Saturday, January 3, 2015

Sinuosity Index

One of the ways earth scientists classify rivers and streams is by their degree of deviation from a straight line. This metric is called sinuosity index or sinuosity coefficient. It is a simple calculation in this day of powerful geographic information systems such as Google Earth. You divide river kilometers by air (straight line) kilometers. A stream section (specialists typically call it a 'reach') with a sinuosity index less than 1.05 is nearly a straight line. Man-made canals achieve this level of rectitude, but it rarely occurs in nature. A stream reach with a sinuosity index between 1.05 and 1.25 is winding. A stream reach with a sinuosity index between 1.25 and 1.5 is twisting but still has low sinuosity. A stream reach with an index of 1.5 or more has high sinuosity and is meandering. A sinuosity index higher than 2 indicates extreme meandering. An S curve with identical 270 degree oxbows offset from each other (270 degrees is 3/4 the circumference of a circle) has a sinuosity index of 3.33. If the oxbows close to 300 degrees, the sinuosity index increases to 5.24 and if they reach the very tight 330 degrees, the sinuosity index increases further to 11.13. In reality, stream reaches longer than 10 kilometers with a sinuosity index higher than 3 are rare.
Idealized River Oxbows with a Sinuosity Index of 3.33
There is generally an inverse relationship between slope gradient and sinuosity. Steeper slopes tend to produce straighter stream flows. Gentler slopes mean the stream is more susceptible to resistance in the channel (heavy vegetation is a prime source of resistance). Higher resistance creates more sinuosity.

We saw in the article "Water Fight on the River - Round Five" that higher sinuosity index numbers correlate with more traveler disorientation. In other words, the more a river meanders, the more likely a traveler is to get lost trying to follow it.

There are two places in the Book of Mormon text that are associated with travelers getting lost. One is the land of Manti which first appears chronologically ca. 90 B.C. Alma 22:27 as the southernmost outpost of Nephite settlement along the central Sidon corridor. All the narratives about travelers getting lost pre-date Manti. Once Manti was settled and the route Zarahemla/Manti was established via Gideon, travel along the central Sidon corridor became routine Alma 17:1.

The land of Helam is also associated with traveler disorientation. Both the priests of Noah and their Lamanite army overlords had to ask Almafor directions from Helam back to the land of Nephi Mosiah 23:35-36.

This means it is likely that both the lands of Manti and Helam are located in regions where the Sidon has high sinuosity index numbers.

In our correlation, the lands of Manti and Helam are both bounded by the Chixoy which has a very high sinuosity index of 2.58.
Sinuosity Indices along Reaches of the Proposed River Sidon
The Chixoy meanders and changes direction through sparsely-populated, hilly country covered with thick vegetation and tall trees. The entire main stem of the Usumacinta from source to mouth is an unusually sinuous river with an overall sinuosity index of 1,111/386 = 2.88.
Sinuosity Index = 2.88 along Entire Length of Proposed River Sidon
That portion of the river we think the Nephites called the Sidon (Chixoy/Salinas/Usumacinta) also has very high sinuosity (936/435 = 2.15).
Sinuosity Index = 2.15 along Proposed Nephite Rivr Sidon
Long distances, high sinuosity, low population density, hilly terrain, high forest canopies - the Chixoy/Salinas/Usumacinta region has many characteristics that made it easy for even seasoned travelers to get lost.