Determining the shortest Site-to-Shoreline path. Considerations.

 “A common mistake is to assume, implicitly or explicitly, that Bronze Age and modern coastal morphology are essentially the same.” [1]

 

Well (pace Tartaron) we have to start somewhere. 

In order to understand the possible relationship of Bronze Age sites both to the sea and to nodes of trade a good first step would be to determine the straight line distance between each BA site and the nearest seacoast.  By examining a map on which such straight-line links are plotted we can begin to understand the relationship of such sites to the shoreline and the focusing effect that shoreline irregularities have in mapping inland sites to the sea.  First, however, we must have a model of the seashore of sufficient accuracy to allow us to say with some confidence what those distances are and we have no choice but to start with the modern shoreline.  A picture should make these initial themes clear.

Figure 1. Straight lines drawn from BA sites in Arcadia to the nearest seashore.

In this map I have projected (straight-line) each BA site in Arcadia onto the nearest seacoast.   Arcadia is entirely landlocked and its communication with the greater outside world is through neighboring territories; Messenia and the Gulf of Messenia to the S near modern Kalamata, across Triphylia to the W and the Gulf of Kyparissia, and across Achaea to the N (perhaps near ancient Helike).  The primary contact between Arcadia and the ocean is through the southern Argolid near the head of the Gulf of Argos.  It is this concentration of land-to-sea contacts created by the closest gulfs and inlets that I am speaking of.  An accurate representation of site-shoreline direct lines will make this concentration effect clear and it will fulfill another function: that of classification.  We would like an easy way of generating lists of onshore sites as distinct from those inland

But how is this to be done with a database and software?  The first thing that is required is an accurate representation of the shoreline for the entire Bronze Age world.

In the end I decided to make my own.   To be sufficiently accurate the nodes should be no more than 20 m apart for the area being mapped.  The region of Locris is a good example of the technique that I adopted.  Here is an image of the coast of Locris:

Figure 2.  The shore of Locris (Euboea at the top).

First let us superimpose on this map a representation of the database BA sites in this area:

Figure 3.  The north coast of Locris with BA sites as white squares.

Here the sites are represented by white squares.  The problem now is to create a straight line from each site to the nearest seashore irrespective of any land obstacles, mountains, canyons, rivers, etc.  The algorithm adopted should be sufficiently rigorous to be reasonably convincing.  To draw a line to a point withing 30 m of the ‘ideal and perfect’ location should be rigorous enough.  In most cases we can do better than that.  But how should  this be done?

The algorithm I chose was as follows:

a.    Trace by hand the outline of the several land masses

b.   Each node in this line had to be 30 m or less from the next node.

c.    Produce software that would try each (and every) site against all the outline nodes until it found the smallest distance. 

d.   The output of this software would be a set of sql insert statements for a new table, coast, that would hold, for each site, the minimum distance to the shore along with the lat/lon coordinates for the location on the shore closest to the site.

e.    Modifying the production software to generate a distance to shoreline report from the  coast table.  I described this report in my last blog post.

What did this process look like.  In Google Earth Professional I generated a ‘path’ structure that would follow the coast.  When visible, I followed the wet sand mark along the coast.  It looked like this:

Figure 4. Kamares Beach on Sifnos. 
The red dots are interpolated coastal points.

In this figure we see the Paralia Kamares on Sifnos (36.990171° N, 24.678167° E).  I have interpolated a coastline for this beach (blue line).  My interpolated points are the red dots.  The beach is 525 m long (I used the yellow segmented line to measure it) and the dots divide the beach into 67 segments.  Each node (dot) therefore is separated from the next by ~7.83 m.  The next figure shows a detailed view:

Figure 5.  Detail of Kamares Beach.

In figure 4 the yellow measuring line has been removed and the reader will get a better idea of the spaces between the nodes (red dots on the blue coast line).

The site closest to Kamares Beach is C7406, which is a Sanctuary of the Nymphs on Sifnos.  The minimum distance from this sanctuary to the closest shoreline is ~508.8 m.  Given tides, erosion, and other factors the figure should be accurate to +/- 5 m (503.8 to 513.8 m) at worst.

Figure 6. Detail of closest marker to C7406.

In this extreme closeup we see the specific node that marks the closest approach of the shoreline to C7406.  Its next nearest node on the left is  ~15 m.  From C7406 to the closest node is an angle of 332.56°.  To the next closest point on the left the azimuth is 330.81°.  So, an angular displacement of something over 1.75° per node and a lateral error distance of about 15 m. arises from this scheme.   Other sites will provide widely varying parameters of distance and angle but I present this example of C7406 as a typical case and it is this sort of accuracy or better which I have striven for in all the coast tracing exercises I have undertaken.

Which Approach?

I began this extended coastal exercise with the assumption that the entire coastline of the several land masses and islands had to be traced in detail.  In Crete I attempted to trace the entire coastline.  The yellow outline in the next picture represents what I was able to accomplish:

Figure 7.   Crete.  The yellow outline represents my attempt to trace the coast.

Even this (not entirely satisfactory) outline required 8000 points placed by hand.  It required several days of steady work but, in the end, I decided that this approach has serious drawbacks.  First of all the human factor of such eye-straining repetitive work is a drawback.  Second, even 8000 points do not result in the accuracy which I desired to achieve.  The coastline of Crete is about 985 km (985000 m).  Dividing this figure by 8000 gives an average distance between nodes of about 123.1 m.  This is about six times worse than the accuracy given for the Sifnos example above.   There would need to be at least 48000 nodes in the outline of Crete in order to render both a complete outline of Crete and one which was of sufficient accuracy to use for closest shoreline point determination.  I was forced to abandon one criterion or the other and I decided to jettison the idea of creating complete outlines of the landmasses the eastern Mediterranean and just concentrating of those stretches of coastline most likely to be closest to BA sites.

To create an accurate least-distance placing (and with minimal effort) it is necessary to center a circle on each site and note where that circle touches the coast.  Then we draw detailed coastline nodes only at these specific points.  This approach immediately dispenses with having to outline projecting capes and peninsulas since these are highly unlikely to be the closest points to anything.  Here is an example.

Figure 8. Eupalion (C562) in Phocis. Corinthian Gulf

In figure 8 the site of Eupalion/Gouva (C562) is represented by the square rectangle in the center.  Centered on that rectangle is a red circle that just touches the shoreline.  The coastal outline (blue line) is only elaborated in the vicinity of the red circle.  Now it is only necessary to place one or more nodes around the tangent of circle/line segment.  This results in considerable time savings and accuracy is enhances.  In the neighborhood of the intersection of the red circle and the coast it might pay to lay  down points that are much closer together and so ensure greater accuracy.

.  Figure 9.  Southern Phocis on the Gulf of Corinth

In figure 9 C562 (Eupalion) is on the left and two more sites in southern Phocis (C563, C564) are on the right (east).  The coast outline only touches the coast at spots where the closest shoreline has already been determined by circles centered on the sites themselves.  Proceeding in this way means that most the rugged south coast of Phocis will not require modeling in this typical example.

In the example of Crete that I mentioned achieving the desired accuracy with the ‘whole coast model’ approach requires about 48000 points in the shore outline.   As there are 1500+ sites on Crete the computational cost will be 48000 * 1500 or 72,000,000 separate distance computation routine calls.  If we allow only 10 points per site using the previously described circle-focus method then it would require only 15000 outline points and so 1500 * 15000 = 22,500,000 routine calls – a computational savings of about 2/3.   This would run is something under 2 minutes on GoDaddy's servers which is where I run this utility-type software.

Another approach is to take advantage of the fact that Crete is divided into subregions in the Mycenaean Atlas database and so it's possible to model just one region at a time.  This would considerably reduce and spread out the workload into manageable chunks.

Figure 10.  Gulf of Atalantis.  Northern Locris.

 

Figure 10 is an example of the circle-focus method as I applied it to Northern Locris.  Here the sites are represented by white squares.  Each is the center of a circle which extends to the closest coastline.  The blue line is the coast outline.  Notice that it only touches the shoreline where the circles do.  Only those segments are carefully modelled.  The rest of the line is ‘armature’.  The software algorithm adopted for calculating the minimal distance traverses this entire blue outline (node to node) and, for each site, returns that distance along with the lat/lon  pair of that specific closest point on the coast.  In figure 11 we see what that this same region of Locris looks like after processing and with the shortest distance lines properly placed.

Figure 11. North coast of Locris with lines
drawn from sites to nearest seashore.

I represent the nearest approach of site to seashore with a blue line that starts at the site (indicated by a diamond) and ends at the closest seashore point (indicated by a red circle).

These are some of the considerations that I had in mind when performing the task of automating the task of finding the closest seashore to every BA site.  The reader should keep in mind that the ‘shortest distance’ is not from the site, exactly.  It measures the distance from my site marker to the seashore.

In another blog post I would like to discuss what algorithm my software used and whether there are any other useful coastal outline databases available.

 

 

Footnotes

[1] Tartaron [2017] 140.

 

 

Bibliography

Tartaron [2017] : Tartaron, Thomas F.,  Maritime Networks in the Mycenaean World.  Cambridge University Press,  ISBN: 978-1-108-43136-1.  Paperback edition of 2017.