For single-thread stream channels, the sinuosity index is calculated for each reach using its two endpoints (Upstream point A, Downstream point B). The ratio of the sinuous length tho the straight-line distance is Channel Sinuosity value for the reach. The sinuous length is measured down the centerline of the channel. Divide the sinuous length by the straight-line distance between the same two points.
Sinuosity values range from 1 to 4 (or so). A completely straight channel will have a sinuosity of 1. Channels with ratios ~1.5 are called sinuous channels. Channels with higher ratios are called meandering channels (Wolman and Miller, 1964). Values are commonly reported to two decimal places, but there’s no firm rule.
There are many ways to do this, depending on what data you have in hand (i.e., stream centerline shapefile or paper topo map). If I have no GIS layers for a channel, I have my students work in Google Earth (GE) and Excel.
1.) Define a study segment of the channel (50 miles long?). Create a series of Placemarks along a channel at fairly regular intervals (2-3 per mile?) and at identifiable locations (bridge crossings, prominent bars, tributary confluences, etc.). These points define the reaches.
2.) Collect all the placemark points in a single folder in My Places sidebar, then File > Save Places As > .kmz. Make sure to save the .kmz file to hard drive filespace (not just to GE’s My Places > Temporary Places folder). If needed, the .kmz can be converted to .shp later if you want to use the points in ArcGIS using ArcToolbox > Conversion tools. Join the Excel table you create in Step #5 to its attribute table after conversion.
3.) Use the path ruler tool in GE to determine the sinuous length between points. Be sure to zoom fairly close and click at a regular interval.
4.) Use the same tool to find straight-line distances between reach endpoints.
5.) Populate an Excel spreadsheet with ReachPoints, SinDist, StraightDist, Elevation, and Sinuosity. Lengths and sinuosity values are placed in the row of the downstream point. Hover the mouse over each point to determine elevation (GE uses a 30m DEM, integer).
6.) Create a long profile figure by charting Downstream Distance (X) vs. Elevation (Y).
Alternatively, you could segment a stream centerline (polyline) at regular intervals. Extract DEM values to points, etc. (see Long Profile lesson). Or create streamlines via steps described in Watershed lesson.
– If a single sinuosity value for an entire channel is needed, sum the sinuous lengths for all reaches and divide by sum of the straight-line lengths for all reaches.
– For braided channels, the “total length index” (Richards, 1982) is more appropriate.
– Other versions of the sinuosity index are provided in articles referenced below. See Bridge (2003, p. 151, Table 5.1) textbook for a summary of sinuosity indices.
Howard et al. (1970)
Engelund and Skovgaard (1973)
Hong and Davies (1979)
Friend and Sinha (1993)
Stark et al. (2010)