Biological and Environmental Engineering
Creating a Topographic
Index
So you can spend the next 3 yrs of you life figuring out what to do with it
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•  Topographic Index maps are grids derived from
digital elevation models (DEMs). These grid include
only topographical information. It makes use of an
index of hydrological similarity based on topographic
data.
•  Originally developed in the TOPMODEL framework (Beven
et al., 1984).
•  TOPMODEL was one of the first attempts to model
distributed hydrological responses based on variable
contributing area concepts.
•  Has since been applied outside of the TOPMODEL
framework in GWLF, SWAT.
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•  Topographic Indices assume that topography
drives flows.
•  Thus, the index may not capture conditions in areas
where there are other more dominant processes
governing the flow.
•  However, it generally correctly predicts the
accumulation of flow in topological low spots (e.g.,
areas where the flows accumulate).
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The Topographic Index
⎛ α ⎞
⎟⎟
λ = ln⎜⎜
⎝ tan β ⎠
where λ is the topographic index, α is the upslope
contributing area per unit length of contour, and β is the
topographic slope of the cell.
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1) Begin with a DEM:
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• Since raster processing can be computationally intensive, we
will work with a single sub watershed
• We need to clip the larger DEM to the extent of the Town Brook
watershed
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There are several ways to do this.
1. Open spatial analyst options and set the Analysis mask.
Here we use a shape file of the watershed boundary
previously defined by the USGS
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Open the raster calculator and select the raster, and hit evaluate.
Now we have a well
defined watershed to
work with.
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2) In Arc Catalog create a new shapefile under “file> new”, make it a point
file. Import into Arc Map and digitize a point at the outlet of the watershed.
Open Arc ToolBox and “Spatial Analyst”, and “Watershed” and input the
flow direction raster and the point shapefile. Note, you will need to calculate
the flow directions first, so it is a bit more intensive.
There are several other ways to extract various shapes and sizes and attributes
in the DEMs. Explore.
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Creating a TI
2) Open ArcTool Box “Spatial Analyst Tools” under “Hydrology”
select fill to fill any sinks in the DEM:
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3) In “Spatial Analyst Tools” under “Hydrology” select flow
direction map:
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4) In “Spatial Analyst Tools” under “Hydrology” select flow
accumulation:
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5) In “Spatial Analyst Tools” under “Surface” select slope map in
degrees (from filled DEM):
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6) Calculate tangent of slope (radians), by typing
“Tan(([TB_Slope] * 1.570796) / 90)” in Raster Calculator:
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7) Remove zeros values by typing “con(TB_Rads == 0, 0.0001,
[TB_Rads])” in Raster Calculator: This prevents any undefined
cells in the final output.
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8) Calculate TI by typing “Ln((([FlowAcc_flow1] + 1) * 10) /
[TB_Rads_No0] )” in Raster Calculator (note that 10 is cell size
in meters):
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Notice that in areas with complex topology or on divergent hillslopes there is a
“streaking” effect. This is due to the flow accumulation algorithm used in Arc,
which uses a computationally efficient single direction flow algorithm. That is, if
water were placed on a cell, it is only allowed to flow down slope in one
direction based on the path of steepest decent, and not in several or many
directions like we might expect. Thus, on simple hillslopes the single direction
method works fine, but in complex basins it is lacking.
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• Using the single direction flow routing, slope is evaluated in
the direction of steepest descent and is reported as drop/
distance, i.e. tangent of the angle.
• All flow leaving any given pixel with the single direction method
(or the area contributing flow to the pixel) is assumed to flow into
a single downstream neighbor pixel.
• While these simplifications are valid in regions where the flow is
convergent, such as the channelized portion of the landscape,
they do not work well on divergent hillslopes.
• This leads to potentially large errors in the calculation of
contributing area (or basin area) for hillslope pixels, even though
computed values for channel pixels are correct.
• Accurate contributing areas for hillslope pixels are needed for
process-based models of erosion, landslide potential, or source
areas.
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• So we need a better flow partitioning methods to
capture complex landscapes. We have gone through
the basics of topographic indices, and their calculation.
Now comes the easy part, where we download an
extension for Arc that incorporates a more robust flow
direction method. This extension “TauDEM” is available
free at http://hydrology.neng.usu.edu/taudem/90info.htm
and uses what is called a multi-direction flow algorithm.
• The methodology is outlined at
http://hydrology.neng.usu.edu/taudem/
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Method: The D-Infinity (dinfi) algorithm was proposed by Tarboton (1997) in an
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effort
to compute contributing area more accurately on divergent hillslopes. While it
does not provide a completely rigorous solution to this challenging "flow tube"
problem, it is a fairly robust and pragmatic approach and gives visually appealing
results. The dinfi (infinity) flow routing is encoded as an angle 'ang' in radians counterclockwise from east as a continuous (floating point) quantity between 0 and 2 pi. The
flow direction angle is determined as the direction of the steepest downward slope on
the eight triangular facets formed in a 3 x 3 grid cell window centered on the grid cell
of interest. A block-centered representation is used with each elevation value taken to
represent the elevation of the center of the corresponding grid cell. Eight planar
triangular facets are formed between each grid cell and its eight neighbors. Each of
these has a downslope vector which when drawn outwards from the center may be at an
angle that lies within or outside the 45o (pi/4 radian) angle range of the facet at the
center point. If the slope vector angle is within the facet angle, it represents the steepest
flow direction on that facet. If the slope vector angle is outside a facet, the steepest flow
direction associated with that facet is taken along the steepest edge. The slope and flow
direction associated with the grid cell is taken as the magnitude and direction of the
steepest downslope vector from all eight facets. Slope is measured as drop/distance, i.e.
tan of the slope angle. In the case where no slope vectors are positive (downslope), the
flow direction is set using the method of Garbrecht and Martz (1997) for the
determination of flow across flat areas. This makes flat areas drain away from high
ground Soil
and& towards
low ground.
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Flow direction defined as steepest downward slope
on planar triangular facets on a block centered grid.
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We install the interface
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Select the DEM, and let the program run
You will get lots of maps as output. You need only the flow accumulation grid
“…sca”, which uses the multi-direction flow method, and the slope grid “…slp”,
which is already the tangent of the slope. Therefore, you now have everything
you need to calculate a TI. In the raster calculator type “Ln(([flowAcc_flow] *
10) /[slope_tb_dem))” (note that 10 is cell size in meters):
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The resulting TI appears much “smoother” because flow is now
partitioned among several cells
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References:
Beven, K.J., M.J. Kirkby, N. Schofield, A.F. Tagg, (1984), “A physically based flood
forecasting model (TOPMODEL) for 3 UK catchments”, Journal of Hydrology,
69:119-143.
Garbrecht, J. and L. W. Martz, (1997), "The assignment of drainage direction over
flat surfaces in raster digital elevation models," Journal of Hydrology, 193: 204-213.
Tarboton, D. G., (1997), "A new method for the determination of flow directions and
contributing areas in grid digital elevation models," Water Resources Research,
33(2): 309-319.
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