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Robert Tulip
2015-Jul-18, 10:33 AM
In wondering about how the positions of the sun and moon drive the tides, I downloaded data from the Australian Bureau of Meteorology of tide levels in Sydney Harbour for 2014. I converted the data from the pdf (http://www.bom.gov.au/ntc/IDO59001/IDO59001_2014_NSW_TP007.pdf) into excel (http://rtulip.net/yahoo_site_admin/assets/docs/Sydney_Tides_2014.19831632.xlsx) and made the attached chart (http://rtulip.net/yahoo_site_admin/assets/images/Sydney_Tides_2014.19831408_std.png). There are a number of interesting patterns which I would like to understand.

Why is there such a clear six monthly rather than annual pattern around the apsidal axis, ie, Why are the biggest tides at both perihelion and aphelion (January and July) instead of on a twelve month cycle around the perihelion?

Why does the six monthly pattern appear to shift from full moon to new moon?
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grapes
2015-Jul-18, 01:20 PM
In wondering about how the positions of the sun and moon drive the tides, I downloaded data from the Australian Bureau of Meteorology of tide levels in Sydney Harbour for 2014. I converted the data from the pdf (http://www.bom.gov.au/ntc/IDO59001/IDO59001_2014_NSW_TP007.pdf) into excel (http://rtulip.net/yahoo_site_admin/assets/docs/Sydney_Tides_2014.19831632.xlsx) and made the attached chart (http://rtulip.net/yahoo_site_admin/assets/images/Sydney_Tides_2014.19831408_std.png). There are a number of interesting patterns which I would like to understand.

Why is there such a clear six monthly rather than annual pattern around the apsidal axis, ie, Why are the biggest tides at both perihelion and aphelion (January and July) instead of on a twelve month cycle around the perihelion?

Probably has nothing to do with perihelion at all. The tides are mostly lunar. Perihelion is close to winter solstice, when the new moon is higher over head (over Sydney). Aphelion is close to summer solstice, when the full moon is higher over head.


Why does the six monthly pattern appear to shift from full moon to new moon?
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a1call
2015-Jul-18, 09:13 PM
Perhaps what you are observing is the interference frequency between the frequencies of tides governed by the moon and the sun.
Generally such modulation has a frequency that is equal to the higher frequency minus the lower frequency.

Robert Tulip
2015-Jul-19, 01:21 AM
Probably has nothing to do with perihelion at all. The tides are mostly lunar. Perihelion is close to winter solstice, when the new moon is higher over head (over Sydney). Aphelion is close to summer solstice, when the full moon is higher over head.


Perhaps what you are observing is the interference frequency between the frequencies of tides governed by the moon and the sun. Generally such modulation has a frequency that is equal to the higher frequency minus the lower frequency.
Thanks both.

The interference frequency is just part of it. If the tides were only driven by the moon there would be equal amplitude through the month and the year. The changes over each month are synodic, with spring tides when the moon is on the earth-sun axis and neap tides when the moon is orthogonal to the earth sun axis as animated by noaa (http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide06a.html). (text below)

Over the year, the pattern looks to match the apsides rather than the solstices. The perihelion is now approaching Epiphany (actually 4 Jan (http://www.observingstars.com/perihelion_aphelion.htm)) and was at the solstice in 1246 AD (http://vanwardstat.com/climate.htm), advancing one day every 59 years. The graph shows the turning points are well after the solstices.

It seems weird to me that when the earth is furthest from the sun in July the tides are at their biggest, because the gravity is less.

The natural production of the week by the orbital patterns is simple, but what I don’t understand is why from April to October the biggest tides are at full moon while from November to March the biggest tides are at the new moon, or why for the two halves of the year the tidal patterns mirror each other at swapped moon phases. The BOM predictions (http://www.bom.gov.au/oceanography/projects/ntc/nsw_tide_tables.shtml) are produced by a mathematical formula since the Bureau has the same charts for 2015 and 2016 linked below. It would be interesting to compare this predictive data against observation.

Links
http://www.bom.gov.au/ntc/IDO59001/IDO59001_2016_NSW_TP007.pdf
http://www.bom.gov.au/ntc/IDO59001/IDO59001_2015_NSW_TP007.pdf



NOAA: Together, the gravitational pull of the moon and the sun affect the Earth’s tides on a monthly basis. When the sun, moon, and Earth are in alignment (at the time of the new or full moon), the solar tide has an additive effect on the lunar tide, creating extra-high high tides, and very low, low tides — both commonly called spring tides. One week later, when the sun and moon are at right angles to each other, the solar tide partially cancels out the lunar tide and produces moderate tides known as neap tides. During each lunar month, two sets of spring and two sets of neap tides occur (Sumich, J.L., 1996).

Robert Tulip
2015-Jul-19, 02:26 AM
I have now looked at the BOM 2016 chart and it does show the highest tides in June and December. So I have to take back my assumption from the 2014 chart that the annual pattern is driven by the apsides. Grapes may be right.

grapes
2015-Jul-19, 03:12 AM
The interference frequency is just part of it. If the tides were only driven by the moon there would be equal amplitude through the month and the year.

Definitely not.

The moon shares the same orbit as the sun, more or less, and it is the principal driver of the tides, obviously. Sometimes, when the moon is full, it is lower on the horizon just like the sun in winter. That would make the tide less at the spot that you are observing the tide (the principle component of the tide-raising equipotential surface is shaped like two periods of the cosine curve wrapped around the world and then rotated, so the highs are directly under and opposite the moon)

You're analyzing data from a single station and a single year and generalizing it to the whole world.


The changes over each month are synodic, with spring tides when the moon is on the earth-sun axis and neap tides when the moon is orthogonal to the earth sun axis as animated by noaa (http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide06a.html). (text below)

Over the year, the pattern looks to match the apsides rather than the solstices. The perihelion is now approaching Epiphany (actually 4 Jan (http://www.observingstars.com/perihelion_aphelion.htm)) and was at the solstice in 1246 AD (http://vanwardstat.com/climate.htm), advancing one day every 59 years. The graph shows the turning points are well after the solstices.

That year the full moon/new moon probably did not line up with the solstices.


It seems weird to me that when the earth is furthest from the sun in July the tides are at their biggest, because the gravity is less.

And it's the sun, whose distance only varies +-2% :)


The natural production of the week by the orbital patterns is simple, but what I don’t understand is why from April to October the biggest tides are at full moon while from November to March the biggest tides are at the new moon, or why for the two halves of the year the tidal patterns mirror each other at swapped moon phases. The BOM predictions (http://www.bom.gov.au/oceanography/projects/ntc/nsw_tide_tables.shtml) are produced by a mathematical formula since the Bureau has the same charts for 2015 and 2016 linked below. It would be interesting to compare this predictive data against observation.

I think my explanation accounted for that as well. Although, I haven't actually checked it against the moon and your tide chart.

Robert Tulip
2015-Jul-19, 06:42 AM
Thanks Grapes, I get your explanation now I think.

In summer, the ecliptic is high in the day and low at night. So when the moon is close to the sun in summer it travels overhead high, and when it is opposite the sun it travels overhead low.

In winter, the ecliptic is low in the day and high at night. So when the moon is close to the sun in winter it travels overhead low, and when it is opposite the sun it travels overhead high.

So in winter the biggest tides are at full moon as the moon goes overhead at night, and in summer the biggest tides are at new moon as the moon goes overhead through the day.

Why would that not be a general statement, with the exception of places with single or no tides?

grapes
2015-Jul-19, 10:36 AM
So in winter the biggest tides are at full moon as the moon goes overhead at night, and in summer the biggest tides are at new moon as the moon goes overhead through the day.

Why would that not be a general statement, with the exception of places with single or no tides?
It's more or less what I said, but the generalization was "It seems weird to me that when the earth is furthest from the sun in July the tides are at their biggest, because the gravity is less." When it's summer in Sydney it's winter in New York so New York's pattern is going to be different.

Interesting question though.

Places with single tides are sometimes complicated by resonances local geography, but I haven't looked into that much.

Cougar
2015-Jul-19, 11:05 AM
As grapes says, the tides are mostly lunar. But you seem to be monitoring the effect with respect to the earth-sun distance. The earth-moon distance varies between 363,104 km and 405,696 km. Throw that monthly variation into the annual mix, and I believe you get your pattern.

Robert Tulip
2015-Jul-19, 01:02 PM
I have added tide charts for 2015 (http://rtulip.net/yahoo_site_admin/assets/images/Sydney_Tides_2015.19954248_std.png) and 2016 (http://rtulip.net/yahoo_site_admin/assets/images/Sydney_Tides_2016.19954352_std.png), including on the Sydney Tide Spreadsheet (http://rtulip.net/yahoo_site_admin/assets/docs/Sydney_Tides_2014.19954200.xlsx).


As grapes says, the tides are mostly lunar. But you seem to be monitoring the effect with respect to the earth-sun distance. The earth-moon distance varies between 363,104 km and 405,696 km. Throw that monthly variation into the annual mix, and I believe you get your pattern.
Unfortunately no. This year the super moon (nearest perigee) is on 28 September 2015, while the Micro Moon (nearest apogee) was on 6 March 2015. But the September full moon tide is the smallest for the year. The perigee does not mark the biggest tide.

In 2014, on July 12th and Sept 9th the Moon became full on the same day as perigee. On August 10th it became full during the same hour as perigee. The July full moon tide was the biggest for the year. In 2016 perigee full moon is in November, while the biggest tides are in June and December.

https://en.wikipedia.org/wiki/Lunar_precession explains that the long axis (line of the apsides: perigee and apogee) of the Moon's elliptical orbit precesses eastward by one full cycle in 8.85 years. This means that each year the date of the nearest to perigee full moon is about one month later.
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Hornblower
2015-Jul-19, 02:12 PM
We need to remember that the dynamics of the tides are not as simple as the strength and direction of the combined gravitational gradient at any given moment. There is a lot of water sloshing around and constituting a driven oscillator, and it does not respond instantly to changes in the gradient. I will leave it to real experts to elaborate.

Jeff Root
2015-Jul-19, 07:13 PM
Because of the sloshing, I would expect huge differences in
both height and time between tides along northern or southern
coasts compared to tides along eastern or western coasts, as
well as huge differences between eastern and western coasts.

And even bigger differences due to differences in the shape
of the sea bottom, bays, and channels.

-- Jeff, in Minneapolis
.

a1call
2015-Jul-19, 08:31 PM
So in winter the biggest tides are at full moon as the moon goes overhead at night, and in summer the biggest tides are at new moon as the moon goes overhead through the day.

Lunar phases are a function of Sun-Earth-Moon alignment and not the moon being overhead.
I think what Grapes was referring to is Lunar-Altitude.
This is a valid factor since Earth is a 3-D Sphere rather than a circle. When Moon has a higher altitude where you are then you are closer to the apex of the tide and thus will experience higher tides.
Indeed there seems to be a correlation between the lunar high altitudes in Sydney in 2014 and your chart.


January 1 - 74.9°
January 28 - 75.2°
February 24 - 75.1°
March 23 - 74.8°
April 20 - 74.8°
May 17 - 74.9°
June 14 - 74.8°
July 10 - 74.9°
.....

grapes
2015-Jul-19, 09:28 PM
Lunar phases are a function of Sun-Earth-Moon alignment and not the moon being overhead.
I think what Grapes was referring to is Lunar-Altitude.

To be fair, I think that's what Robert was referring to as well. Overhead vs on-horizon, or lunar altitude as you say

Cougar
2015-Jul-21, 01:16 PM
This year the super moon (nearest perigee) is on 28 September 2015, while the Micro Moon (nearest apogee) was on 6 March 2015. But the September full moon tide is the smallest for the year. The perigee does not mark the biggest tide.

Not alone, but in conjunction with the sun-moon alignment. The lowest September tide was on the 15th, two weeks before lunar perigee. I'm not giving up on my theory yet. :)

grapes
2015-Jul-21, 01:29 PM
Not alone, but in conjunction with the sun-moon alignment. The lowest September tide was on the 15th, two weeks before lunar perigee. I'm not giving up on my theory yet. :)
In order to be most effective at a particular spot on earth though, the geometry only gives the "highest tides" to the sublunar/subsolar points (when they're aligned) and "lowest tides" to a band 90 degrees away. It's not necessarily going to hold true at a single specific recording station.

George
2015-Jul-21, 04:35 PM
IIRC, tidal strength is 1/3 for the Sun, 2/3 for the Moon, varying with other factors noted already.

Interestingly, Galileo recognized the sloshing effect but muffed it thereafter.

a1call
2015-Jul-21, 05:09 PM
While sun and moon governed tides have constructive/destructive results in overall terrestrial tides, per most locations the effects are dwarfed by the more prominent monthly lunar altitude cycles (as is clearly shown by Robert's chart). Again this is due to cyclic variation in proximity of each location to the apex of the total terrestrial lunar tide. In other words each point along a latitude will have cyclic high-and-low high tides as the highest point of the tide on earth approaches and distances from them periodically at about 28 day cycles.

Robert Tulip
2015-Jul-26, 12:14 PM
Here are some additional charts that I have derived from the data in the Sydney Tide Charts for 2014, 2015 and 2016. They display the fourfold sine wave patterns of the tidal cycle against the synodic month, the range of tide times against lunar phases over these three years, and the correlation between spring tides and perigee (which appears to be surprisingly inexact).

My understanding of this is that "sloshing" of the driven oscillator explains the three hour delay between dawn or dusk or culmination and tidal phase. Sloshing does not simply explain the lack of simple correlation between the perigee and the pattern of spring tides.

Lunar altitude is a semi-annual factor not a monthly factor in its impact on tidal patterns.

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grapes
2015-Jul-26, 02:05 PM
The period between perigees is 27.55 days (moon's orbital period is 27.32 days but there is a precession of perigee), the period between full moons or new moons (when spring tides occur) is 29.53/2 days, so you should kinda expect them to not be correlated.

What do the elongated ellipses in your graph (third) represent?

a1call
2015-Jul-26, 02:55 PM
Lunar altitude is a semi-annual factor not a monthly factor in its impact on tidal patterns.



I don't think so.
Here are a few consecutive (extremes ie highest and lowest daily highs) daily highs for 2014 for Sydney which shows its monthly and the most significant factor as it corresponds to the most major value changes in your original chart.

January 28 - 75.2°
February 9 - 36.1°
February 24 - 75.1°
Match 9 - 36.4°
March 23 - 74.8°

ETA My source for the lunar altitude values is an app called LunaSolCal.

ETA II The highest point of the tide on Earth at any given time is where the moon is directly overhead i.e. Has a lunar altitude of 90° (which has nothing to do with the full moon). Sydney's monthly cycle of approaching and distancing from this highest tide point (on earth) is the most significant factor in Sydney's daily tides (among other factors such as destructive/constructive solar tides, geographic features, water temperature, tide momentum, ...).

Jeff Root
2015-Jul-27, 12:16 AM
I see that the dates at the bottom of the third chart are
31 to 32 days apart. They almost match up with the highest
tides connected by the heavy curve at the top -- but not quite.
What are those dates?

-- Jeff, in Minneapolis

Robert Tulip
2015-Jul-27, 02:54 AM
The period between perigees is 27.55 days (moon's orbital period is 27.32 days but there is a precession of perigee), the period between full moons or new moons (when spring tides occur) is 29.53/2 days, so you should kinda expect them to not be correlated.
What do the elongated ellipses in your graph (third) represent?

Every seven months the perigee aligns to a full moon or new moon. These are the elongated ellipses in the graph, with the darker ellipses showing a perigee new moon and the lighter ellipses showing a perigee at full moon, drawn from the referenced source fourmilab.ch (sorry for not labelling).

The expected correlation would be that the highest spring tide would occur when perigee is either at full moon (the so-called super moon) or at new moon. However, there appears to be a discrepancy, as indicated by the line showing highest tides at full or new moon at the top of the chart, as follows:


Jan 2014: Perigee at new moon is when highest tide is decreasing
Jun-Sep 2014: Perigee at full moon is when highest tide is decreasing
Jan-Feb 2015: Perigee at new moon is at small highest tide peak (<2m)
June 2015: same tidal peak as Jan-Feb 2015, but no perigee
July-Sep 2015 – Small full moon tidal peak similar to Jan 2015
Dec 2015: Tidal peak not at perigee
March-May 2016: Tidal peaks rising at perigee new moon
June 2016: Tidal Peak not at perigee
Nov-Dec 2016: Perigee at full moon when highest tide is increasing.


These data show there is obviously a strong correlation between perigee and spring tides, but perigee does not seem to be the only factor.


I don't think so.
Here are a few consecutive (extremes ie highest and lowest daily highs) daily highs for 2014 for Sydney which shows its monthly and the most significant factor as it corresponds to the most major value changes in your original chart.

January 28 - 75.2°
February 9 - 36.1°
February 24 - 75.1°
Match 9 - 36.4°
March 23 - 74.8°

ETA My source for the lunar altitude values is an app called LunaSolCal.

ETA II The highest point of the tide on Earth at any given time is where the moon is directly overhead i.e. Has a lunar altitude of 90° (which has nothing to do with the full moon). Sydney's monthly cycle of approaching and distancing from this highest tide point (on earth) is the most significant factor in Sydney's daily tides (among other factors such as destructive/constructive solar tides, geographic features, water temperature, tide momentum, ...).


https://en.wikipedia.org/wiki/Tide#Lunar_altitude appears to incorrectly define lunar altitude as “The changing distance separating the Moon and Earth.” I used this definition in preparing my previous comment.

Thanks grapes and a1call.

a1call
2015-Jul-27, 03:27 AM
My pleasure Robert,
That is the correct definition of geometric altitude.
The astronomical definition is:


The altitude of a point on the celestial sphere is defined as the angular distance measured positive toward the astronomical zenith from the astronomical horizon along the great circle passing through the point and the astronomical zenith.


https://www.google.ca/?gws_rd=ssl#q=define:astronomical+altitude

A more complete definition is here:

http://heavens-above.com/glossary.aspx?term=altitude

grapes
2015-Jul-28, 10:13 AM
These data show there is obviously a strong correlation between perigee and spring tides, but perigee does not seem to be the only factor.

You have to be careful in how you phrase that.

Perigee will obviously contribute to a stronger tide, there's no denying that when the moon is closer to the earth, the tidal effect is greater.

But spring tides can occur at ninety degrees away from perigee, so that is why there is very little correlation between spring tide and perigee. Your graph with the line (the irregular wave connecting the extremes of the spring tide) shows only the perigees that match spring tide--and I still don't understand the method. Why do you indicate those perigees, as events, with elongated ellipses that overlap a few *month*s of data?

Or am I misunderstanding that graph still?

Robert Tulip
2015-Jul-30, 12:15 PM
Here are a few consecutive (extremes ie highest and lowest daily highs) daily highs for 2014 for Sydney which shows its monthly and the most significant factor as it corresponds to the most major value changes in your original chart.
January 28 - 75.2°
February 9 - 36.1°
February 24 - 75.1°
March 9 - 36.4°
March 23 - 74.8°

My source for the lunar altitude values is an app called LunaSolCal. The highest point of the tide on Earth at any given time is where the moon is directly overhead i.e. Has a lunar altitude of 90° (which has nothing to do with the full moon). Sydney's monthly cycle of approaching and distancing from this highest tide point (on earth) is the most significant factor in Sydney's daily tides (among other factors such as destructive/constructive solar tides, geographic features, water temperature, tide momentum, ...).

I have checked this data and do not agree with your claims here regarding the priority of lunar altitude over the synodic month. The OP chart shows the following timings. The attached more detailed chart shows the following relationships at these dates in 2014:

January 28 - 75.2° 3 days before highest tide
February 9 - 36.1° Lowest high tide
February 24 - 75.1° 5 days before highest tide
March 9 - 36.4° 1 day before lowest high tide
March 23 - 74.8° 7 days before highest tide

The lunar altitude is the angle of the moon above the horizon at meridian. The highest and lowest lunar altitudes are two weeks apart, and rotate around the lunar and tidal phases with the ecliptic as a function of the solstices and equinoxes. With this Sydney example, at the winter solstice in June, highest lunar altitude is at full moon. This is because in the southern winter the northern lower half of the ecliptic goes across the sky in the day with the sun, and the southern higher half goes across the sky at night with the moon. Similarly, at the summer solstice in December the highest lunar altitude is at new moon. (This pattern appears in 2014 but it seems not in 2015 and 2016, perhaps because of the influence of the perigee cycle?)

The data a1call has provided is at the autumn equinox (remember we are talking southern hemisphere here). So as expected, the highest lunar altitude at the March equinox is at the third quarter, precessing by about two days per month towards its alignment with the full moon in winter. This lunar altitude relation with the seasonal cycle drives the oscillation of highest tides between full moon in winter and new moon in summer. The influence of lunar altitude on the tides is a function of the solar year.

Overlaid on this seasonal cycle there is also the nine year lunar perigee cycle which has a seven month pattern, driven by the periodic conjunction of perigee and full or new moon.

My plan now is to do a Fourier Transform of the tidal wave function over 4096 data points from 1/1/14 to 25/11/16. I expect the spectral analysis to show power spikes driven by the 25 hour lunar day, the solar day, the synodic month, the solar year and the perigee cycle.
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Jeff Root
2015-Jul-30, 01:08 PM
I apologize if I'm being very stupid, but I still don't understand
the 31-32-day numbering across the bottom of the third chart
in post #19. Why 31-32 days? Is it a resonance of two other
periods?

-- Jeff, in Minneapolis
.

Robert Tulip
2015-Jul-30, 11:54 PM
Jeff, these charts are all produced in excel, which automatically creates the markers for the axes based on size of font, etc. There is no significance to the 31-32 day gap, as I used the dates just to show the march of time over the three years. As I explained, the large light and dark ovals indicate the times of year when the new or full moons are at perigee, so for example this includes the supermoon next week.