More Probability Distributions of Tides

David Pugh, in Sea Level Science introduces probability distribution diagrams as an analytical tool.  The beeswarm plots from a couple of posts ago are another way of representing distributions along one axis.  The idea is to plot a span of data (or in my case, usually predictions) along a single axis.

What does a probability distribution tell us?  It can give us an idea how many hours per day an organism in a particular zone will be exposed to the air.  It would be more interesting to know the tides of exposure to sunlight.  For corals this is essential.  David Pugh says that the S2 harmonic constituent can give us an idea without graphs.  This is a subject for a future project.

For how, the following is an effort from several months back, breaking down the probability distributions of heights month by month, for San Francisco's venerable tide gauge (thought these may be predictions).  I wonder what this has to say in comparison with St. Petersburg, Florida's beeswarm plot.  Obviously, it's impossible to compare them well using these two distinctly different methods.  The top row shows frequency distributions for January, February, and March, and so on in the other rows; all graphs are from predictions. 

One thing I noticed was a similarity of the distributions for June and December, around times of Solstices.  The same may be said for the months of the Equinoxes, March and September.  I now want to see another graph, the specific one-day distributions for the exact days of Solstices and Equinoxes.  Other parameters, like apogee and perigee, perihelion and aphelion, lunar declination have important effects.

Comparing Two Sites (Full year of predictions for each)

San Simeon is on the exposed California Coast. 
Port Chicago some 30 miles up the Northern Reach of San Francisco Bay, in Suisun Bay.

Months of Solstices and Equinoxes, 

Chuuk Lagoon

 

December

March

June

 

September

 

Equinoxes are in March and September.  Solstices are in December and September.  Why do the Equinoxes resember one another?  Why do the Solstices resemble one another?  ???  

 

Elkhorn Slough December, March, June, and September

The differences between Elkhorn Slough and Chuuk Lagoon are notable.

March

December

June

September

 

 

 

 

 

 

 

 

 

 

 

Another distribution diagram: a continuous distribution curve.

 This time, each month is traced in a different color.  This is experimental; I did not keep a record of the colors for each month!

 And another way to represent similar data, with transparent fill:

Redwood City Tide Station

This morning I visited the Redwood City Tide Station.  Awesome.

The business end.

A Beeswarm plot, for St. Petersburg, Florida

I'll try any kind of graph.  Distribution frequency plots are described in Pugh's 1984 Sea Level Science.  I saw a beeswarm plot, don't remember where; it seemed an interesting way to do a distribution frequency plot.  

In a beeswarm plot, data is plotted along a single axis, in this case, tide water levels.  No overlapping points are allowed; each overlapping point is "jittered" off to one side of the other point(s) at the  

Are beeswarm plots informative?  i tried.  As usual I had to fiddle (speaking of which, a "violin plot" does something similar.  Perhaps I'll try one).  The "beeswarm" package for R makes production of these plots pretty easy.  My first attempt suggested to me that a smaller amount of data might be more manageable. Eventually, something like this appeared, for St Petersburg, FL:

A first approximation: Predictions for June 17--28 

Does the Moon figure into the distribution of water levels.  I think this information is useful when considering intertidal zonation.  The following is a beeswarm plot for  hourly predictions for June, from New Moon to First Quarter June 17--26).  What, then, is this prominaent horizontal feature

 Comparing with a plot for a couple of these days

Below, the same plot has been placed together with a plot of the tide at St Petersburg for two days in this period of time.  The hold ups seem to be encoded as the horizontal line

 

A Month at a Time

As a first approximation, I wondered whether it would be useful to divide time into quarter moons.  The first reason: a useful number of points plotted on a single vertical beeswarm axis looks stupidly cluttered.  Maybe it would be easier to plot short periods of time, like a month?  No, a month was waaay to cluttered.  A week looked alright.

 A month at a time 

So I used quarter moons.  I have some misgivings about this choice.  Next time I may CENTER the time division on a full moon, quarter moon, or new moon.  Here, while it looks interesting, I'm pretty sure that much information about the actual full or new moon's influence.

I like it.  It says something.  The tides of St Petersburg exhibit some interesting quirks, reflected in these plots.

These are Beeswarm plots, a kind of univariate distribution plot, like histograms, and maybe a stem and leaf diagram of a kind.  Each vertical plot represents a week (or so), hourly predictions for a quarter of the moon.  Black, for example, represents the span between New Moon and First Quarter. 

Maybe an inverted colorscheme would look better on the screen.  The following was inverted in The Gimp, and exported as PNG, from a PDF. 

Each vertical plot is a distribution plot, for one Quarter of a Lunar Cycle.  The first one, in January, represents the period between NM and First Quarter (Q1), then Q1-> FM; FM -> Q3; Q3->NM, etc.  48 of these quarters are represented, from January into December of 2019.

These are predictions, from Xtide.

I don't know why almost everywhere I graph a tide, no matter how, something interesting pops up!  What are we visualizing here? 

Seasonal Distribution of the Time of Day of HIgh and LowTides

ERRATUM:  A previous post of a graph for Kawaihae is in serious error: the timezone was not accounted for.  Correction in preparation.


The following graphs are the result of my attempt to visualize the way that lower low tides and higher high tides are distributed in time.  What do they say about the tides?  Especially striking to me is their overall shapes.  H. A. Marmer's study of the various nature of mixed tides is pertinent.

Marmer, Fig. 3

"The mixed type of tide merits more detailed consideration since this type comprises a great variety of different forms.  These different forms may, however, be grouped into three large classes, namely those which feature the difference between the morning and afternoon tides chiefly in the low waters, those which feature it chiefly in the high waters, and those which feature it in approximately equal degree in both the high and low waters."  

H. H. Marmer. 1931.  Tidal Characteristics from Harmonic Constants.  The International Hydrographic Review 2. 

In the above graph, Marmer refers to Seattle, Honolulu, and San Diego as examples of these three categories of tide regime.  

The making of the following began from a desire to understand the distribution of higher and lower tides from a seasonal perspective.  Perhaps they will also do, to elaborate on the theme of Marmer.  The distribution of times over the seasons seem remarkably bimodal.  The different forms of these three mixed tides is striking.  There is much more to Marmer's analysis, perhaps best left for another time.  

Seattle, WA: Differences in Low Waters.

Transitional between Seattle and La Jolla.

Differences in both high and low waters

A Gem of Untold Worth: Pages Torn out from Albert Defant's Physical Oceanography, V.II.

I have tried to at least review all the literature I can lay my hands on, about anything having to do with tides.  Several books, and a number of papers stand apart.  Another time, I plan to generate a list.  Real Soon Now (TM).  Among books, one of the classic textbooks of Oceanography is the 1961 two-volume Physical Oceanography, by Albert Defant. In Volume 2 are found lengthy treatments of various aspects of tides.  It is available in English translation on Archive.org, in various formats: Defant. Physical Oceanography, V. II.  No other book has gone to that much extent, particularly in discussion of the features of tides of various locations around the world.

As I prefer printed books, I checked volume II out from the UC Berkeley Libraries.  A troubling revelation was received.

It has been my unfortunate observation that not all academics are community minded.  At UCSB, for example, many of the previously numerous volumes dealing with fishing have been stolen or otherwise have disappeared.  Of those that remained as of about 1983-1984, I found several with pages removed, presumably because of their overriding usefulness to someone---hopefully who would make a contribution to the greater body of knowledge, to compensate for this selfish act.

More distressing was to find pages torn out in exactly two places in one copy of Defant's volume II from the UC Berkeley Library. These pages I was able to locate in the Internet Archive (archive.org), as *tif files; I printed these pages out and placed them in the books so they would be available to anyone who referred to this book in the future---possibly me!  

Bookmarks left in Defant by an astute reader

Beyond the thoughtless act of removing these pages, the perpetrator left behind a bookmark: once I had noticed these pages were missing: the content of the missing pages was astounding.  May I turn a blind eye to copyrights?  Well, I think this book is no longer covered by those draconian and troublesome restrictions; I shall present the missing pages here.

The first page was an accounting of Harmonic Constituents. 

The first of these two pages is the most important: a listing of Principal harmonic components (constituents).  All of these images are *.tif files.  You may click on them to enlarge them, and they are printable.

 2.  Pages later in the book: remarkable!  How to interpret the above.

 I do not know who removed these pages.  One can appreciate their unique value, even from the distance of over 50 years.

In the Caroline Islands, experts value their knowledge---particularly of navigation, fishing, or cures---highly.  They fear to share it with others, lest it be squandered, and their personal power diminished.  A traditional expert will choose very carefully whom he may train in his knowledge or skills.  Likewise, A prospective pupil, would cultivate the expert's favor, even to the extent of sharing a fish with a navigator every time he goes fishing, for tens of years!  Eventually, the expert may take the hopeful understudy aside and offer to tutor him.  This is a very serious matter.

Likewise in Western society, knowledge is jealously guarded.  Beyond arcane practices in academic culture, and, say, the scribbled handwriting and esoteric vocabulary, or even shoptalk among craftsmen, many more examples could be adduced.

I cannot know what was going through the mind of the thief of these pages.  Perhaps this was in a time preceding xerox machines.  Or maybe he had no change, was late for his ride, or faced a deadline that he or she could not make without this precious knowledge.  Did a librarian---whose annoying dispositions used to be legendary---refuse to check the book out to our aspirant to this knowledge?

Unfortunately, I cannot render judgement on this seemingly callous and self-serving act.  The outcome, though, is a positive one: I might not have made such careful note of these pages, had they not been missing.

It's good stuff.
 

San Francisco, Hawaii, and Guam exhibit seasonal modes on Tide vs Time of Day graphs

I started to make these graphs because I want to understand the nature of the seasonality of the lowest and highest tides. One of my professors, Roy Tsuda opened my eyes to certain aspects of tidal zonation, and, somehow, to the idea that there is some kind of seasonality to tides.  MY interest in the Tidepool, in all of the Intertidal have biased my point of view toward the times of lowest LLW during different months of the year.  However, as the graph of Kawaihae, Hawaii shows, some sites show more variation in HHW (Higher High Water) through the year.

These graphs take a certain amount of manual data manipulation to generate times of day from the times of the tide predictions. I will be making more of them.  In his book Sea Level Science, David Pugh discusses various varieties and aspects of tides.  Especially, Albert Defant's Physical Oceanography, Volume II gives detailed discussions.  One of these, or perhaps others, certainly will have information about the astronomical and oceanographic factors behind the differences in these profiles. 


Looking at these, I know there is more to learn about this.  I'm willing to have posters printed, if anyone is interested.   One possibility would be a large poster with several such graphs.   I've tried to use colorblind-friendly colors, but this is a work in progress.   For one thing, gri does not have the same color palette support as R.  And for another, there are a number of varieties of color blindness, each of them just as different from the next, as from my own "Normal" color vision.   What would these look like to a stomatopod (with 10 cone types, I think)?

San Francisco

 

Kawaihae, Hawaii Island

 

Apra Harbor, Guam

Article: High Tide Flooding Days in 2018

https://www.noaa.gov/media-release/us-ties-record-for-number-of-high-tide-flooding-days-in-2018

Distribution plots of times of day of high and low tides. A work in progress.

Roy Tsuda, professor of Marine Botany at the University of Guam, is an enthusiast of tides.  His lecture on the ideas of one of his professors, Max Doty about intertidal zonation made an impression on me.  I'm not sure now, some 35 years later, whether he had something to do with instilling me a strong interest in the times of high and low tides.   I think he did.

In Chuuk Lagoon, I learned that at the time when "a pwopwooisor" (the tide was pregnant or swollen [pwopwo} in the morning [isor], certain bivalves are ripe to eat---with a growth of orange matter, obviously eggs.  I also heard a casual remark that "the tide has changed" in reference to the times of high and low tides.

How to graph this relationship, to analyze and grow our understanding?  Ideas pop out of the graphs, ideas the inkling that prodded me to start in the first place.  These are distribution plots, not a track through time, like a tide calendar.  I want to see what times of day are the tides highest or lowest, and during which months?  When it takes several years to produce something, is it  a work in progress? 

Time of day is the independent variable, the X axis.  Predicted heights are the dependent variable. Different colors encode the months. 

Studying some of the graphs it is apparent that  a "month" is not a natural division of time; in certain cases there are what look like different modes within a "month."  A lunar calendar might work better.  Or maybe not.  Tides are complicated.  Traditional fishermen, without the benefit of calendars, ephemerides, or clocks, understand the division of time in a more practical sense.  

Seasons of High and Low TIdes

This is an important topic.  I will not discuss it.  Here is a graph I have been working on to try to understand this question.  What times are highest and lowest tides?  Is there a seasonal difference?

This may make better sense than the accompanying post.

This is still a work in progress.  In this instance I am manually inducing "jitter" by using differing increments of time for the predictions for each month.  This is not ideal yet.  

The original with a gray background.  Better for printing.  Still a work in progress.   Are these colors colorblind friendly? 

New Blog: Studies and Notes on Tides

I am learning. Studying about Tides, and here I mean to keep track of all things Tides. My approach is to embrace the broadest range of topics possible, all connected with tides.  Tidepooling and intertidal ecology.  I have become more interested in the Physics of tides.  I have been collecting literature of tide science; as time progresses, the incredible number of publications on tides has become more apparent, and this has been so for centuries.  The Tides are one of the more interesting and complex applications of physics, and the biology of intertidal fauna and flora is extensive.  Theories of intertical zonation comprise a subliterature of themselves.

For three decades I have been making graphical tide calendars, monthly tide predictions, and along the way other ways of visualizing tides have captured my attention.  I will post graphs, and collect interesting graphs and links, and information about data visualization.

Sea levels are rising.  On Pacific Islands, including Micronesia and the Philippine Islands, this is a more immediate issue.  Like many problems that seem peripheral, or are imagined to be imaginary to continent dwellers---endangered species, invasive species, solid waste management debacles, range shifts and other biogeography issues, overfishing and other resource depletion issues, plastic trash on the high seas, for some, nuclear waste containment---sea level rise is a serious and immediate problem for islanders on small islands.  These problems seem more tractable, in terms of study, than in larger, continental situations.   Micronesians already are grappling with truly existential issues (what happens when the wells and taro patches turn salty?), virtually all of which were brought on by the actions of humans in other places, from other cultures, in more advantaged economic straits.  I find the diversity of tidal regimes of compelling interest, including some remarkable ones on islands.

Besides, tides are essential environmental variables to islanders, and have been for as long as they have lived on these islands.  What can they tell us about tides?   Shall I call this Ethno-Oceanography?   I am keenly interested in this area of knowledge as well.

Many years ago, when I encountered EL Nino, when living in Chuuk Lagoon, tides took on a more important role to me.  Study of the graphs showing sea levels during El Nino convinced me that tide levels are a deterministic indicator of El Nino and La Nina.  The following graph has haunted me. 

This is an enhanced version of the graph in Mark A. Cane. 1983.  Oceanographic events during El Nino.  Science 222(4629):189-1195. 

 This blog serves as a catchall personal library of eclectic matters, mostly connected with The Tides.  References, links, lists, ideas, graphs, all of these are intended to be vouchsafed.  If others find it of interest, I would be pleased to learn of it, perhaps by an email or comment.