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).
  2. Convert the graphic to a feature layer and save as a shapefile named “Converted_Graphics”.
  3. Next, snap the “Converted_Graphics” to the nearest pixel using Spatial Analyst Tools  Hydrology  Snap Pour Point.
  4. Input raster or feature pour point data = Converted_Graphics
  5. Input accumulation raster = flow_accum
  6. Output raster = name downpoint or something similar
  1. 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).
  2. Spatial Analyst Tools  Distance  Cost Path
  3. Point Source = downpoint
  4. Cost Distance = flow_accum
  5. Cost Backlink = flow_direc
  6. Name the output “trunk_stream” or something similar.
  1. Clip “trunk_stream” to the bounds of the watershed.
  2. Raster  Raster Processing  Clip
  3. Use clip tool using the outline of the watershed as the constraining boundary.
  4. 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
  2. Input raster = DEM_Fill
  3. Feature Mask Data = ws_trunk
  4. Output:trunk_DEM or something similar.
  5. ***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
  2. Input raster: trunk_DEM
  3. Change Output Measurement to % Rise instead of degrees.
  4. Output: trunk_slopeor something similar.

Step 4: Extract flow accumulation data along the trunk stream.

  1. Spatial Analyst  Extraction  Extract by mask
  2. Input raster = flow_accum
  3. Feature Mask Data = ws_trunk
  4. Output: trunk_flow or something similar.

Step 5: Convert ws_trunk into points

  1. Conversion Tools  From Raster  Raster to Point
  2. Input raster = ws_trunk
  3. 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
  2. Input Rasters: trunk_flow, trunk_slope
  3. Input Location Data: trunk_points
  4. Output: concavity_data.dbf or something similar.
  5. ***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
  2. Open the concavity_data.dbf file that you created using ArcMap.
  3. OR: Open the attribute table and copy/paste directly into an excel spreadsheet.
  1. Scan your data and delete all zero values from the slope data
  2. 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.
  3. ***Note: for our dataset of >1900 points, less that 1% contained zero values.
  1. Create a new column and name it “Drainage_Area”.
  2. In this step, you will convert the data (pixel count) in trunk_flowinto upstream drainage areain km² using the following formula.
  3. =(F2*(Pixel Size * Pixel Size))/1,000,000
  4. ***Note:the size of the pixel may vary depending on the resolution of the original DEM (e.g., 30m DEM, 10m DEM).
  1. Select the trunk_slope and drainage_area columns and plot the data in a scatter plot.
  2. Convert the x and y axis to logarithmic scale and add a “power” trend line.
  3. The concavity index (i.e., θ) is the exponent from the power trend line equation.