Low-order stream valleys comprise most of the total area in a given mountain watershed. First order streams have no tributaries and are located in headwater areas where colluvial processes dominate. Low order streams are shaped by and preserve evidence of recent tectonic, depositional, and climatic perturbations. In some mountains, the low order streams feel the effects of the perturbation sooner than downstream reaches. Higher elevation watersheds (non-glaciated) tend to be steeper, colder, rockier (thinner soils, more impervious), attract more precipitation, and have flashier flood profiles.
Derive a stream network using standard ArcGIS watershed functions (see Watershed Delineation). You need to have the stream ordered and each segment its own object (record). Calculate stream gradients for first-order channels using endpoint elevations of the channels and either a.) the as-the-crow-flies length or b.) sinuous length of the channel segment. The first option finds an approximate slope because it uses the linear slope between channel head and first confluence (ignores sinuosity, concavity). The second more faithfully approximates the channel slope because it uses the actual line length. Both methods ignore the concavity of the stream profile, thus both methods produce an “average first-order stream gradient”. Slope is in percent rise. Map projection will affect measurements.
The Frankel-Pazzaglia method (modified from work by D. Merritts) is outlined below. They compare two adjacent mountain ranges in New Mexico, one dominated by exhumation, the other active tectonism. Their methods are repeatable. Adjust inputs as appropriate for your study area. Review the referenced articles to see how authors reported their results (maps, charts, tables).
Southern Rocky Mountains, NM
Sierra Nacimiento and Taos Range
Swath covers fault-bound slope of uplifted mountain block to just past the drainage divide. DEM swath includes approximately 5km of piedmont beyond the range front.
Channel Initiation Threshold
0.025 km2 = 25,000m2 = 250 10-meter pixels
Gradient value placed at channel head location and contoured. Black contours with in-line labels over a hillshade for grayscale images/copy machine compatibility. Contour Interval = 0.02.
Contour data using Inverse Distance Weighting (IDW)* or Trend Surface** least-squares regression analysis.
* Spatial Analyst Tools > Interpolation > IDW tool
** See ‘Trend Surface’ post
Charts & Figures
a.) Vertical bar histogram of first-order stream gradients for both ranges. X-axis = First-order Stream Gradient (0.0-0.8), Y-axis = Frequency (0-50). Mode is reported in text atop chart for each mountain range in both percent and degrees slope.
b.) Dot-and-whisker plot of RVA* (X) vs. First-order Stream Gradient (Y). Show variance in whiskers, linear trendline, and corresponding r2 value. Basin size and degree of basin integration will affect results.
* See ‘RVA’ post.
c.) It is interesting to see stream segments plotted in relation to one another. See Merritts and Hesterberg (1994) or Fig. 9.8-B in Burbank and Anderson textbook.
d.) Departure of first-order stream gradients from an idealized profile curve can reveal tectonic tilting. See Fig 9.8-C in Burbank and Anderson textbook.
Frankel and Pazzaglia (2007), GSA Special Paper 398
Font et al. (2010) Geomorphology 119
Merritts and Vincent (1989), GSA Bulletin 101
Merritts and Hesterberg (1994), Science 265
Burbank and Anderson (2012), Tectonic Geomorphology (2nd edition), p. 286, Fig. 9,8