Concavity Index (θ) for Stream Channels
The Downstream Rate of Channel Profile Flattening
Jamie Wade & Michael Brucker
Boise State University
2014
Definition of Concavity:
Theta θ is the slope of a line regressed through a log-log
plot of channel Slope % Rise and Drainage Area (km2)
Step 1: Extract Trunk Stream
1. Use Toolbars  Draw to create a point graphic and place the point somewhere along the
trunk stream (must be in the headwaters of the watershed).
a. Convert the graphic to a feature layer and save as a shapefile named
“Converted_Graphics”.
b. Next, snap the “Converted_Graphics” to the nearest pixel using Spatial Analyst
Tools  Hydrology  Snap Pour Point.
i. Input raster or feature pour point data = Converted_Graphics
ii. Input accumulation raster = flow_accum
iii. Output raster = name downpoint or something similar
2. Isolate the trunk stream using the “cost path” tool, (imagine dropping a ball into the
headwaters of the watershed and trace the balls path of least resistance along the trunk stream).
a. Spatial Analyst Tools  Distance  Cost Path
i. Point Source = downpoint
ii. Cost Distance = flow_accum
iii. Cost Backlink = flow_direc
b. Name the output “trunk_stream” or something similar.
3. Clip “trunk_stream” to the bounds of the watershed.
a. Raster  Raster Processing  Clip
i. Use clip tool using the outline of the watershed as the constraining boundary.
ii. Name the output “ws_trunk” or something similar.
Step 2: Extract the properties of the ws_trunk raster using the filled DEM.
1. Spatial Analyst  Extraction  Extract by Mask
a. Input raster = DEM_Fill
b. Feature Mask Data = ws_trunk
c. Output: trunk_DEM or something similar.
d.
***Note: if the unit of the DEM is in feet instead of in meters, convert the DEM to meters using Data
Management Tools  Map Algebra  Raster Calculator  Command: (“DEM”)/(3.2808)
Step 3: Obtain slope values for each pixel along the trunk stream channel.
1. Spatial Analyst  Surface  Slope
a. Input raster: trunk_DEM
b. Change Output Measurement to % Rise instead of degrees.
c. Output: trunk_slope or something similar.
Step 4: Extract flow accumulation data along the trunk stream.
1. Spatial Analyst  Extraction  Extract by mask
a. Input raster = flow_accum
b. Feature Mask Data = ws_trunk
c. Output: trunk_flow or something similar.
Step 5: Convert ws_trunk into points
1. Conversion Tools  From Raster  Raster to Point
a. Input raster = ws_trunk
b. Output point features: trunk_points of something similar.
Step 6: Create a data table that will be used in Excel to create the concavity graph.
1. Spatial Analyst  Extraction  Sample
a. Input Rasters: trunk_flow, trunk_slope
b. Input Location Data: trunk_points
c. Output: concavity_data.dbf or something similar.
i. ***Note: add file extension .dbf to your output so the table can be opened in MS excel.
Step 7: Open concavity_data in an excel spreadsheet
1. Open Microsoft Excel and create a new, blank spreadsheet
a. Open the concavity_data.dbf file that you created using ArcMap.
b. OR: Open the attribute table and copy/paste directly into an excel spreadsheet.
2. Scan your data and delete all zero values from the slope data
a. The power-trendline (see below) cannot be computed if there are zero values in the
data. Deleting these values will have a negligible impact on the graphical data.
i. ***Note: for our dataset of >1900 points, less that 1% contained zero values.
3. Create a new column and name it “Drainage_Area”.
a. In this step, you will convert the data (pixel count) in trunk_flow into upstream
drainage area in km² using the following formula.
i. =(F2*(Pixel Size * Pixel Size))/1,000,000
ii. ***Note: the size of the pixel may vary depending on the resolution of the original DEM (e.g.,
30m DEM, 10m DEM).
4. Select the trunk_slope and drainage_area columns and plot the data in a scatter plot.
a. Convert the x and y axis to logarithmic scale and add a “power” trend line.
b. The concavity index (i.e., θ) is the exponent from the power trend line equation.
Concavity Index
10
y = 1.2244x-0.394
Channel Slope % Rise
1
0.1
1
10
0.1
0.01
0.001
Drainage Area (km²)
100