphidromic points. There are two in the North Sea and (at least in this image) one just on-shore in Norway (others have that point just off-shore). The cotidal lines are in red, spaced by about one hour. The blue curves represent tidal responses. From this image one can see that its always high tide somewhere in the North Sea.

Explaining the tides becomes rather ad hoc at the local level. If you look for a tidal station (e.g., Key West, Florida), you'll inevitably see harmonic constituents to a number of different aspects of the overall tidal forcing function. For example, at Key West, Florida, the lunar semi-diurnal (M2) tidal coefficient is the dominant cause of the tides, but there are several other frequencies that come into play. Understanding this as a physicist is easy: Just think of it in terms of Fourier analysis.

With regard to your original question, snorkack, I suspect it was based on the idea that the equilibrium tidal bulge is what governs the tides.

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Last edited: Apr 16, 2014
15. Apr 18, 2014

### snorkack

No. See the quote from the first post:
If there were an equilibrium tidal bulge, the phase of tides across the ocean or in the middle would depend only on the width of the ocean and be independent of the depth of the ocean, as I mentioned from the start.