Saturday, December 27, 2014

Strahler Stream Order

In 1952 Arthur Newell Strahler (1918 - 2002), a professor of geoscience at Columbia, published an influential article entitled "Hypsometric (Area-Altitude) Analysis of Erosional Topography" in Geological Society of America Bulletin 63. Strahler introduced a numbering system he called "stream order" to quantify the hierarchical branching networks that typify watercourses in drainage basins. A 1st order stream is very small and has no tributaries. The confluence of 2 or more 1st order streams creates a 2nd order stream. If a 1st order stream flows into a 2nd order stream, the result remains a 2nd order stream. But, when 2 or more 2nd order streams converge they form a 3rd order stream. Obviously, as a stream increases in upstream network complexity its stream order number increases.

The Allegheny and Monongahela are both 7th order streams as they converge at Pittsburgh, Pennsylvania. The Ohio is an 8th order stream at its confluence with the Mississippi at Cairo, Illinois. The Columbia is a 9th order stream as it discharges into the Pacific downstream from Portland, Oregon. The Mississippi is a 10th order stream at its mouth below New Orleans. The Nile is an 11th order stream as it flows through Egypt into the Mediterranean. The Amazon, largest river on earth, is a 12th order stream by the time it reaches the Atlantic.
Strahler Stream Order Classification System
Stream order has proven so useful it has become a global standard among limnologists. In contemporary usage, 1st - 3rd order watercourses are called headwaters streams or small streams. 4th - 6th order streams are called medium streams. 7th - 12th order streams are considered significant rivers or large streams. The Usumacinta, our candidate for river Sidon, is a 7th order stream. Other 7th order streams of note include the Colorado, Hudson, James, Potomac, Rio Grande, Susquehanna, and Trinity, The Tennessee is an 8th order stream, as is the Rhone south of Lyon, France. The Missouri is a 9th order stream by the time it reaches St. Louis as is the Illinois which joins the Mississippi 37 kilometers upstream.

The journal of the International Society of Limnology (SIL from the Latin) is Inland Waters. An important article appeared in Inland Waters (2012) 2 entitled "Global Abundance and Size Distribution of Streams and Rivers." It was written by John A. Downing of Iowa State University and 9 other co-authors from 6 different countries. Depending heavily on satellite imagery, they have compiled data estimates from more than 36 million streams of water across the planet. Their results show startling consistency that will help us understand what to expect as we analyze the Sidon.

J.A. Downing, et al. Anaylsis of all Streams Worldwide
Going from left to right, the first column is the Strahler stream order number. The second column is the total number of streams of surface water on the planet. The third column is the mean stream length from the source in kilometers. The fourth column is the combined length of all streams in kilometers and the fifth column is the mean stream channel width in meters. There is only one 12th order stream on earth, the  Amazon, while there are an estimated 28.55 million 1st order streams. These tiny brooks average 1.6 km in length and .8 meters in width. It is important to note that only one of the five 11th order streams - the Nile - is an independent river flowing to the sea. The other four 11th order streams are all tributaries of the Amazon. And, only three of the 10th order streams are independent rivers flowing to the sea, the Mississippi being one of them and the Niger in western Africa another. The other twenty 10th order streams are all tributaries of either the Nile or the Amazon.

These columns demonstrate what the authors call "well-defined scaling laws" that apply to branching patterns "applicable across diverse geological and geographical regions." For example, column two in the chart shows generally a 1 to 5 relationship between main streams and lesser streams of a lower order. In other words, any given stream will have an average of five tributaries of the next lower order. Column three shows generally a 1 to 2 relationship between tributaries and the length of their main stream. In other words, as two streams of a lesser order join, the resulting higher order stream will be on average twice as long as the tributaries. The actual branching algorithms involve more elegant math, but you get the idea. Drainage basins, like many other kinds of networks with branches and nodes, follow the tenets of branching theory whose laws and coefficients are so consistent as to be "tautologous" and "statistically inevitable" (J.A. Downing, et al.). Trees and blood vessels also follow branching theory laws.

Any given river may vary considerably from the norm. This chart shows the relationship between stream order and width for 400+ well-documented main streams. The dotted line plots median stream channel width in meters with data points scattered in normal distribution patterns.
J.A. Downing, et al. Analysis of 400+ Well-Known Streams
The relatively narrow Nile, the only 11th order main stream on earth, is an obvious outlier. Wetter regions have wider streams. For example, one study of the River Tyne basin in NE England found 1st order streams with a mean channel width of 3.5 meters and 2nd order streams with a mean channel width of 6 meters.

So what does all this imply for the river Sidon in the Book of Mormon? We know that Almaand his converts traveled a distance of 21 Nephite "days" to get from the city of Nephi to the local land of Zarahemla Mosiah 23:3, Mosiah 24:20, Mosiah 24:25. Our best estimate of the distance they traveled in one day is 15 air (straight-line) kilometers (see the blog article Land Southward Travel Times). This makes the city of Nephi/local land of Zarahemla distance about 320 air kilometers. We know the head of Sidon was south of Manti in the narrow strip of wilderness that separated the greater lands of Nephi and Zarahemla Alma 22:27, Alma 22:29, Alma 43:22, Alma 50:11. So, the distance head of Sidon/local land of Zarahemla probably did not exceed about 250 air kilometers. How far was it from the local land of Zarahemla to the sea? The land Bountiful lay north of the local land of Zarahemla Alma 22:29 (see the blog article Downstream from Zarahemla). The distance local land of Zarahemla/seacoast probably did not exceed about 200 air kilometers. So, the entire length of the river from head of Sidon to the sea likely did not exceed about 450 air kilometers. According to the chart above, we would expect the river Sidon to be a 7th or 8th order stream. A 9th order stream (mean global length 1,256 kilometers) seems long, even taking sinuosity (the tendency of a river to meander) into account. A 10th order stream (mean global length 2,891 kilometers) is entirely out of the question. Keep in mind there are only 5 rivers on earth that are 10th, 11th or 12th order streams flowing to the sea. Conversely, a 6th order stream (mean global length 103 kilometers seems short. A 5th order stream (mean global length 45 kilometers) is  entirely out of the question.

The fact that our candidate for Sidon - the Usumacinta - is a 7th order stream puts it in the ballpark of reasonableness. From our head of Sidon (the Salama/Chixoy Negro confluence) to salt water at the mouth of the Palizada (distributary of the Usumacinta) on the Laguna de Terminos is 382 air kilometers and to the principal mouth of the Usumacinta at Frontera is 435 air kilometers or 936 river kilometers. Principal tributary, the Chixoy Negro, adds another 175 river kilometers for a total length source to mouth of 1,111 kilometers. The Usumacinta, among the 50 largest independent rivers on earth by annual average volume of water discharged (2,271 cubic meters per second), is a large 7th order river.
Usumacinta - Candidate for River Sidon
Geographers place the head of the Usumacinta at the Pasion Confluence which is 328 air kilometers or 590 river kilometers from the principal mouth at Frontera, Tabasco. The Mezcalapa-Grijalva since 1675 has been a tributary of the Usumacinta (See the blog article "Wandering River"). Their combined annual average streamflow is 3,664 cubic meters

Stream orders point out another important characteristic of water flow nomenclature. Headwaters streams (1st, 2nd & 3rd order) are generally not called rivers. They may be brooks, creeks, rivulets, forks, runs, burns or becks, but not rivers. The term "river" implies a certain size and a minimum level of upstream network complexity. Large streams (7th order or higher) are universally called rivers. Medium streams (4th - 6th order) are sometimes called rivers based on local custom. If a stream flows to the sea it is more likely to be called a river. If a stream is wide or carries a relatively high volume of water it is more likely to be called a river. These are the rivers of England. The noted Thames flowing past London is a 5th order stream, as are most English rivers. The Severn, longest river in the UK at 354 kilometers, is a 6th order stream.
The Rivers of England
The language of the Book of Mormon text that fell from the lips of the Prophet Joseph is now thought to be Early Modern English. See the article "Early Modern English." On the streets of London when Shakespeare was a child (ca. A.D. 1570) it is unlikely the term "river" would have referred to a stream smaller than 5th order.

The map above shows that many of England's rivers are longer than the 44.8 kilometers we would expect given the mean length of 5th order streams worldwide. The Thames, for example, is 346 kilometers long (7.7 X mean), the Trent measures 297 km (6.6 X mean) and the Great Ouse runs for 230 km (5.1 X mean). Compare that with our Sidon, which at 1,111 kilometers, is 4.7 X the global mean length of 7th order streams (237.4 km).

The following two images are from a spreadsheet listing well-known 7th order streams from 5 different countries.
Length of Selected 7th Order Streams a
56 rivers comprise our sample set.
Length of Selected 7th Order Streams b
8 7th order streams in our sample are longer than the Usumacinta, although none carries a greater volume of water.

Additional relevant information is in the article "OED on Rivers."